Since ancient times, new knowledge and new inventions have periodically remade human societies. Today, however, knowledge is assuming greater importance than ever before. Now more essential to the wealth of nations than either capital or labor, Peter Drucker argues here, it has already created a “postcapitalist” society and promises further transformations on a global scale. How do interest rates and raising capital like bonds help the “postcapitalist” society? Use the Peter Drucker article in Week 4 to help aid your post.
1. Write a 300 word description in which you discuss and answer the above questions by Wednesday.
2. Leave two questions for peers in your answer. (50 words for each)
3. Cite and use APA format if you use outside sources.
Corporate Finance
Fifth Edition
Chapter 5
Interest Rates
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1
Chapter Outline
5.1 Interest Rate Quotes and Adjustments
5.2 Application: Discount Rates and Loans
5.3 The Determinants of Interest Rates
5.4 Risk and Taxes
5.5 The Opportunity Cost of Capital
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Learning Objectives (1 of 3)
Define effective annual rate and annual percentage rate.
Given an effective annual rate, compute the n-period effective annual rate.
Convert an annual percentage rate into an effective annual rate, given the number of compounding periods.
Describe the relation between nominal and real rates of interest.
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Learning Objectives (2 of 3)
Given two of the following, compute the third: nominal rate, real rate, and inflation rate.
Describe the effect of higher interest rates on net present values in the economy.
Explain how to choose the appropriate discount rate for a given stream of cash flows, according to the investment horizon.
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Learning Objectives (3 of 3)
Discuss the determinants of the shape of the yield curve.
Explain why Treasury securities are considered risk-free, and describe the impact of default risk on interest rates.
Given the other two, compute the third: after-tax interest rate, tax rate, and before-tax interest rate.
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5.1 Interest Rate Quotes and Adjustments (1 of 2)
The Effective Annual Rate
Indicates the total amount of interest that will be earned at the end of one year
Considers the effect of compounding
Also referred to as the effective annual yield (E A Y) or annual percentage yield (A P Y)
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5.1 Interest Rate Quotes and Adjustments (2 of 2)
Adjusting the Discount Rate to Different Time Periods
Earning a 5% return annually is not the same as earning 2.5% every six months.
General Equation for Discount Rate Period Conversion
Note: n = 0.5 since we are solving for the six month (or half year) rate.
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Textbook Example 5.1 (1 of 3)
Valuing Monthly Cash flows
Problem
Suppose your bank account pays interest monthly with the interest rate quoted as an effective annual rate (E A R) of 6%. What amount of interest will you earn each month? If you have no money in the bank today, how much will you need to save at the end of each month to accumulate $100,000 in 10 years?
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Textbook Example 5.1 (2 of 3)
From Eq. 5.1, a 6% E A R is equivalent to earning
per month. We can write the timeline for
our savings plan using monthly periods as follows:
That is, we can view the savings plan as a monthly annuity with
monthly payments. We can calculate the total
amount saved as the future value of this annuity, using Eq. 4.10:
We can solve for the monthly payment C using the equivalent monthly interest rate r = 0.4868%, and n = 120 months:
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Textbook Example 5.1 (3 of 3)
We can also compute this result using the annuity spreadsheet:
BLANK NPER RATE PV PMT FV Excel Formula
Given 120 0.4868% 0 blank 100,000 blank
Solve for PMT blank blank blank − 615.47 blank = PMT(0.004868,120,0,100000)
Thus, if we save $615.47 per month and we earn interest monthly at an effective annual rate of 6%, we will have $100,000 in 10 years.
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Alternative Example 5.1 (1 of 2)
Problem
Suppose an investment pays interest quarterly with the interest rate quoted as an effective annual rate (E A R) of 9%.
What amount of interest will you earn each quarter?
If you have no money in the bank today, how much will you need to save at the end of each quarter to accumulate $25,000 in five years?
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Alternative Example 5.1 (2 of 2)
Solution
From Eq. 5.1, a 9% E A R is approximately
equivalent to earning
per quarter.
To determine the amount to save each quarter to reach the goal of $25,000 in five years, we must determine the quarterly payment, C:
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Annual Percentage Rates (1 of 4)
The annual percentage rate (A P R), indicates the amount of simple interest earned in one year.
Simple interest is the amount of interest earned without the effect of compounding.
The A P R is typically less than the effective annual rate (E A R).
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Annual Percentage Rates (2 of 4)
The A P R itself cannot be used as a discount rate.
The A P R with k compounding periods is a way of quoting the actual interest earned each compounding period:
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Annual Percentage Rates (3 of 4)
Converting an A P R to an E A R
The E A R increases with the frequency of compounding.
Continuous compounding is compounding every instant.
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Annual Percentage Rates (4 of 4)
Table 5.1 Effective Annual Rates for a 6% A P R with Different Compounding Periods
Compounding Interval Effective Annual Rate
Annual left parenthesis start fraction 1 + 0.06 over 1 end fraction right parenthesis to the first power minus 1 = 6%
Semiannual left parenthesis start fraction 1 + 0.06 over 2 end fraction right parenthesis squared minus 1 = 6.09%
Monthly left parenthesis start fraction 1 + 0.06 over 12 end fraction right parenthesis to the power of 12 minus 1 = 6.1678%
Daily left parenthesis start fraction 1 + 0.06 over 365 end fraction right parenthesis to the power of 365 minus 1 = 6.1831%
A 6% A P R with continuous compounding results in an E A R of approximately 6.1837%.
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Textbook Example 5.2 (1 of 4)
Converting the A P R to a Discount Rate
Problem
Your firm is purchasing a new telephone system, which will last for four years. You can purchase the system for an upfront cost of $150,000, or you can lease the system from the manufacturer for $4,000 paid at the end of each month. Your firm can borrow at an interest rate of 5% A P R with semiannual compounding. Should you purchase the system outright or pay $4,000 per month?
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Textbook Example 5.2 (2 of 4)
Solution
The cost of leasing the system is a 48-month annuity of $4,000 per month:
We can compute the present value of the lease cash flows using the annuity formula, but first we need to compute the discount rate that corresponds to a period length of one month. To do so, we convert the borrowing cost of 5% A P R with semiannual compounding to a monthly discount rate. Using Eq. 5.2,
the A P R corresponds to a six-month discount rate of
To convert
a six-month discount a one-month discount rate, we compound the six-month
rate by
using Eq. 5.1:
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Textbook Example 5.2 (3 of 4)
(Alternatively, we could first use Eq. 5.3 to convert the A P R to an E A R.
Then we can convert the E A R to
a monthly rate using Eq. 5.1: (1.050625)
month.) Given this discount rate, we can use the annuity formula (Eq. 4.9) to compute the present value of the 48 monthly payments:
We can also use the annuity spreadsheet:
Blank N P E R R A T E P V P M T F V Excel Formula
Given 48 0.4124% blank − 4,000 0 blank
Solve for P V blank blank 173,867 blank blank = PV(0.004124,48,4000,0)
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Textbook Example 5.2 (4 of 4)
Thus, paying $4,000 per month for 48 months is equivalent to paying a present value of $173,867 today. This cost is
higher than the cost of
purchasing the system, so it is better to pay $150,000 for the system rather than lease it. We can interpret this result as meaning that at a 5% A P R with semiannual compounding, by promising to repay $4,000 per month, your firm can borrow $173,867 today. With this loan it could purchase the phone system and have an additional $23,867 to use for other purposes.
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Alternative Example 5.2 (1 of 3)
Problem
A firm is considering purchasing or leasing a luxury automobile for the C E O. The vehicle is expected to last three years. You can buy the car for $65,000 up front , or you can lease it for $1,800 per month for 36 months. The firm can borrow at an interest rate of 8% A P R with quarterly compounding. Should you purchase the system outright or pay $1,800 per month?
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Alternative Example 5.2 (2 of 3)
Solution
The first step is to compute the discount rate that corresponds to monthly compounding. To convert an 8% rate compounded quarterly to a monthly discount rate, compound the quarterly rate using Eqs. 5.3 and 5.1:
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Alternative Example 5.2 (3 of 3)
Solution
Given a monthly discount rate of 0.66227%, the present value of the 36 monthly payments can be computed:
Paying $1,800 per month for 36 months is equivalent to
paying $57,486 today. This is
lower than the cost of purchasing the system, so it is better to lease the vehicle rather than buy it.
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5.2 Application: Discount Rates and Loans (1 of 4)
Computing Loan Payments
Payments are made at a set interval, typically monthly.
Each payment made includes the interest on the loan plus some part of the loan balance.
All payments are equal and the loan is fully repaid with the final payment.
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5.2 Application: Discount Rates and Loans (2 of 4)
Computing Loan Payments
Consider a $30,000 car loan with 60 equal monthly payments, computed using a 6.75% A P R with monthly compounding.
6.75% A P R with monthly compounding corresponds
to a one-month discount rate of
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5.2 Application: Discount Rates and Loans (3 of 4)
Computing Loan Payments
Financial Calculator Solution
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5.2 Application: Discount Rates and Loans (4 of 4)
Computing the Outstanding Loan Balance
One can compute the outstanding loan balance by calculating the present value of the remaining loan payments.
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Textbook Example 5.3 (1 of 3)
Computing the Outstanding Loan Balance
Problem
Two years ago your firm took out a 30-year amortizing loan to purchase a small office building. The loan has a 4.80% A P R with monthly payments of $2,623.33. How much do you owe on the loan today? How much interest did the firm pay on the loan in the past year?
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Textbook Example 5.3 (2 of 3)
Solution
After 2 years, the loan has 28 years, or 336 months, remaining:
The remaining balance on the loan is the present value of these
remaining payments, using the loan rate of
During the past year, your firm made total payments of
on the loan. To determine the amount that was interest, it is
easiest to first determine the amount that was used to repay the principal. Your loan balance one year ago, with 29 years (348 months) remaining, was
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29
Textbook Example 5.3 (3 of 3)
Therefore, the balance declined by
in the past year. Of the total payments made, $8,022
was used to repay the principal and the remaining
was used to pay interest.
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5.3 The Determinants of Interest Rates (1 of 2)
Inflation and Real Versus Nominal Rates
Nominal Interest Rate: The rates quoted by financial institutions and used for discounting or compounding cash flows
Real Interest Rate: The rate of growth of your purchasing power, after adjusting for inflation
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31
5.3 The Determinants of Interest Rates (2 of 2)
The Real Interest Rate
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32
Textbook Example 5.4 (1 of 3)
Calculating The Real Interest Rate
Problem
In May of 2014, one-year U.S. government bond rates were about 0.1%, while the rate of inflation over the
following year was around
At the
start of 2017, one-year interest rates were about 0.8%, and inflation over the following year was approximately 2.1%. What were the real interest rates in May 2014 and in 2017?
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Textbook Example 5.4 (2 of 3)
Solution
Using Eq. 5.5, the real interest rate in May 2014 was
In 2017, the real interest rate was
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Textbook Example 5.4 (3 of 3)
Solution
Note that the real interest rate was negative in 2017, indicating that interest rates were insufficient to keep up with inflation: Investors in U.S. government bonds were able to buy less at the end of the year than they could have purchased at the start of the year. On the other hand, because prices actually decreased (deflation) in the year following May 2014, the real interest rate briefly exceeded the nominal interest rate.
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Alternative Example 5.4 (1 of 2)
Problem
On December 31, 2015, the average one-year Treasury Constant Maturity rate was about 0.65% and the 2015 annual inflation rate was about 0.70%.
What was the real interest rate in 2015?
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Alternative Example 5.4 (2 of 2)
Solution
Using Eq. 5.5, the real interest rate in 2008 was
Which is equal to the difference between the nominal
rate and inflation:
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Figure 5.1 U.S. Interest Rates and Inflation Rates, 1962–2017
Interest rates are one-year Treasury rates, and inflation rates are the increase in the U.S. Bureau of Labor Statistics’ consumer price index over the coming year, with both series computed on a monthly basis. The difference between them thus reflects the approximate real interest rate earned by holding Treasuries. Note that interest rates tend to be high when inflation is high.
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Both plots rise and fall numerous times, and although there is not a perfect correlation between them, changes in inflation rate tend to be followed by similar changes in the nominal interest rate. The plot for inflation rate begins at (1962, 1.2) and has large upward spikes peaking at (1974, 12.5), (1980, 14.5), (1990, 6), and (2008, 5.5). Small peaks appear at (2011, 3.9) and (2016, 2.5). The plot for nominal interest rate begins at (1962, 3.5), and its corresponding peaks are at (1974, 9.5), (1982, 17), (1989, 9.5), and (2008, 5.75). After 2008, the interest rates drop almost near to 0. The gap between the plots was largest during the 1980s, with nominal interest rates 9% above inflation during 1985. All values estimated.
38
Investment and Interest Rate Policy (1 of 2)
An increase in interest rates will typically reduce the N P V of an investment.
Consider an investment that requires an initial investment of $10 million and generates a cash flow of $3 million per year for four years. If the interest rate is 5%, the investment has an N P V of
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39
Investment and Interest Rate Policy(2 of 2)
If the interest rate rises to 9%, the N P V becomes negative and, the investment is no longer profitable:
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40
Monetary Policy, Deflation, and the 2008 Financial Crisis
When the 2008 financial crisis struck, the Federal Reserve responded by cutting its short-term interest rate target to 0%.
While this use of monetary policy is generally quite effective, because consumer prices were falling in late 2008, the inflation rate was negative, and so even with a 0% nominal interest rate, the real interest rate remained positive.
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The Yield Curve and Discount Rates (1 of 2)
Term Structure: The relationship between the investment term and the interest rate
Yield Curve: A graph of the term structure
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42
Figure 5.2 Term Structure of Risk-Free U.S. Interest Rates, November 2006, 2007, and 2008
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The graph in panel b shows interest rate, E A R, in percentage, versus term, in years. The plot for November 2006 is a curve that falls from (0.5, 5.23) to (4, 4.63), rises to (15, 4.89), then falls to (20, 4.87). The plot for November 2007 is a curve that falls from (0.5, 3.32) to (3, 3.12), then rises through (15, 4.44) and (20, 4.45). The plot for November 2008 is a curve that rises from (0.5, 0.47) through (2, 0.98), (15, 3.86), and (20, 3.87). All values from panel a.
43
The Yield Curve and Discount Rates (2 of 2)
The term ‘structure’ can be used to compute the present and future values of a risk-free cash flow over different investment horizons.
Present Value of a Cash Flow Stream Using a Term Structure of Discount Rates
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44
Textbook Example 5.5 (1 of 2)
Using the Term ‘Structure’ to Compute Present Values
Problem
Compute the present value in November 2008 of a risk-free five-year annuity of $1,000 per year, given the yield curve for November 2008 in Figure 5.2
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Textbook Example 5.5 (2 of 2)
Solution
To compute the present value, we discount each flow by the corresponding interest rate:
Note that we cannot use the annuity formula here because the discount rates differ for each cash flow.
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Alternative Example 5.5 (1 of 2)
Problem
Compute the present value of a risk-free three-year annuity of $500 per year, given the following yield curve:
Treasury Rates Blank
Term (Years) Rate
1 0.261%
2 0.723%
3 1.244%
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Alternative Example 5.5 (2 of 2)
Solution
Each cash flow must be discounted by the corresponding interest rate:
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48
The Yield Curve and the Economy (1 of 2)
Interest Determination
The Federal Reserve determines very short-term interest rates through its influence on the federal funds rate, which is the rate at which banks can borrow cash reserves on an overnight basis.
All other interest rates on the yield curve are set in the market and are adjusted until the supply of lending matches the demand for borrowing at each loan term.
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The Yield Curve and the Economy (2 of 2)
Interest Rate Expectations
The shape of the yield curve is influenced by interest rate expectations.
An inverted yield curve indicates that interest rates are expected to decline in the future.
Because interest rates tend to fall in response to an economic slowdown, an inverted yield curve is often interpreted as a negative forecast for economic growth.
Each of the last six recessions in the United States was preceded by a period in which the yield curve was inverted.
The yield curve tends to be sharply increasing as the economy comes out of a recession, and interest rates are expected to rise.
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Figure 5.3 Short-Term Versus Long-Term U.S. Interest Rates and Recessions
One-year and ten-year U.S. Treasury rates are plotted, with the spread between them shaded in blue if the shape of the yield curve is increasing (the one-year rate is below the ten-year rate) and in red if the yield curve is inverted (the one year rate exceeds the ten-year rate). Gray bars show the dates of U.S. recessions as determined by the National Bureau of Economic Research. Note that inverted yield curves tend to precede recessions by 12–18 months. In recessions, interest rates tend to fall, with short-term rates dropping further. As a result, the yield curve tends to be steep coming out of a recession.
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1969 to 1970, 1973 to 1957, 1980, 1981 to 1982, 1990 to 1991, 2001, and 2008 to 2009. With the exception of the recession in 1990, each recession was preceded, within 2 years, by a brief period wherein 1-year interest rates were higher than 10-year interest rates. These narrow, red areas showing inverted yield curve are followed by wider blue areas showing increasing yield curve.
51
Textbook Example 5.6 (1 of 4)
Comparing Short- and Long-Term Interest Rates
Problem
Suppose the current one-year interest rate is 1%. If it is known with certainty that the one-year interest rate will be 2% next year and 4% the following year, what will the interest rates r1, r2, and r3 of the yield curve be today? Is the yield curve flat, increasing, or inverted?
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Textbook Example 5.6 (2 of 4)
Solution
We are told already that the one-year rate r1 = 1%. To find the two-year rate, note that if we invest $1 for one-year at the current one-year rate and then reinvest next year at the new one-year rate, after two-years we will earn
We should earn the same payoff if we invest for two-years at the current two-year rate r2:
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Textbook Example 5.6 (3 of 4)
Otherwise, there would be an arbitrage opportunity: if investing at the two-year rate led to a higher payoff, investors could invest for two-years and borrow each year at the one-year rate. Investing at the two-year rate could led to a lower payoff. Investors could invest each year at the one-year rate and borrow at the two-year rate.
Solving for r2, we find that
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Textbook Example 5.6 (4 of 4)
Similarly, investing for three years at the one-year rates should have the same payoff as investing at the current three-year rate:
We can solve for
Therefore, the current yield curve has r1 = 1%, r2 = 1.499%, and r3 = 2.326% The yield curve is increasing as a result of the anticipated higher interest rates in the future.
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Alternative Example 5.6 (1 of 4)
Problem
Suppose the current one-year interest rate is 3%. If it is known with certainty that the one-year interest rate will be 2% next year and 1% the following year, what will the interest rates r1, r2, and r3 of the yield curve be today? Is the yield curve flat, increasing, or inverted?
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Alternative Example 5.6 (2 of 4)
Solution
We are told already that the one-year rate r1 = 3%.
To find r2, we know that if we invest $1 for one year at the current one-year rate and then reinvest next year at the new one-year rate, after two years we will earn:
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Alternative Example 5.6 (3 of 4)
Solution
We should earn the same payoff if we invest for two-years at the current two-year rate r2:
Otherwise, there would be an arbitrage opportunity.
Solving for r2, we find that:
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Alternative Example 5.6 (4 of 4)
Solution
Similarly, investing for three years at the one-year rates should have the same payoff as investing at the current three-year rate:
We can solve for
Therefore, the current yield curve has r1 = 3%,
The yield curve is decreasing as a result of the anticipated lower interest rates in the future.
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5.4 Risk and Taxes
Risk and Interest Rates
U.S. Treasury securities are considered “risk-free.” All other borrowers have some risk of default, so investors require a higher rate of return.
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Figure 5.4 Interest Rates on Five-Year Loans for Various Borrowers, July 2018
Source: FINRA.org.
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• U.S. Treasury: 2.7
• Microsoft: 3.1
• Carnival Corp.: 3.5
• Union Pacific: 4.0
• Kia Motors: 4.1
• Netflix: 5.1
• Rite Aid: 5.7
• Mattel: 6.1
• J.C. Penney: 7.3
• Sprint: 9.4
• Avon Products: 11.0
61
Textbook Example 5.7 (1 of 2)
Discounting Risky Cash Flows
Problem
Suppose the U.S. government owes your firm $1,000 to be paid in five years. Based on the interest rates in Figure 5.4, what is the present value of this cash flow? Suppose instead J CPenney owes your firm $1,000. Estimate the present value in this case.
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Textbook Example 5.7 (2 of 2)
Solution
Assuming we can regard the government’s obligation as risk free (there is no change you won’t be paid), then we discount the cash flow using the risk-free Treasury interest rate of 2.7%:
The obligation from JCPenney is not risk-free. J C Penney may face financial difficulties and fail to pay the $1,000. Because the risk of this obligation is likely to be comparable to the five-year bond quoted in Figure 5.4, the 7.3% interest rate of the loan is a more appropriate discount rate to use to compute the present value in this case:
Note the substantially lower present value of JCPenney’s debt compared to the government debt due to JCPenney’s higher risk of default.
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After-Tax Interest Rates
Taxes reduce the amount of interest an investor can keep, and we refer to this reduced amount as the after-tax interest rate.
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Textbook Example 5.8 (1 of 3)
Comparing After-tax Interest Rates
Problem
Suppose you have a credit card with a 14% A P R with monthly compounding, a bank savings account paying 5% E A R, and a home equity loan with a 7% A P R with monthly compounding. Your income tax rate is 40%. The interest on the savings account is taxable, and the interest on the home equity loan is tax deductible. What is the effective after-tax interest rate of each instrument, expressed as an E A R? Suppose you are purchasing a new car and are offered a car loan with a 4.8% A P R and monthly compounding (which is not tax deductible). Should you take the car loan?
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Textbook Example 5.8 (2 of 3)
Solution
Because taxes are typically paid annually, we first convert each interest rate to an E A R to determine the actual amount of interest earned or paid during the year. The savings account has a 5% E A R. Using Eq. 5.3, the E A R of the credit card is
and the E A R of the home equity loan is
Next, we compute the after-tax rate for each. Because the credit card interest is not tax deductible, its after after-tax interest rate is the same as its pre-tax interest rate, 14.93%. The after-tax interest rate on the home
equity loan ,which is tax deductible, is
The after-tax interest rate that we will earn on the savings account is
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Textbook Example 5.8 (3 of 3)
Now consider the car loan. Its E A R is
It is not tax deductible, so this rate is also its after-tax interest rate. Therefore, the car loan is not our cheapest source of funds. It would be best to use savings, which has an opportunity cost of foregone after-tax interest of 3%. If we don’t have sufficient savings, we should use the home equity loan, which has an after-tax cost of 4.34%. And we should certainly not borrow using the credit card!
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Alternative Example 5.8 (1 of 2)
Problem
The yield on a 10-year A A municipal bond is 1.73%, while a 10-year A A corporate bond has a yield of 2.49%. What is the marginal tax rate that would result in the same after-tax yield?
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Alternative Example 5.8 (2 of 2)
Solution
Since the municipal security is tax-exempt, its yield is the after-tax yield. Thus,
Solving for t,
At a marginal tax rate of 30.5%, an investor would be indifferent between investing in a taxable security yielding 2.49% and a tax-exempt security yielding 1.73%.
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5.5 The Opportunity Cost of Capital
Investor’s Opportunity Cost of Capital: The best available expected return offered in the market on an investment of comparable risk and term to the cash flow being discounted
Also referred to as Cost of Capital
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Chapter Quiz (1 of 2)
What is the difference between an E A R and an A P R quote?
Why can’t the A P R itself be used as a discount rate?
What is an amortizing loan?
What is the difference between a nominal and real interest rate?
Why do corporations pay higher interest rates on their loans than the U.S. government?
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Chapter Quiz (2 of 2)
How do taxes affect the interest earned on an investment? What about the interest paid on a loan?
What is the opportunity cost of capital?
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Corporate Finance
Fifth Edition
Chapter 5
Appendix
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73
Continuous Rates and Cash Flows (1 of 5)
Discount Rate of a Continuously Compounded A P R
Some investments compound more frequently than daily.
As we move from daily to hourly to compounding every second, we approach the limit of continuous compounding, in which we compound every instant. The E A R for a Continuously Compounded A P R
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74
Continuous Rates and Cash Flows (2 of 5)
Discount Rate of a Continuously Compounded A P R Alternatively, if we know the E A R and want to find the corresponding continuously compounded A P R, the formula is:
The Continuously Compounded A P R for an E A R
Continuously compounded rates are not often used in practice.
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75
Continuous Rates and Cash Flows (3 of 5)
Continuously Arriving Cash Flows
Consider the cash flows of an online book retailer. Suppose the firm forecasts cash flows of $10 million per year. The $10 million will be received throughout each year, not at year-end, that is, the $10 million is paid continuously throughout the year.
We can compute the present value of cash flows that arrive continuously using a version of the growing perpetuity formula.
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76
Continuous Rates and Cash Flows (4 of 5)
Continuously Arriving Cash Flows
If cash flows arrive, starting immediately, at an initial rate of $C per year, and if the cash flows grow at rate g per year, then given a discount rate of r per year, the present value of the cash flows is as follows:
Present Value of a Continuously Growing Perpetuity
where rcc = In(1+r) and gcc = In(1+g) are the discount and growth rates expressed as continuously A P Rs, respectively.
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77
Continuous Rates and Cash Flows (5 of 5)
Continuously Arriving Cash Flows
The present value of a continuously growing perpetuity can be approximated by:
where
is the total cash received during the first year.
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78
Textbook Example 5A.1 (1 of 3)
Valuing Projects with Continuous Cash Flows
Problem
Your firm is considering buying an oil rig. The rig will initially produce oil at a rate of 30 million barrels per year. You have a long-term contract that allows you to sell the oil at a profit of $1.25 per barrel. If the rate of oil production from the rig declines by 3% over the year and the discount rate is 10% per year (E A R), how much would you be willing to pay for the rig?
Copyright © 2020, 2017, 2014 Pearson Education, Inc. All Rights Reserved
Textbook Example 5A.1 (2 of 3)
Solution
According to the estimates, the rig will generate profits at an
initial rate of
million per year. The 10% discount rate is equivalent to a
continuously compounded A P R of
Similarly, the growth rate has an A P R of
From Eq. 5A.3, the present value of the profits from the rig is
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Textbook Example 5A.1 (3 of 3)
Alternatively, we can closely approximate the present value as follows. The initial profit rate of the rig is $37.5 million per year. By the end of the year, the profit rate will have declined by 3% to
million per year, Therefore , the average
profit rate during the year is approximately
million. Valuing the cash flows as though they occur at the middle of each year, we have
Note that both methods produce very similar results.
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81
Chapter Appendix Quiz
What is a continuously compounded E A R? How does this differ from a continuously compounded A P R?
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Copyright
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83
n
Equivalent n -Period Discount Rate=(1+r)
-1
1.5
(1.05)1=1.02471=.0247=2.47%
—
(
)
1
12
1.061=0.4868%
–
10 × 12 = 120
(
)
(
)
n
1
FVannuity=C×1+r-1
r
éù
ëû
(
)
1
4
1.091=
–
2.1778%
n20
FV(Annuity)$25,000
C===$1,010.82 per quarter
11
[(1+r)1][1.0217781]
r.02
–
178
–
7
APR
Interest Rate per Compounding Period =
k periods
year
æö
ç÷
èø
k
APR
1 + EAR = 1 +
k
æö
ç÷
èø
1
1+0.06
-1=6%
1
æö
ç÷
èø
2
1+0.06
-1=6.09%
2
æö
ç÷
èø
12
1+0.06
-1=6.1678%
12
æö
ç÷
èø
365
1+0.06
-1=6.1831%
365
æö
ç÷
èø
5%
=2.5%.
2
1
6
(
)
1
16
1.025-1=0.4124% per month
2
0.05
1 + EAR = (1 + ) = 1.050625.
2
1
12
– 1 = 0.4124% per
4848
11
PV=4000×1-=$173,867
0.0041241.004124
æö
ç÷
èø
$173,867 – $150,000 = $23,867
1
4
12
.08
(1+)=1.082432®1.082432-1=0.66227% per mo
nth
4
36
11
PV=$1,800×1-=$57,486
0.00662271.0066227
æö
ç÷
èø
$65,000 – $57,486 = $7,514
6.75%
=0.5625%.
12
N60
P30,000
C = = = $590.50
1111
1 – 1 –
r(1 + r)0.005625(1 + 0.005625)
æöæö
ç÷ç÷
èøèø
4.8%
=0.4% per month:
12
336
11
Balance after 2 years = $2623.33 × 1-=$
484,332
0.0041.004
æö
ç÷
èø
$2,623.33× 12
= $31,480
348
1
Balance after one year = $2623.33×1-=$49
2,354
1.004
æö
ç÷
èø
$492,354 – $484,332 =
$8,022
$31,480 – $8,022= $23,458
r
1 + rGrowth of Money
Growth in Purchasing Power = 1 + r = =
1 + i Growth of Prices
r
r i
r = » r i
1 i
–
–
+
(
)
-0.05% deflation.
(
)
(
)
0.1%+0.05%
=0.15%.
0.9995
(
)
(
)
0.8%2.1%
=1.27%.
–
1.21
–
0
0.65%0.70%
=0.05%
70
–
100
–
.
0.65%-0.70% = -0.05%
234
3333
NPV= -10++++=$0.638 million
1.051.051.051.05
234
3333
NPV = -10 + + + + = $0.281 million
1.091.091.091.09
n
n
n
C
PV =
(1 + r)
N
12NN
2Nn
n = 1
12Nn
CCCC
PV = + + ××× + =
1 + r(1 + r)(1 + r)(1 + r)
å
2345
10001000100010001000
PV=++++=$4775.25
1.00911.00981.01261.01691.0201
23
$500$500$500
PV=++
1.002611.007231.01244
PV=$498.70+$492.85+481.79=$1,473.34
(
)
(
)
$1 × 1.01 × 1.02 = $1.0302
(
)
2
2
$1×1+r=$1.0302
(
)
1
2
2
r=1.032-1=1.499%
(
)
(
)
(
)
(
)
3
3
1.01×1.02×1.04=1.0714=1+r
(
)
1
3
3
r=1.07141=2.326%.
–
(
)
(
)
$1 × 1.03 × 1.02 = $1.0506
(
)
2
2
$1 * 1+r=$1.0506
(
)
1
2
2
r=1.0506-1=2.499%
(
)
(
)
(
)
(
)
3
3
1.03×1.02×1.01=1.0611=1+r
(
)
1
3
3
r=1.0611-1=1.997%.
3
2
r=2.499%, and r=1.997%.
(
)
5
PV =$1000÷1.027=$875.28
(
)
5
PV =$1000÷1.073=$703.07
(
)
r-(
τ
× r) = r 1 +
τ
12
0.14
1+-1=14.93%,
12
æö
ç÷
èø
12
0.07
1+-1=7.23%.
12
æö
ç÷
èø
(
)
7.23% × 1 – 0.40 = 4.34%.
(
)
5% × 1 – 0.40 = 3%.
12
0.048
1+-1=4.91%.
12
æö
ç÷
èø
1.73% = 2.49% 1
(
-t
)
.
1.73%
t=1-=30.5%.
2.49%
APR
(1+EAR)=e
APR=ln(1+EAR)
cccc
C
PV=
r-g
1
1
2
cccc
C
C
PV=»×(1+r)
r-gr-g
1
C
$1.25
(30 million barrels per year)×=$37.5
barrel
æö
ç÷
èø
cc
r=ln(1+0.10)=9.531%.
cc
g=ln(1-0.03)=-3.046%.
37.537.5
PV(Profits)===$298.16 million
(r-g)(0.09531+0.03046)
cccc
(
)
37.5 × 1 – 0.03 = $36.375
(37.5+36.375)
=$36.938
2
1
2
36,938
PV(profits)=[]×(1+r)
(r-g)
1
2
36,938
=[]×(1.10)=$298.01 million
(0.10+0.03)
.MsftOfcThm_Text1_Fill {
fill:#000000;
}
.MsftOfcThm_MainDark1_Stroke {
stroke:#000000;
}
The Rise of the Knowledge Society
Author(s): Peter F. Drucker
Source: The Wilson Quarterly (1976-) , Spring, 1993, Vol. 17, No. 2 (Spring, 1993), pp.
52-71
Published by: Wilson Quarterly
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https://www.jstor.org/stable/40258682
The Rise
of the
Knowledge
Society
BY PETER F. DRUCKER
Since ancient times, new knowledge and new
inventions have periodically remade human societies.
Today, however, knowledge is assuming greater importance
than ever before. Now more essential to the wealth of
nations than either capital or labor, Peter Drucker argues
here, it has already created a “postcapitalist” society
and promises further transformations on a global scale.
only 150 years, between about 1750
and 1900, capitalism and technology
conquered the globe and created a
world civilization. Neither capitalism
nor technical innovations were new;
both had been common, recurrent
phenomena throughout the ages in both the
West and the East. What was new was the
speed of their diffusion and their global reach
across cultures, classes, and geography. And it
was this speed and scope that converted tech-
nical advances into the Industrial Revolution
and capitalism into Capitalism. Instead of be-
ing one element in society, as all earlier ex-
pressions of capitalism had been, Capital-
ism – with a capital C – became society.
Instead of being confined, as always before, to
a narrow locality, Capitalism prevailed
throughout all of Western and Northern Eu-
rope by 1850. Within another 50 years it
spread throughout the entire inhabited world.
This transformation was driven by a radi-
cal change in the meaning of knowledge. In
both the West and Asia knowledge had al-
52 WQ SPRING 1993
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George Segal’s Machine of the Year (1983)
ways been seen as applying to being. Almost
overnight, it came to be applied to doing. It
became a resource and a utility. Knowledge
had always been a private good. Almost over-
night it became a public good.
For 100 years – in the first phase – knowl-
edge was applied to tools, processes, and prod-
ucts. This created the Industrial Revolution.
But it also created what Marx called “alien-
ation” and new classes and class war, and
with them communism. In its second phase,
beginning around 1880 and culminating
around World War H, knowledge in its new
meaning came to be applied to work. This
ushered in the Productivity Revolution, which
in 75 years converted the proletariat into a
middle-class bourgeoisie with near-upper-
class income. The Productivity Revolution
thus defeated class war and communism. The
last phase began after World War H. Knowl-
edge is being applied to knowledge itself. This
is the Management Revolution. Knowledge is
now fast becoming the one factor of produc-
tion, sidelining both capital and labor. It may
KNOWLEDGE SOCIETY 53
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be premature (and certainly would be pre-
sumptuous) to call ours a “knowledge soci-
ety.” So far we have only a knowledge econ-
omy. But our society today is surely
“postcapitalist.”
earliest times, new tools, new pro-
cesses, new materials, new crops, new
techniques – what we now call “tech-
nology” – diffused swiftly throughout the Old
World. Few modern inventions, for instance,
spread as rapidly as a 13th-century one: eye-
glasses. Derived around 1270 from the optical
experiments of an English Franciscan friar,
Roger Bacon, reading glasses for the elderly
were in use at the papal court at Avignon by
1290, at the sultan’s court in Cairo by 1300,
and at the court of the Mongol emperor of
China no later than 1310. Only the sewing
machine and the telephone, fastest-spreading
of all 19th-century inventions, moved as
quickly.
But earlier technological change almost
without exception remained confined to one
craft or one application. It took another 200
years, until the early 16th century, before Ba-
con’s invention acquired a second application:
to correct nearsightedness. Similarly, the rede-
sign of the windmill around ad. 800, which
converted it from the toy it had been in antiq-
uity into a true machine, was not applied to
ships for more than 300 years. Ships were still
oared; if wind was used at all to propel them
it was as an auxiliary and only if the breeze
blew in the right direction.
The inventions of the Industrial Revolu-
tion, however, were immediately applied
across the board, and across all conceivable
crafts and industries. They were immediately
seen as technology. James Watt’s redesign of
the steam engine between 1765 and 1776
made it into a cost-effective provider of
power. Watt himself throughout his own pro-
ductive life focused on only one use of his
engine: to pump water out of mines – the use
for which the steam engine had first been de-
signed by Thomas Newcomen in the early
years of the 18th century. But one of En-
gland’s leading iron masters immediately saw
that the redesigned steam engine could also
be used to blow air into a blast furnace, and
so he put in a bid for the second engine Watt
built. Furthermore, Watt’s partner, Matthew
Boulton, promptly promoted the steam en-
gine as a provider of power for all kinds of
industrial processes, especially, of course, for
what was then the largest of all manufactur-
ing industries, textiles. Thirty-five years later,
an American, Robert Fulton, floated the first
steamboat on New York’s Hudson River.
Twenty years later the steam engine was put
on wheels and the locomotive was born. And
by 1840- at the latest by 1850- the steam
engine had transformed every single manu-
facturing process, from glassmaking to print-
ing. It had transformed long-distance trans-
portation on land and sea, and it was
beginning to transform fanning. By then, too,
it had penetrated almost the entire world –
with Tibet, Nepal, and the interior of tropical
Africa the only exceptions.
in the 19th century, most people to-
day still believe that the Industrial
Revolution was the first time a
change in the “mode of production” (to use
Karl Marx’s term) changed social structure
and created new classes, the capitalist and the
proletarian. It was not. Between a.d. 700 and
1100 two new classes emerged in Europe as a
result of technological change: the feudal ar-
istocracy and urban craftsmen. The knight
was created by the invention of the stirrup, an
innovation coming out of Central Asia around
the year ad. 700; the craftsman by the rede-
sign of water wheel and windmill into true
Peter F. Drucker is Clarke Professor of Social Science & Management at the Claremont Graduate School He is
the author of 27 books and a consultant on management to businesses and nonprofit organizations. This essay is
adapted from the book Post-Capitalist Society by Peter F. Drucker, published this month by HarperCollins
Publishers. Copyright © 1993 by Peter F. Drucker. Reprinted by permission of HarperCollins Publishers.
54 WQ SPRING 1993
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The age of the feudal knight, an invincible fighter supported on horseback by stirrups, was already
succumbing to technological and social change at the time of this 13th-century French painting.
machines that, for the first time, used inani-
mate forces rather than muscle as motive
power.
The stirrup made it possible to fight on
horseback. Without it a rider wielding a lance,
sword, or heavy bow would have been
thrown off his horse by the force described in
Newton’s Third Law: “To every action there
is always opposed an equal reaction.” For
several hundred years the knight was an in-
vincible fighting machine. But this machine
had to be supported by a “military-agricul-
tural complex” – something quite new in his-
tory. Germans until this century called it a
rittergut, a knight’s estate endowed with legal
status and with economic and political privi-
leges, and populated by at least 50 peasant
families to produce the food needed to sup-
port the fighting machine: the knight, his
squire, his three horses, and his 12 to 15
grooms. The stirrup, in other words, created
feudalism.
The craftsmen of antiquity had been
slaves. The craftsmen of the first “machine
age,” the craftsmen of Europe’s Middle Ages,
became the urban ruling class, the “burghers”
who created Europe’s unique city, and both
the Gothic period and the Renaissance.
technical innovations – stirrup, wa-
ter wheel, and windmill – traveled
throughout the entire Old World, and
fast. But the social transformations involved
in this earlier industrial revolution remained
largely contained within Europe. Only in Ja-
pan around ad. 1100 did there arise proud
and independent craftsmen who enjoyed
high esteem and, until 1600, considerable
power. But while the Japanese adopted the
stirrup for riding, they continued to fight on
foot. The rulers in rural Japan were the com-
manders of foot soldiers – the daimyo. They
levied taxes on the peasantry but possessed
no feudal estates. In China, in India, and in
KNOWLEDGE SOCIETY 55
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the world of Islam, the new technologies had
no social impact whatever. Craftsmen in
China remained serfs without social status.
The military did not become landowners but
remained, as in Europe’s antiquity, profes-
sional mercenaries. Even in Europe, the social
changes generated by this early industrial
revolution took almost 400 years to take full
effect.
By contrast, the social transformation of
society brought about by Capitalism and the
Industrial Revolution took fewer than 100
years in Western Europe. In 1750 capitalists
and proletarians were still marginal groups. In
fact, proletarians in the 19th-century meaning
of the term – that is, factory workers – hardly
existed at all. By 1850 capitalists and proletar-
ians were the dynamic classes of Western Eu-
rope. They rapidly became the dominant
classes wherever capitalism and modern tech-
nology penetrated. In Japan the transforma-
tion took fewer than 30 years, from the Meiji
Restoration in 1867 to the war with China in
1894. It took not much longer in Shanghai
and Hong Kong, Calcutta and Bombay, or in
the tsar’s Russia. Capitalism and the Indus-
trial Revolution – because of their speed and
their scope – created a world civilization.
those “terrible simplifiers,” He-
gel, Marx, and other 19th-century
ideologues, we know that major his-
torical events rarely have just one cause and
just one explanation. They typically result
from the convergence of a good many sepa-
rate and independent developments. Many
disparate trends – most of them probably
quite unconnected with one another – went
into making capitalism into Capitalism and
technical advance into the Industrial Revolu-
tion. The best-known theory – that Capital-
ism was the child of the “Protestant Ethic”-
expounded in the opening years of this cen-
tury by the German sociologist Max Weber,
has been largely discredited. There is simply
not enough evidence for it. There is only a
little more evidence to support Karl Marx’s
earlier thesis that the steam engine, the new
prime mover, required such enormous capital
investment that craftsmen could no longer fi-
nance their “means of production” and thus
had to cede control to die capitalist. There is
one critical element, however, without which
capitalism and technical advance could not
possibly have turned into a worldwide social
pandemic. It is the radical change in the
meaning of knowledge that occurred in Eu-
rope around the year 1700.
are as many theories about what
we can know and how we know it as
there have been metaphysicians, from
Plato in antiquity to Ludwig Wittgenstein and
Karl Popper in our own century. But since
Plato’s time there have been only two theo-
ries in the West – and since roughly the same
time, two theories in Asia – regarding the
meaning and function of knowledge. Accord-
ing to Plato, Socrates held that the only func-
tion of knowledge is self-knowledge, that is
the intellectual, moral, and spiritual growth of
the person. Socrates’ ablest opponent, the
brilliant and learned Protagoras, held, how-
ever, that the purpose of knowledge is to
make the holder effective by enabling him to
know what to say and how to say it. For
Protagoras knowledge meant logic, grammar,
and rhetoric – later to become the trivium, the
core of learning in the Middle Ages and still
very much what we mean by a “liberal edu-
cation” or what the Germans mean by
allgemeine Bildung (general education). In Asia
there were essentially the same two theories
of knowledge. Knowledge for the Confucian
was knowing what to say and how to say it,
the way to advancement and earthly success.
Knowledge for the Taoist and the Zen monk
was self-knowledge, and it was the road to
enlightenment and wisdom. But while the
two sides thus sharply disagreed about what
knowledge means, they were in total agree-
ment about what it did not mean. It did not
mean ability to do. It did not mean utility. Util-
ity was not knowledge; it was skill – the
Greek word for which is technê.
Unlike their Eastern contemporaries, the
56 WQ SPRING 1993
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Chinese Confucians, with their infinite con-
tempt for anything but book learning, both
Socrates and Protagoras respected techné. But
even to Socrates and Protagoras, technè, how-
ever commendable, was not knowledge. It
was confined to one specific application and
involved no general principles. What the
shipmaster knew about navigating from
Greece to Sicily could not be applied to any-
thing else. Furthermore, the only way to learn
a technè was through apprenticeship and ex-
perience. A techné could not be explained in
words, whether spoken or written. It could
only be demonstrated by one who had mas-
tered it. As late as 1700 or even later, the Eng-
lish did not speak of “crafts.” They spoke of
“mysteries” – not only because the possessor
of a craft skill was sworn to secrecy but also
because a craft by definition was inaccessible
to anyone who had not been apprenticed to a
master and taught by example.
Then, beginning after 1700 – and within
the incredibly short span of 50 years – tech-
nology was invented. The very word is a
manifesto in that it combines techné, that is
the mystery of a craft skill, with logy, orga-
nized, systematic, purposeful knowledge. The
first engineering school, the French École des
Pontes et Chaussées, was founded in 1747,
followed around 1 770 in Germany by the first
school of agriculture, and in 1776 by the first
school of mining. In 1794 the first technical
university, France’s École Polytechnique, was
founded and with it was born the profession
of engineering. Shortly thereafter, between
1820 and 1850, medical education and medi-
cal practice were reorganized as a systematic
technology.
As part of a parallel development in Brit-
ain, the meaning of patents shifted between
1750 and 1800. Once monopolies to enrich
royal favorites, patents now were granted to
encourage the application of knowledge to
tools, products, and processes, and to reward
inventors, provided they published their in-
ventions. This not only triggered a century of
feverish mechanical invention in Britain; it
finished craft mystery and secretiveness.
The great document of this dramatic shift
from skill to technology – one of the more im-
portant books of all time – was the
Encyclopédie (1751-72), edited by Denis Dide-
rot and Jean d’Alembert. This monumental
work attempted to bring together in orga-
nized and systematic form the knowledge of
all crafts, and in such a way that the non-
apprentice could learn to be a “technologist.”
It was by no means accidental that articles in
the Encyclopédie that describe individual crafts
such as spinning or weaving were not written
by craftsmen. They were written by “informa-
tion specialists”: people trained as analysts, as
mathematicians, as logicians. Both Voltaire
and Rousseau were contributors. The under-
lying thesis of the Encyclopédie was that effec-
tive results in the material universe – in tools,
processes, and products – are produced by
systematic analysis, and by systematic pur-
poseful application of knowledge. But the
Encyclopédie also preached that principles that
produced results in one craft would produce
results in any other. That was anathema,
however, to both the traditional man of
knowledge and the traditional craftsman.
of the technical schools of the
18th century aimed at producing
new knowledge – nor did the
Encyclopédie, None even talked of the applica-
tion of science to tools, processes, and prod-
ucts, that is, to technology. This idea had to
wait until around 1840, when Justus liebig, a
German chemist, applied science to invent ar-
tificial fertilizers and a way to preserve animal
protein, in the form of meat extract. What the
early technical schools and the Encyclopédie
did, however, was perhaps more important.
They brought together, codified, and pub-
lished the techné, the craft mystery, as it had
been developed over millennia. They con-
verted experience into knowledge, ap-
prenticeship into textbook, secrecy into meth-
odology, doing into applied knowledge.
These are the essentials of what we have
come to call the Industrial Revolution, in
other words, the transformation by technol-
KNOWLEDGE SOCIETY 57
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Diderot’s Encyclopédie included descriptions of some 250 crafts. This illustration is one of more than
a dozen accompanying a lengthy technical article on paper- and book-making.
58 WQ SPRING 1993
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ogy of society and civilization worldwide.
It is this change in the meaning of knowl-
edge that then made modern Capitalism inev-
itable and dominant. Above all, the speed of
technical change created a demand for capital
far beyond anything the craftsman could pos-
sibly supply. The new technology also re-
quired the concentration of production: thus
die shift to the factory. Knowledge could not
be applied in thousands of small individual
workshops and in the cottage industries of the
rural village. The new technology also re-
quired large quantities of energy, whether wa-
ter power or steam power, which also encour-
aged concentration. Although they were
important, these energy needs were secon-
dary. The central point was that production
almost overnight moved from being craft-
based to being technology-based. As a result
the capitalist moved into the center of econ-
omy and society.
As late as 1750, large-scale enterprise was
governmental rather than private. The earliest
and for many centuries the greatest of all
manufacturing enterprises in the Old World
was the famous arsenal owned and run by
the government of Venice. And the 18th-cen-
tury “manufactories” such as the porcelain
works of Meissen and Sèvres were still gov-
ernment-owned. But by 1830 large-scale pri-
vate capitalist enterprise dominated in the
West. By the time Karl Marx died in 1883,
private capitalist enterprise had penetrated
everywhere except to such remote comers of
the world as Tibet and the Empty Quarter of
Arabia.
Smith’s Wealth of Nations ap-
peared in the same year – 1776 – in
which James Watt patented the per-
fected steam engine. Yet the Wealth of Nations
pays practically no attention to machines or
factories or industrial production. The produc-
tion it describes is still craft-based. Even 40
years later, after the Napoleonic Wars, fac-
tories and machines were not yet seen as cen-
tral even by acute social observers. They play
practically no role in the economics of David
Ricardo. Even more surprising, neither factory
workers nor bankers can be found in the nov-
els of Jane Austen, England’s most perceptive
social critic. Her society (as has often been
said) is thoroughly bourgeois. But it is still to-
tally preindustrial, a society of squires and
tenants, parsons and naval officers, lawyers,
craftsmen, and shopkeepers. Only in far-
away America did Alexander Hamilton see
very early that machine-based manufacturing
was fast becoming the central economic activ-
ity. But few even among his followers paid
much attention to his 1791 Report on Manu-
factures until long after his death.
the 1830s, however, Honoré de Bal-
zac was turning out best-selling novel
after best-selling novel depicting a cap-
italist France whose society was dominated
by bankers and the stock exchange. And 15
years later, capitalism, the factory system, and
the machine, were central in the mature
works of Charles Dickens, as were the new
classes, the capitalists and the proletarians. In
Bleak House (1852), the new society and its
tensions form the subplot in the contrast be-
tween two able brothers, both sons of the
squire’s housekeeper. One becomes a great
industrialist in the North who plans to get
himself elected to Parliament to fight the
landowners and break their power. The other
chooses to remain a loyal retainer of the bro-
ken, defeated, ineffectual, precapitalist “gen-
tleman.” And Dickens’s Hard Times (1854) is
the first and by far the most powerful indus-
trial novel, the story of a bitter strike in a cot-
ton mill and of class war at its starkest.
The social tensions and conflicts of the
new order were created by the unheard-of
speed with which society was transformed.
We now know that there is no truth in the
nearly universal belief that factory workers in
the early 19th century were worse off and
treated more harshly then they had been as
landless laborers in the preindustrial country-
side. They were badly off, no doubt, and
harshly treated. But they flocked to the fac-
tory precisely because they were still better off
KNOWLEDGE SOCIETY 59
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there than they were at the bottom of a static,
tyrannical, and starving rural society. The new
factory workers experienced a much better
“quality of life.” In the factory town infant
mortality immediately went down and life ex-
pectancy rose, thus triggering the enormous
population growth of industrializing Europe.
Today – in fact, since World War II – we have
the example of the Third World countries.
Brazilians and Peruvians stream into the
favelas and barrios of Rio de Janeiro and lima.
However hard, life there is better than in the
impoverished Noreste of Brazil or on Peru’s
altiplano. As an Indian saying goes, “The
poorest beggar in Bombay still eats better
than the farm hand in the village.”
industrialization from the be-
ginning meant material improve-
ment rather than Marx’s famous
“immiseration,” the pace of change was so
breathtaking as to be deeply traumatic. The
new class, the “proletarians,” became “alien-
ated,” to use Marx’s term. Their alienation,
Marx predicted, would make inevitable their
exploitation. They were becoming totally de-
pendent for their livelihood on access to the
“means of production,” which were owned
and controlled by the capitalist. This, Marx
predicted, would increasingly concentrate
ownership in fewer and bigger hands and in-
creasingly impoverish a powerless proletar-
iat – until the day when the system would
collapse of its own weight, with the few re-
maining capitalists being overthrown by pro-
letarians who “had nothing to lose but their
chains.”
Most of Marx’s contemporaries shared his
view of capitalism even if they did not neces-
sarily share his prediction of the outcome.
Even anti-Marxists accepted Marx’s analysis
of the “inherent contradictions of capitalism.”
Some, such as J. P. Morgan, the American
banker, were confident that the military
would keep the proletarian rabble in check.
Liberals of all stripes believed that somehow
there could be reform and amelioration. But
practically every thinking person of the late
19th century shared with Marx the conviction
that capitalist society was a society of inev-
itable class conflict – and in fact by 1910 most
“thinking people,” at least in Europe (but also
in Japan), were inclining toward socialism.
The greatest of 19th-century conservatives,
Benjamin Disraeli, saw capitalist society very
much as Marx did. So did his conservative
counterpart on the Continent, Otto von Bis-
marck, and it motivated him, after 1880, to
enact the social legislation that ultimately pro-
duced the 20th-century welfare state.
By 1950 a good many observers already
knew that Marxism had failed both morally
and economically. (I had said so already in
1939, in my book, The End of Economic Man.)
But Marxism was still the one coherent ideol-
ogy for most of the world. And for most of
the world it looked invincible. What finally
overcame the “inevitable contradictions of
capitalism,” the “alienation” and “immisera-
tion” of the proletarians and with it the “pro-
letarian” condition altogether? The answer is
the Productivity Revolution.
When knowledge changed its meaning
250 years ago, it began to be applied to tools,
processes, and products. This is still what
“technology” means to most people and what
is being taught in engineering schools. But
two years before Marx’s death the Productiv-
ity Revolution began. In 1881, Frederick
Winslow Taylor, then a foreman in a steel
plant, first applied knowledge to the study of
work, the analysis of work, and the engineer-
ing of work.
In the West the dignity of work has re-
ceived lip service for a long time. The second
oldest Greek text, following the Homeric ep-
ics by only 100 years or so, is a poem by
Hesiod (eighth century b.c.), entitled Works
and Days, which sings of the work of the
farmer. One of the finest Roman poems is Vir-
gil’s Georgics, a cycle of songs about the farm-
er’s labor written in the first century b.c. Al-
though there is no such concern with work in
Asia’s literary traditions, the emperor of
China once a year touched a plow to celebrate
rice planting. But neither in the West nor in
60 WQ SPRING 1993
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/^f/uk ^–^ The steam engine’s influence
rlinf^ (~*)\ ^–^ was felt in many different
rlinf^ Will vpr i realms- including the popular
«///Hi Sk>) imagination-
Asia did work receive more than token ges-
tures. Neither Hesiod nor Virgil actually
looked at what a farmer does. Nor did any-
body else throughout most of recorded his-
tory. Work was beneath the attention of the
educated, the well-to-do, and the powerful.
Work was what slaves did. “Everybody
knew” that the only way a worker could pro-
duce more was by working longer hours or
by working harder. Marx too shared this be-
lief, as did every other 19th-century econo-
mist or engineer. ^sr*
It was by pure accident that ^%^ ^sr*
Taylor, a well-to-do, educated fl\ g$*tfe!
man, became a worker. Poor \Sg\i Âk ^)éi
eyesight forced him to ^ W \\/f\
abandon plans to enter iZL ^ {\y ^J
Harvard, where he had ft ^T^ c
been accepted, and to ■ Jl \J 1 I c
take instead a job as an i rW V ) –
apprentice machinist. Be- \\ |/| AuU
ing highly gifted, Taylor 1 1 W^W^k
very soon rose to be one of j(| Jffl|\ I [pâteT
the bosses. His metalwork- ‘s=^ j\|i I
ing inventions made him a ^ U* <--> ^T^**
rich man very early. What got r “”
Taylor started on the study of **”^-^^r’3» c-^
work was his shock at the mu-
tual and growing hatred between capital-
ists and workers, which had come to domi-
nate the late 19th century. Taylor, in other
words, saw what Marx saw and what Disraeli
and Bismarck saw. But he also recognized
something else: The conflict was unnecessary.
He set out to make workers productive so that
they would earn decent money.
Taylor’s goal was not to improve effi-
ciency. It was not to create profits for the own-
ers. To his death he maintained that the major
beneficiary of rising productivity had to be the
worker, not the owner. His main concern was
the creation of a society in which owners and
workers, capitalists and proletarians, had a
common interest in productivity and could
build a relationship of harmony based on the
application of knowledge to work. His lesson
has been best understood by Japan’s post-
World War II employers and unions.
Few thinkers in history have had greater
impact than Taylor. And few have been so
willfully misunderstood and so assiduously
misquoted. In part, Taylor has suffered be-
cause history has proven him right and the
intellectuals wrong. In part, Taylor is ignored
because contempt for work still lingers, above
all among the intellectuals. Surely shoveling
sand – the subject of Taylor’s most famous
analysis – is not something an “educated per-
son” would appreciate, let alone consider
important. In much larger part, how-
^^ Cy^çs^ever, Taylor’s reputation has suf-
\) .'””‘N ) fered precisely because he ap-
» rÇ^y^ ) 6. plied knowledge to the study
^V^*3/V °f work. This was anath-
LJ // *^\5i ema to *e ^a^°r unions °f
:=J) LJ ~\^J / his day, and they mounted
^>- ‘// i’VA – a8ainst Taylor one of the
_^J<^^r£'A^ - more vicious campaigns of
c::> <:j^^ character assassination in
===!1~ American history. Taylor’s crime,
in the eyes of the unions, was his assertion
that there is no “skilled work.” In manual op-
erations there is only “work.” All work can be
analyzed the same way. Any worker who is
willing to do the work the way analysis
shows it should be done, is a “first-class
man,” deserving a “first-class wage” – that is,
as much as, or more than, the skilled worker
got with his long years of apprenticeship.
The unions that were most respected and
powerful in Taylor’s America were the unions
in the government-owned arsenals and ship-
yards in which, prior to World War I, virtually
all peacetime U.S. defense production oc-
curred. These unions were craft monopolies,
and membership in them was largely re-
stricted to sons or relatives of members. They
required an apprenticeship of five to seven
years but had no systematic training or work
study. The unions allowed nothing to be writ-
KNOWLEDGE SOCIETY 61
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ten down. There were not even blueprints or
any other drawings of the work to be done.
Union members were sworn to secrecy and
forbidden to discuss their work with non-
members. Taylor’s assertion that work could
be studied, analyzed, and divided into a series
of simple repetitive motions, each of which
had to be done in its one right way, in its own
best time, and with its own right tools, was
indeed a frontal attack on such encrusted
guild practices. And so the unions vilified
him. They even succeeded in persuading
Congress to ban Taylor’s “task study” method
in government arsenals and shipyards, a ban
that remained in force until after World War II.
dealings with owners were as
bad as those with unions, a fact that
further hurt his cause. While he had
little use for unions, he was contemptuous of
owners. His favorite epithet for them was
“hogs.” And then there was his insistence
that the workers rather than the owners
should get the lion’s share of the increased
revenue that the application of his theory of
“Scientific Management” would produce.
Adding insult to injury, his “Fourth Principle”
demanded that work study be done in con-
sultation, if not in partnership, with the
worker. Finally, Taylor held that authority in
the plant should be based not on ownership
but solely on superior knowledge. He de-
manded, in other words, what we now call
“professional management” – and that was
anathema to 19th-century capitalists. They
bitterly attacked him as a troublemaker and a
socialist. (Some of his closet disciples and as-
sociates, especially Carl Barth, his right-hand
man, were indeed avowed leftists and
strongly anticapitalist.)
Taylor’s axiom that all manual work,
skilled or unskilled, could be analyzed and
organized by the application of knowledge
seemed preposterous to his contemporaries.
The ancient belief that there was a mystique
to craft skill continued to be accepted for
many years after Taylor made his case. This
belief encouraged Hitler in 1941 to welcome
war with the United States. For the United
States to field an effective force in Europe
would require a large fleet to transport troops,
and America at that time had almost no mer-
chant marine or destroyers to protect it. Mod-
ern war, Hitler further argued, required preci-
sion optics in large quantities for bombsights
and other devices, and there were no skilled
optical workers in America.
Hitler was absolutely right. The United
States did not have much of a merchant ma-
rine, and its destroyers were few and ludi-
crously obsolete. It also had almost no optical
industry. But by applying Taylor’s “task
study,” American industry, which played a far
more important role in war production than
the old government arsenals, learned how to
train totally unskilled workers, many of them
former sharecroppers raised in a preindustrial
environment, and convert them in 60 or 90
days into first-rate welders and shipbuilders.
The United States trained within a few
months the same kind of people to turn out
precision optics superior in quality to what
the Germans produced, and did this, further-
more, on an assembly line.
greatest impact was in showing
the importance of training. Only a cen-
tury before Taylor, Adam Smith had
taken for granted that it took at least 50 years
of experience (and more likely a full century)
for a country or a region to acquire the neces-
sary skills to turn out high-quality products.
His examples were the production of musical
instruments in Bohemia and Saxony and of
silk fabrics in Scotland. Seventy years later,
around 1840, August Borsig – one of the first
people outside England to build a steam loco-
motive – invented what is still the German
system of apprenticeship, combining practical
plant experience under a master with theoreti-
cal grounding in school. This system remains
the foundation of Germany’s industrial pro-
ductivity. But even Borsig’s apprenticeship
took three to five years. Then, first during
World War I, but especially during World War
H, the United States systematically applied
62 WQ SPRING 1993
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Taylor’s “optimum shovel load” was a significant dis-
covery at a time when workers still moved mountains
of coal, coke, and other materials by hand.
Taylor’s approach, training “first-class men”
(and women) to perform simplified tasks in a
few months’ time. This, more than any other
factor, explains why the United States was
able to defeat Japan and Germany.
All earlier economic powers in modern
history – England, the United States, Ger-
many – emerged through leadership in new
technology. The new post-World War II eco-
nomic powers – first Japan, then South Korea,
Taiwan, Hong Kong, and Singapore – all owe
their rise to an appreciation of Taylor’s teach-
ings about training. It enabled them to endow
a still largely preindustrial and therefore still
low-wage work force with world-class pro-
ductivity in practically no time. In the post-
World War II decades Taylor-based training
became the one truly effective engine of eco-
nomic development.
The application of knowledge to work af-
ter 1880 explosively increased productivity.*
For hundreds of years there had been no in-
crease in the ability of workers to turn out
goods or to move goods. Machines created
greater capacity. But workers themselves were
no more productive than they had been in the
workshops of ancient Greece, in building the
roads of imperial Rome, or in producing the
highly prized woolen doth that gave Renais-
sance Florence its wealth. But within a few
years after Taylor began to apply knowledge
to work, productivity began to rise at a rate of
3.5 to four percent annually, which meant
that productivity doubled every 18 years or
so. Ever since Taylor’s principles took hold at
the turn of the century, productivity has in-
creased some 50-fold in all advanced coun-
tries. On this unprecedented expansion rest
all the increases in both standard of living and
quality of life in developed countries.
Half of this additional productivity has
been used to increase purchasing power –
creating a higher standard of living. But peo-
ple have used between one-third and one-
half to increase their leisure time. As late as
*The term productivity was unknown in Taylor’s time. In fact, it
was unknown until World War II, when it first began to be used
in the United States. As late as 1950 the most authoritative Eng-
lish dictionary, the Concise Oxford, still did not define the term as
it is used today.
KNOWLEDGE SOCIETY 63
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1910, workers in developed countries still la-
bored as long as they ever had before, that is,
at least 3,000 hours per year. Today even the
Japanese work only 2,000 hours, Americans
around 1,850, and Germans at most 1,600 –
and all three nations produce 50 times as
much per hour as they produced 80 years
ago. Other substantial shares of the increased
productivity have been taken in the form of
health care, which has grown from a negligi-
ble percentage of gross national product
(GNP) to between eight and 12 percent in de-
veloped countries, and in the form of educa-
tion, which has grown from around two per-
cent of GNP to 10 percent or more.
Most of this increase – as Taylor pre-
dicted – has been taken by the workers, that
is, by Marx’s proletarians. Henry Ford
brought out the first cheap automobile, the
Model T, in 1908. It was cheap, however,
only by comparison with all other automo-
biles on the market, which in terms of aver-
age incomes cost as much as a two-engine
private plane costs today. At $825, the Model
T cost what an American industrial worker
earned in three to four years – 80 cents was
then a good day’s wage (and, of course, there
were no benefits). Today, a unionized auto-
mobile worker in the United States, Japan, or
Germany, working only 40 hours a week,
earns $50,000 in wages and benefits –
$45,000 after taxes – which is roughly six
times what a cheap new car costs today.
1930 Taylor’s Scientific Manage-
ment – despite resistance from unions
and intellectuals – had swept the de-
veloped world. As a result Marx’s proletarian
became a bourgeois. The blue-collar manufac-
turing worker rather than the capitalist be-
came the true beneficiary of Capitalism and
the Industrial Revolution. This explains the
total failure of Marxism in the highly devel-
oped countries for which Marx had predicted
revolution by 1900. It explains why, after
1918, there was no proletarian revolution,
even in the defeated countries of Central Eu-
rope where there was misery, hunger, and un-
employment. It explains why the Great De-
pression did not lead to a communist
revolution, as Stalin and practically all Marx-
ists had confidently expected. By the 1930s,
Marx’s proletarians had not yet become afflu-
ent. But they had already become middle
class. They had become productive.
Darwin, Marx, and Freud make up the
trinity often cited as the “makers of the mod-
ern world.” Marx would be taken out and re-
placed by Taylor if there were any justice. But
that Taylor is not given his due is a minor
matter. It is a serious matter, however, that too
few people realize that it is the application of
knowledge to work that created developed
economies by setting off the productivity ex-
plosion of the last hundred years. Technolo-
gists give credit to machines, economists to
capital investment. But both elements were as
plentiful in the first hundred years of the cap-
italist age, that is before 1880, as they were
afterward. But there was absolutely no in-
crease in worker productivity during the first
hundred years – and consequently also little
increase in workers’ real incomes or any re-
duction in their working hours. What made
the second hundred years so critically differ-
ent can be explained only as the result of the
application of knowledge to work.
The Productivity Revolution, however,
has come to an end. When Taylor started pro-
pounding his principles, nine out of every 10
working people did manual work, making or
moving things, whether in manufacturing,
farming, mining, or transportation. The pro-
ductivity of people engaged in making and
moving things is still going up at the historical
rate of 3.5 to four percent annually – and in
American and French agriculture, even faster.
Forty years ago people who engaged in work
to make or to move things were still a major-
ity in all developed countries. By 1990 this
group had shrunk to one-fifth of the work
force. By 2010 it will constitute no more than
one-tenth. Increasing the productivity of man-
ual workers in manufacturing, in farming, in
mining, in transportation, can no longer cre-
ate wealth by itself. The Productivity Revolu-
64 WQ SPRING 1993
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tion has become a victim of its own success.
From now on what matters is the productivity
of nonmanual workers. And that requires ap-
plying knowledge to knowledge.
I decided in 1926 not to go to
college after finishing secondary
school, my father was quite dis-
tressed. Ours had long been a family of law-
yers and doctors. Yet my father did not call
me a dropout. He did not try to change my
mind. And he did not even predict that I
would never amount to anything.
I was a responsible adult wanting to work
as an adult. (That I then also got a doctorate
on the side had more to do with my trying to
annoy my father than with any belief on my
part that it would make any difference in my
life and career.) Thirty years later, when my
son reached age 18, 1 practically forced him to
go to college, like his father, he wanted to be
an adult among adults. like his father, he felt
that in 12 years of sitting in school he had
learned little, and that his chances of learning
much by spending four more years in school
were not particularly great. And yet by 1958,
31 years after I had moved from being a high-
school graduate to being a trainee in an export
firm, the college degree had become a neces-
sity. It had become the passport to virtually all
careers. Not to go to college in 1958 was
“dropping out” for an American boy who had
grown up in a well-to-do family and who had
done well in school. My father did not have
the slightest difficulty finding a trainee job for
me in a reputable merchant house. Thirty
years later such firms would not have ac-
cepted a high-school graduate as a trainee. All
of them would have said, “Go to college for
four years – and then you probably should go
on to graduate school.”
In my father’s generation – he was born in
1876 – going to college was either for the
sons of the wealthy or for a very small num-
ber of poor but exceptionally brilliant young-
sters (such as himself). Of all the American
business successes of the 19th century, only
one went to college: J. P. Morgan, who went
to Goettingen to study mathematics but
dropped out after one year. Few others even
attended high school, let alone graduated
from it. By my time, going to college was al-
ready desirable. It gave social status. But it
was by no means necessary, nor much of a
help in one’s life and career. When I made my
first study of a major business corporation,
General Motors (published as Concept of the
Corporation in 1946), the GM public-relations
department tried very hard to conceal the fact
that a good many of the company’s top exec-
utives had gone to college. The proper thing
then was to start as a machinist and work
one’s way up. As late as 1960, the quickest
route to a middle-class income – in the
United States, Great Britain, and Germany
(though already no longer in Japan) – was to
go to work at age 16 in one of the unionized
mass-production industries. There one earned
a middle-class income after a few months –
the result of the productivity explosion. These
opportunities are practically gone. Now there
is virtually no access to a good income with-
out a formal degree attesting to the acquisition
of knowledge that can be obtained only sys-
tematically and in a school.
change in the meaning of knowl-
edge that began 250 years ago has
transformed society and economy. For-
mal knowledge is seen as both the key per-
sonal resource and the key economic re-
source. Knowledge is the only meaningful
resource today. The traditional “factors of pro-
duction” – land (i.e. natural resources), labor,
and capital – have not disappeared, but they
have become secondary. They can be ob-
tained, and obtained easily, provided there is
knowledge. And knowledge in this new
meaning is knowledge as a utility, knowledge
as the means to obtain social and economic
results.
These developments, whether desirable or
not, are responses to an irreversible change:
Knowledge is now being applied to knowledge.
This is the third and perhaps the ultimate step
in the transformation of knowledge. Supply-
KNOWLEDGE SOCIETY 65
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An Interview With Peter Drucker
WQ: American schools now seem incapable of educat-
ing students even in the traditional curriculum. How
can they hope to prepare youngsters for the new era
you describe?
Drucker: It isn’t true that American schools are in-
capable of educating students. The parochial
schools, both Catholic and Protestant, do a reason-
able job by being totally old-fashioned, that is, by
running the way they did during the 1950s. This is
exactly what the Japanese are doing, too. In fact,
the various Christian schools, Catholic and Protes-
tant, are almost indistinguishable – except for the
cross on the wall and the absence of “examination
hell” – from Japanese schools. And a good many
experimental schools, such as those in Harlem’s
District Four in New York City, do a good job.
There is an old saying of mountaineers and
hikers: If you have lost your way, don’t try to be
clever. Go back to where you last knew where you
were. I am an old “progressive educator” – I taught
at two ultraprogressive colleges, Sarah Lawrence
and Bennington, during the 1940s – but it’s clear to
me that we have lost our way since the 1950s.
Other countries – Japan, Germany, France – stayed
where they were, and their schools still work. We
have to go back, I have become increasingly con-
vinced. That’s why I believe that we have no
choice but to go ahead with voucher plans that
allow parents to put their children in schools of
their choice. At least the kids will acquire core skills
and – the most important things – standards and
self-confidence.
Above all there are three things children need
to obtain very early: the ability to read, which is
still the foundation skill; self-confidence, which
means success in one area; and the ability to learn
in other areas. None of these do America’s public
schools pay much attention to today.
WQ: You emphasize the need to educate people
broadly in what you call the “knowledges,” or various
technical disciplines. Which ones?
Drucker: I have an old answer that I used to give
to students 50 years ago (and which Montaigne
had, though he formulated it differently): Be a first-
rate expert in one area and at least a journeyman in
a second and totally unrelated one. This way you’ll
understand. If you know only one area you can’t
understand; and if you try to cover more than two
you’ll be a dilettante.
This kind of exposure does not have to come in
school. One of the more successful people I know
today, for instance, is a physician who at the same
time has learned enough to manage successfully a
fair-size medical clinic. Another is the head of a
medium-size company who came up through the
financial route but has learned enough biology to
work closely with his scientists.
Or look at what volunteers get when they join
groups at one of the pastoral churches. The groups
cut across all social layers and people work to-
gether in, say, the church’s drug-abuse program.
While they are volunteers, they are not dilettantes.
Counseling is professional work. The volunteers
gain respect for one another and also for a very
different kind of work.
WQ: Although the Japanese colossus seems somewhat
diminished today, Japan will remain one of America’s
major competitors in the future. What are the advan-
tages and disadvantages of the two countries in the
new economy you describe?
Drucker: Never underrate the Japanese. That said,
they may be in for many years of transition. The
competitors to watch out for now may no longer
be primarily the Japanese but the Chinese and
other economic newcomers.
The Japanese advantage is dearly shrinking –
the Japanese are wedded to a “bigger is better and
the biggest is best” approach. Our main competi-
tive advantage in the knowledge economy is that
the young people increasingly get training with the
big companies but then quit – something you still
cannot easily do in Japan – and go to work for me-
66 WQ SPRING 1993
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dium-size or small businesses. As a result, these
businesses have the talent they need to succeed.
And it is becoming increasingly clear that the fu-
ture no longer belongs to the giants. They are too
slow, too bureaucratic, and too focused on what
worked yesterday.
Our competitive disadvantage is rooted in the
failure so far to work out the implications of the
shift of corporate ownership from individuals to
institutional investors and as a result the absence of
any paradigm for corporate governance – some-
thing which I have written about at considerable
length in the past, most recently in my book Man-
aging for the Future (1992). This failure largely ex-
plains the short-term preoccupations of America’s
large companies.
WQ: In Frederick W. Taylor’s time the key conflict
was between “capital” and “labor.” Is there a com-
parable conflict today?
Drucker: The significant division in postcapitalist
society is between knowledge workers and
nonknowledge, service workers, between, for in-
stance, lawyers, advertising copywriters, and
teachers, on the one hand, and salespeople, clerks,
and window washers, on the other. But it isn’t a
conflict, and I hope it never will become one. The
two kinds of workers are moving in different direc-
tions. There will be tension between the two
groups unless a way is found for the service work-
ers to rapidly increase their productivity and their
income potential.
The situation today is very different from any
the world has seen before. The nature of social
mobility has changed. The idea that there was no
upward mobility in earlier society is a kind of
Marxist nonsense. In fact, mobility was probably
greater in 18th- and 19th-century Europe than it
has ever been in this country. But if you moved out
of your class, you moved out. You cut your bonds.
That’s what happens in the black community to-
day. A colleague of mine, whose parents were
sharecroppers and who is now a full professor and
a very distinguished one, has totally cut his bonds
with his background. Totally. That was common in
the past. The saying was that if a bright boy from a
blue-collar family got a scholarship, his father
would say, “I’ve lost my son. I’m very proud of
him, but I’ve lost him.” That’s not true in most of
our society today. Now in the same family you
might have a fellow who becomes a doctor while
his brother or sister works at a check-out counter in
a store, yet they remain a faniily. And that is why
the analogy with conflicts antf class war is proba-
bly the wrong analogy. But ‘the division between
knowledge workers and service workers is a source
of tension.
WQ: How does your vision of the knowledge society
differ from that of Daniel Bell, who argued in The
Coming of Post-Industrial Society (1973) that such a
society, unable to provide a transcendent ethic for its
people, was bound to experience a profound cultural
crisis?
Drucker: Daniel Bell and I- I in 1969, he four
years later – started at very different points but
came out at pretty much the same place. Even ear-
lier, in my 1959 book Landmarks of Tomorrow, I
tried to sketch out the kind of philosophy and ethic
Bell was asking for. I called the chapter, overop-
timistically, “The New Philosophy Comes to life.”
It hasn’t. And because I cannot answer the ques-
tion I am profoundly interested in the rapidly
growing pastoral churches in this country, which
the new affluent two-earner families are coming to
in great numbers in a search for community, ethics,
and
responsibility.
Altogether our society will have to be based on
individual responsibility. There are some move-
ments in that direction. We now expect the person
to take responsibility for keeping himself or herself
healthy. We now expect – or are moving toward
expecting – that parents take responsibility for the
education of their children, which is what the
voucher movement is all about. We now increas-
ingly expect individuals – and especially people
with a lot of schooling – to take responsibility for
their careers, since obviously the corporate person-
nel department is unable and unwilling to do so
(despite all the talk about “organization develop-
ment” and “management development”). But
these are still only signs.
There is a great deal of talk today about “em-
powerment” – a term I have never used and never
will. It does not do any good simply to take power
from the top and move it to the bottom. Power
always corrupts unless it is first earned through
responsibility.
KNOWLEDGE SOCIETY 67
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ing knowledge to find out how existing
knowledge can best be applied to produce re-
sults is, in effect, what we mean by manage-
ment. But knowledge is now also being ap-
plied systematically and purposefully to
define what new knowledge is needed,
whether it is feasible, and what has to be
done to make knowledge effective. It is being
applied, in other words, to systematic innova-
tion.
This third change in the dynamics of
knowledge can be called the Management
Revolution. Like its two predecessors –
knowledge applied to tools, processes, and
products, and knowledge applied to work –
the Management Revolution has swept the
earth. It took 100 years, from the middle of
the 18th century to the middle of the 19th
century, for the Industrial Revolution to be-
come dominant and worldwide. It took some
70 years, from 1880 to the end of World War
H, for the Productivity Revolution to do so. It
has taken fewer than 50 years – from 1945 to
1990 – for the Management Revolution to
prevail.
they hear the word “manage-
ment,” most people still hear
“business management.” Manage-
ment did first emerge in its present form in
large-scale business organizations. When I
first began to study management some 50
years ago, I too concentrated on business
management. But we soon learned that man-
agement is needed in all modern organiza-
tions, whether they are businesses or not. In
fact, we soon learned that it is needed even
more in organizations that are not businesses,
whether not-for-profit (what I call “the Social
Sector”) or government agencies. They need
management the most precisely because they
lack the discipline of the bottom line. That
management is not confined to business was
recognized first in the United States. But it is
now becoming accepted in all developed
countries. We now know that management is
a generic function of all organizations, what-
ever their specific mission. It is the generic
organ of the knowledge society.
Management has been around for a very
long time. I am often asked whom I consider
the best or the greatest executive. My answer
is always “the man who conceived, designed,
and built the first Egyptian pyramid more
than 4,000 years ago – and it still stands.” But
management as a specific kind of work was
not seen until after World War I – and then by
a handful of people only. Management as a
discipline emerged only after World War n. As
late as 1950, when the World Bank began to
lend money for economic development, the
word “management” was not even in its
vocabulary. In fact, while management was
invented thousands of years ago, it was not
discovered until after World War H.
One reason for its discovery was the ex-
perience of World War II and especially the
performance of American industry. But per-
haps equally important to the general accep-
tance of management has been the perfor-
mance of Japan since 1950. Japan was not an
underdeveloped country immediately after
World War H, but its industry and economy
were almost totally destroyed and it had prac-
tically no domestic technology. The nation’s
main resource was its willingness to adopt
and to adapt the forms of management that
the Americans had developed during World
War II (especially training). By the 1970s it
had become the world’s second leading eco-
nomic power and a technology leader.
When the Korean War ended in 1953
South Korea was even more devastated than
Japan had been eight years earlier. And it had
never been anything but a backward country;
indeed, the Japanese had systematically sup-
pressed Korean enterprise and Korean higher
education during their 35 years of occupation.
But by using the colleges and universities of
the United States to educate its able young
people and by importing and applying man-
agement, South Korea became a highly devel-
oped country within 25 years.
With this powerful expansion of manage-
ment came a growing understanding of what
management really is. When I began to study
68 WQ SPRING 1993
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management, during and immediately after
World War II, a manager was defined as
“someone who is responsible for the work of
subordinates.” A manager in other words was
a “boss,” and management was rank and
power. This is probably still the definition
many people have in mind when they speak
of managers and management. But by the
early 1950s the definition had already
changed to “a manager is responsible for the
performance of people.” Now we know that
this is also too narrow a definition. The right
definition is “a manager is responsible for the
application and performance of knowledge.” Im-
plicit in this definition is that we now see
knowledge as the essential resource. Land, la-
bor, and capital are chiefly important as re-
straints. Without them even knowledge can-
not produce. Without them even
management cannot perform. Where there is
effective management, that is, application of
knowledge to knowledge, we can always ob-
tain the other resources. The fact that knowl-
edge has become the resource, rather than a
resource, is what makes our society
“postcapitalist.” It changes, and funda-
mentally, the structure of society. It creates
new social dynamics. It creates new economic
dynamics. It creates new politics.
Underlying all three phases in the shift to
knowledge – the Industrial
Revolution, the Productivity
Revolution, the Management
Revolution – is a profound
change in the meaning of
knowledge. We have moved
from knowledge to knowledges.
Traditionally, knowledge
was general. What we now
consider knowledge is of ne-
cessity highly specialized. We
never before spoke of a man
or woman “of knowledge.”
We spoke of an “educated
person.” Educated persons
were generalists. They knew
enough to talk or write about
a good many things, enough
to understand a good many
things. But they did not know
enough to do any one thing.
Knowledge today must prove
itself in action. What we now
mean by knowledge is in-
formation effective in action,
information focused on re-
sults. Results are outside the
person, in society and the
economy, or in the advance-
ment of knowledge itself. To
accomplish anything, this
knowledge has to be highly
specialized. This is the very
KNOWLEDGE SOCIETY 69
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reason why the tradition – beginning with the
ancients but still persisting in what we call
“liberal education” – relegated it to the status
of technê or craft. It could neither be learned
nor taught. Nor did it imply any general prin-
ciple whatever. It was specific and specialized.
It was experience rather than learning, train-
ing rather than schooling. But today we do
not speak of these specialized knowledges as
“crafts.” We speak of “disciplines.” This is as
great a change in intellectual history as any
ever recorded.
A discipline converts a craft into a meth-
odology – such as engineering, the scientific
method, the quantitative method, or the phy-
sician’s differential diagnosis. Each of these
methodologies converts ad hoc experience
into a system. Each converts anecdote into in-
formation. Each converts skill into something
that can be taught and learned. The shift from
knowledge to knowledges has given knowl-
edge the power to create a new society. But
this society has to be structured on the basis
of knowledge being specialized and of
“knowledge people” being specialists. This
gives them their power. But it also raises basic
questions – of values, of vision, of beliefs, in
other words, of all the things that hold society
together and give meaning to life. It also
raises a big – and new – question: What con-
stitutes the educated person in the knowledge
society?
educated person will have
Tomorrow’s to be prepared to live in a global
world. It will be a Westernized world.
But educated people will also live in an in-
creasingly tribalized world. They must be able
to be citizens of the world – in their vision,
their horizons, their information – but they
will also have to draw nourishment from their
local roots and, in turn, enrich and nourish
their own local culture.
Most, if not all, educated people will prac-
tice their knowledge as members of an organ-
ization. The educated person will therefore
have to prepare to live and work simulta-
neously in two cultures, that of the intellec-
tuai, the specialist who focuses on words and
ideas, and that of the manager, who focuses
on people and work. Intellectuals need their
organization as a tool; it enables them to prac-
tice their technê, their specialized knowledge.
Managers see knowledge as a means to the
end of organizational performance. Both are
right. They are poles rather than contradic-
tions. Indeed, they need each other. The intel-
lectual’s world, unless counterbalanced by the
manager, becomes one in which everybody
“does his own thing” but nobody does any-
thing. The manager’s world becomes bureau-
cratic and stultifying without the offsetting in-
fluence of the intellectual. Many people in the
postcapitalist society will actually live and
work in these two cultures at the same time.
And many more could and should be ex-
posed to both by rotation early in their ca-
reer – by having the young computer techni-
cian, for example, serve as a project manager
and team leader. All educated persons in the
postcapitalist society will have to be prepared
to understand both cultures.
the educated person of the 19th cen-
tury technê were not knowledge. They
were already taught in the university.
They had become “professional disciplines.”
Their practitioners were “professionals”
rather than “tradesmen” or “artisans.” But
they were not part of the liberal arts or of the
allgemeine Bildung and thus not part of
knowledge. Now that the technê have be-
come knowledges, they have to be integrated
into knowledge. The classics, whatever that
term may mean, may still be the core of the
educated person’s knowledge. But the techné,
too, have to be incorporated into the educated
person’s learning. TTiat the liberal arts they
enjoyed so much in their college years do not
do that, cannot do that – in fact refuse even to
try – is the reason why many young people
repudiate them a few years out of college.
They feel let down, indeed, betrayed. They
have good reason to feel that way. Liberal arts
and allgemeine Bildung that do not integrate
the knowledges into a “universe of knowl-
70 WQ SPRING 1993
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edge” are neither liberal nor bildung (educa-
tion). They fall down on the first task: to cre-
ate mutual understanding – that “universe of
discourse” without which there can be no
civilization. Instead of uniting, such liberal
arts fragment.
We neither need nor will get polymaths
who are at home in many knowledges. We
will probably become even more specialized.
But what we do need – and what will define
the educated person in the Knowledge Soci-
ety – is the ability to understand the knowl-
edges, from law to computer science. What is
each about? What is it trying to do? What are
its central concerns? What are its central theo-
ries? What major insights has it produced?
What are its important areas of ignorance, its
problems, its challenges? To make knowl-
edges into knowledge requires that the hold-
ers of the knowledges, the specialists, take
responsibility for making both themselves
and their knowledge area understood. The
media, whether magazines, movies, or televi-
sion, can help. But they cannot do the job.
Nor can any other kind of popularization.
The knowledges must be understood as what
they are: serious, rigorous, demanding. And
such understanding can be acquired only if
the leaders in each of the knowledges – be-
ginning with the learned professors in their
tenured university chairs – take responsibility
for making their own knowledge understood
and are willing to do the hard work this re-
quires.
Capitalism had been dominant for over a
century when Karl Marx in the first volume of
Das Kapital (1867) identified it as a distinct
social order. The term capitalism was not
coined until 30 years later, well after Marx’s
death. It would therefore not only be pre-
sumptuous in the extreme to attempt to write
The Knowledge today; it would be ludicrously
premature. All that can be attempted is to de-
scribe society and polity as we begin the tran-
sition from the Age of Capitalism (which, of
course, was also the Age of Socialism). But we
can hope that 100 years hence a book of this
kind, if not a book entitled The Knowledge, can
and will be written. For that would mean that
we have successfully weathered the transition
upon which we have embarked. It would be
as foolish today to predict the Knowledge So-
ciety as it would have been to predict in
1776 – the year of the American Revolution,
of Adam Smith’s Wealth of Nations, and of
James Watt’s steam engine – the society of
which Marx wrote 100 years later, and as it
was foolish of Marx to predict “with scientific
infallibility” 20th-century society.
But one thing is predictable: The greatest
change will be in the form and content of
knowledge, in its meaning and its responsibil-
ity, and in what it means to be an educated
person.
KNOWLEDGE SOCIETY 71
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p. 52
p. 53
p. 54
p. 55
p. 56
p. 57
p. 58
p. 59
p. 60
p. 61
p. 62
p. 63
p. 64
p. 65
p. 66
p. 67
p. 68
p. 69
p. 70
p. 71
The Wilson Quarterly, Vol. 17, No. 2 (Spring, 1993) pp. 1-160
Front Matter
Editor’s Comment [pp. 4-4]
At Issue: Rough Beast Time [pp. 6-8]
The Dragon Stirs [pp. 10-15, 18-34]
China at Dynasty’s End: Background Books [pp. 35-37]
Jefferson in His Time [pp. 38-51]
The Rise of the Knowledge Society [pp. 52-71]
The Knowledge Society: Background Books [pp. 72-73]
Current Books
After Chaos [pp. 74-76]
The Amoralist [pp. 77-79]
Criticizing the Critics [pp. 79-82]
Other Titles
Contemporary Affairs
Review: untitled [pp. 82-83]
Review: untitled [pp. 83-84]
Review: untitled [pp. 84-84]
Review: untitled [pp. 84-84]
History
Review: untitled [pp. 85-85]
Review: untitled [pp. 85-86]
Arts & Letters
Review: untitled [pp. 86-87]
Review: untitled [pp. 87-88]
Review: untitled [pp. 88-89]
Review: untitled [pp. 89-89]
Science & Technology
Review: untitled [pp. 89-90]
Review: untitled [pp. 90-90]
Poetry: Weldon Kees [pp. 92-98]
A Reading Lesson [pp. 99-105]
Republic of the Air [pp. 106-117]
Why Freud Hated America [pp. 118-125]
The Periodical Observer
The New Face of Mexico: A Survey of Recent Articles [pp. 126-128]
POLITICS & GOVERNMENT
The Politics Of Privacy [pp. 128-129]
Roosevelt Redux? [pp. 129-129]
Toward a Prozac Presidency? [pp. 130-130]
FOREIGN POLICY & DEFENSE
The New Jingoes [pp. 130-132]
Patriotism and Other Loves [pp. 131-131]
It Can’t Happen Here? [pp. 132-132]
Rambo Retires [pp. 132-134]
ECONOMICS, LABOR & BUSINESS
The New Wisdom on Minimum-Wage Laws: A Survey of Recent Articles [pp. 134-135]
No More Number Ones? [pp. 135-135]
SOCIETY
Why Black Students Are Making Progress [pp. 136-136]
My Brother’s Keeper [pp. 136-137]
PRESS & MEDIA
The Cheerleaders on the Bus: A Survey of Recent Articles [pp. 137-139]
Journalism’s Worst-Kept Secret Is Out Again [pp. 139-139]
RELIGION & PHILOSOPHY
Dewey and Democracy [pp. 140-140]
The Good News Of Secularism [pp. 140-141]
SCIENCE, TECHNOLOGY & ENVIRONMENT
THE (BIO)DIVERSITY DEBATE: A Survey of Recent Articles [pp. 141-143]
Fatal Glitches [pp. 143-144]
ARTS & LETTERS
Barbershop Dustup [pp. 144-144]
Pablo Picasso, Classicist [pp. 144-145]
When Hollywood Wooed the Censors [pp. 145-147]
Secret Believers [pp. 146-146]
OTHER NATIONS
AFTER THE VELVET DIVORCE: A Survey of Recent Articles [pp. 147-149]
India’s Tilt Toward the West [pp. 149-149]
Research Reports [pp. 150-151]
Commentary
In Defense of Marx [pp. 152-152]
Praise for Poetry [pp. 152-152]
The Western Military Tradition [pp. 152-152]
Confronting Infrastructure [pp. 152-154]
Thinking Animals? [pp. 154-154]
Lapsus Lingua [pp. 154-154]
Reforming American Education [pp. 154-155]
Maybe Milken Was Right [pp. 155-155]
Building the Proper House [pp. 155-156]
Bell Revisited [pp. 156-157]
Corrections: Breaking the Maya Code [pp. 157-157]
Corrections: Toward the 21st Century [pp. 157-157]
From the Center [pp. 160-160]
Back Matter
Corporate Finance
Fifth Edition
Chapter 6
Valuing Bonds
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Chapter Outline
6.1 Bond Cash Flows, Prices, and Yields
6.2 Dynamic Behavior of Bond Prices
6.3 The Yield Curve and Bond Arbitrage
6.4 Corporate Bonds
6.5 Sovereign Bonds
Copyright © 2020, 2017, 2014 Pearson Education, Inc. All Rights Reserved
2
Learning Objectives (1 of 4)
Identify the cash flows for both coupon bonds and zero-coupon bonds, and calculate the value for each type of bond.
Calculate the yield to maturity for both coupon and zero-coupon bonds, and interpret its meaning for each.
Copyright © 2020, 2017, 2014 Pearson Education, Inc. All Rights Reserved
Learning Objectives (2 of 4)
Given coupon rate and yield to maturity, determine whether a coupon bond will sell at a premium or a discount; describe the time path the bond’s price will follow as it approaches maturity, assuming prevailing interest rates remain the same over the life of the bond.
Copyright © 2020, 2017, 2014 Pearson Education, Inc. All Rights Reserved
Learning Objectives (3 of 4)
Illustrate the change in bond price that will occur as a result of changes in interest rates; differentiate between the effect of such a change on long-term versus short-term bonds.
Discuss the effect of coupon rate to the sensitivity of a bond price to changes in interest rates.
Define duration, and discuss its use by finance practitioners.
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Learning Objectives (4 of 4)
Calculate the price of a coupon bond using the Law of One Price and a series of zero-coupon bonds.
Discuss the relation between a corporate bond’s expected return and the yield to maturity; define default risk and explain how these rates incorporate default risk.
Assess the creditworthiness of a corporate bond using its bond rating; define default risk.
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6.1 Bond Cash Flows, Prices, and Yields (1 of 2)
Bond Terminology
Bond Certificate
States the terms of the bond
Maturity Date
Final repayment date
Term
The time remaining until the repayment date
Coupon
Promised interest payments
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6.1 Bond Cash Flows, Prices, and Yields (2 of 2)
Bond Terminology
Face Value
Notional amount used to compute the interest payments
Coupon Rate
Determines the amount of each coupon payment, expressed as an A P R
Coupon Payment
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Zero-Coupon Bonds (1 of 7)
Zero-Coupon Bond
Does not make coupon payments
Always sells at a discount (a price lower than face value), so they are also called pure discount bonds
Treasury Bills are U.S. government zero-coupon bonds with a maturity of up to one year.
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Zero-Coupon Bonds (2 of 7)
Suppose that a one-year, risk-free, zero-coupon bond with a $100,000 face value has an initial price of $96,618.36. The cash flows would be
Although the bond pays no “interest,” your compensation is the difference between the initial price and the face value.
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Zero-Coupon Bonds (3 of 7)
Yield to Maturity
The discount rate that sets the present value of the promised bond payments equal to the current market price of the bond
Price of a Zero-Coupon bond
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Zero-Coupon Bonds (4 of 7)
Yield to Maturity
For the one-year zero coupon bond:
Thus, the Y T M is 3.5%
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Zero-Coupon Bonds (5 of 7)
Yield to Maturity
Yield to Maturity of an n-Year Zero-Coupon Bond
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Textbook Example 6.1 (1 of 2)
Yields for Different Maturities
Problem
Suppose the following zero-coupon bonds are trading at the prices shown below per $100 face value. Determine the corresponding spot interest rates that determine the zero coupon yield curve
Maturity 1 Year 2 Years 3 Years 4 Years
Price $96.62 $92.45 $87.63 $83.06
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Textbook Example 6.1 (2 of 2)
Solution
Using Equation. 6.3, we have
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Alternative Example 6.1 (1 of 2)
Problem
Suppose that the following zero-coupon bonds are selling at the prices shown below per $100 face value. Determine the corresponding yield to maturity for each bond.
Maturity 1 Year 2 Years 3 Years 4 Years
Price $98.04 $95.18 $91.51 $87.14
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Alternative Example 6.1 (2 of 2)
Solution
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Zero-Coupon Bonds (6 of 7)
Risk-Free Interest Rates
A default-free zero-coupon bond that matures on date n provides a risk-free return over the same period
Thus, the Law of One Price guarantees that the risk-free interest rate equals the yield to maturity on such a bond
Risk-Free Interest Rate with Maturity n
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Zero-Coupon Bonds (7 of 7)
Risk-Free Interest Rates
Spot Interest Rate
Another term for a default-free, zero-coupon yield
Zero-Coupon Yield Curve
A plot of the yield of risk-free zero-coupon bonds as a function of the bond’s maturity date
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Coupon Bonds (1 of 2)
Coupon Bonds
Pay face value at maturity
Pay regular coupon interest payments
Treasury Notes
U.S. Treasury coupon security with original maturities of 1–10 years
Treasury Bonds
U.S. Treasury coupon security with original maturities over 10 years
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Textbook Example 6.2 (1 of 2)
The Cash Flows of a Coupon Bond
Problem
The U.S. Treasury has just issued a five-year, $1000 bond with a 5% coupon rate and semiannual coupons. What cash flows will you receive if you hold this bond until maturity?
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Textbook Example 6.2 (2 of 2)
Solution
The face value of this bond is $1000. Because this bond pays coupons semiannually, from Eq. 6.1, you will receive a
coupon payment every six months of
Here is the timeline, based on a six-month period:
Note that the last payment occurs five years (10 six-month periods) from now and is composed of both a coupon payment of $25 and the face value payment of $1000.
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Six month periods, Cash flow in dollars.
Six month period 0, blank.
Six month period 1, $25.
Six month period 2, $25.
Six month period 3, $25.
Six month period 10, $25 + $1000.
22
Alternative Example 6.2 (1 of 2)
Problem
Suppose that Procter & Gamble has just issued a 10-year, $1000 bond with a 4% coupon rate and semiannual coupon payments. What cash flows will you receive if you hold the bond until maturity?
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Alternative Example 6.2 (2 of 2)
Solution:
Here is the timeline, based on a six-month period:
Note that the last payment is composed of both a coupon payment of $20 and the face value payment of $1000.
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Coupon Bonds (2 of 2)
Yield to Maturity
The Y T M is the single discount rate that equates the present value of the bond’s remaining cash flows to its current price
Yield to Maturity of a Coupon Bond
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Date, Cash flow.
Date 0, negative P.
Date 1, C P N.
Date 2, C P N.
Date 3, C P N.
Date N, C P N + F V.
25
Textbook Example 6.3 (1 of 3)
Computing the Yield to Maturity of a Coupon Bond
Problem
Consider the five-year, $1000 bond with a 5% coupon rate and semiannual coupons described in Example 6.2. If this bond is currently trading for a price of $957.35, what is the bond’s yield to maturity?
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Textbook Example 6.3 (2 of 3)
Solution
Because the bond has 10 remaining coupon payments, we compute its yield y by solving:
We can solve it by trial-and-error or by using the annuity spreadsheet:
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Textbook Example 6.3 (3 of 3)
Blank N P E R R A T E P V P M T F V Excel Formula
Given 10 Blank Negative 957.35 25 1,000 Blank
Solve for Rate blank 3.00% Blank Blank Blank = RATE left parenthesis 10, 25, negative 957.35, 1000 right parenthesis
Therefore, y = 3%. Because the bond pays coupons semiannually, this yield is for a six-month period. We convert it to an A P R by multiplying by the number of coupon payments per year. Thus the bond has a yield to maturity equal to a 6% A P R with semiannual compounding.
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Financial Calculator Solution (1 of 9)
Since the bond pays interest semi-annually, the calculator should be set to 2 periods per year.
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In order, they are as follows: Gold, P forward slash Y R, 2. A series of calculator keys and corresponding values are displayed. In order, they are as follows: N, 10; I forward slash Y R, 6; P V, negative 957.35; P M T, 25; F V, 1,000.
29
Alternative Example 6.3 (1 of 2)
Problem
Consider the following semi-annual bond:
$1000 par value
7 years until maturity
9% coupon rate
Price is $1,080.55
What is the bond’s yield to maturity?
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Alternative Example 6.3 (2 of 2)
Solution
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In order, they are as follows: Gold, P forward slash Y R, 2. A series of calculator keys and corresponding values are displayed. In order, they are as follows: N, 14; I forward slash Y R, 7.5; P V, negative 1,080.55; P M T, 45; F V, 1,000.
31
Textbook Example 6.4 (1 of 2)
Computing a Bond Price from Its Yield to Maturity
Problem
Consider again the five-year, $1000 bond with a 5% coupon rate and semiannual coupons presented in Example 6.3. Suppose you are told that its yield to maturity has increased to 6.30% (expressed as an A P R with semiannual compounding). What price is the bond trading for now?
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Textbook Example 6.4 (2 of 2)
Solution
Given the yield, we can compute the price using Eq.65. First, note that a 6.30% A P R is equivalent to a semiannual rate of 3.15%. Therefore, the bond price is
We can also use the annuity spreadsheet:
Blank N P E R R A T E P V
P M T F V Excel Formula
Given 10 3.15% 25 1,000 blank
Solve for P V blank Blank Negative 944.98 blank blank = P V left parenthesis 0.0315, 10, 25, 1000 right parenthesis
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Financial Calculator Solution (2 of 9)
Since the bond pays interest semi-annually, the calculator should be set to 2 periods per year.
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In order, they are as follows: Gold, P forward slash Y R, 2. A series of calculator keys and corresponding values are displayed. In order, they are as follows: N, 10; I forward slash Y R, 6.3; P V, negative 944.98; P M T, 25; F V, 1,000.
34
Alternative Example 6.4 (1 of 2)
Problem
Consider the bond in the previous example.
Suppose its yield to maturity has increased to 10%
What is the bond’s new price?
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Alternative Example 6.4 (2 of 2)
Solution
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In order, they are as follows: Gold, P forward slash Y R, 2. A series of calculator keys and corresponding values are displayed. In order, they are as follows: N, 14; I forward slash Y R, 10; P V, negative 950.51; P M T, 45; F V, 1,000.
36
6.2 Dynamic Behavior of Bond Prices
Discount
A bond is selling at a discount if the price is less than the face value
Par
A bond is selling at par if the price is equal to the face value
Premium
A bond is selling at a premium if the price is greater than the face value
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Discounts and Premiums (1 of 3)
If a coupon bond trades at a discount, an investor will earn a return both from receiving the coupons and from receiving a face value that exceeds the price paid for the bond.
If a bond trades at a discount, its yield to maturity will exceed its coupon rate.
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Discounts and Premiums (2 of 3)
If a coupon bond trades at a premium, it will earn a return from receiving the coupons, but this return will be diminished by receiving a face value less than the price paid for the bond.
Most coupon bonds have a coupon rate so that the bonds will initially trade at, or very close to, par.
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Discounts and Premiums (3 of 3)
Table 6.1 Bond Prices Immediately After a Coupon Payment
When the bond price is We say the bond trades This occurs when
greater than the face value “above par” or “at a premium” Coupon Rate > Yield to Maturity
equal to the face value “at par” Coupon Rate = Yield to Maturity
less than the face value “below par” or “at a discount” Coupon Rate < Yield to Maturity
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Textbook Example 6.5 (1 of 2)
Determining the Discount or Premium of a Coupon Bond
Problem
Consider three 30-year bonds with annual coupon payments. One bond has a 10% coupon rate, one has a 5% coupon rate, and one has a 3% coupon rate. If the yield to maturity of each bond is 5%, what is the price of each bond per $100 face value? Which bond trades at a premium, which trades at a discount, and which trades at par?
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Textbook Example 6.5 (2 of 2)
Solution
We can compute the price of each bond using Eq.6.5. Therefore, the bond prices are
(trades at a premium)
(trades at par)
(trades at a discount)
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Financial Calculator Solution (3 of 9)
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In order, they are as follows: Gold, P forward slash Y R, 1. A series of calculator keys and corresponding values are displayed. In order, they are as follows: N, 30; I forward slash Y R, 5; P V, negative 176.86; P M T, 10; F V, 100.
43
Financial Calculator Solution (4 of 9)
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In order, they are as follows: Gold, P forward slash Y R, 1. A series of calculator keys and corresponding values are displayed. In order, they are as follows: N, 30; I forward slash Y R, 5; P V, negative 100; P M T, 5; F V, 100.
44
Financial Calculator Solution (5 of 9)
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In order, they are as follows: Gold, P forward slash Y R, 1. A series of calculator keys and corresponding values are displayed. In order, they are as follows: N, 30; I forward slash Y R, 5; P V, negative 69.26; P M T, 3; F V, 100.
45
Alternative Example 6.5 (1 of 3)
Problem
Suppose that Procter & Gamble issued a bond that has seven years remaining until maturity, a $1000 face value, and a 4% coupon rate with annual coupon payments. If the current market interest rate is 3%, what is bond’s premium or discount? What if the current market rate is 6%?
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Alternative Example 6.5 (2 of 3)
Solution:
At a market rate of 3%, the price of the bond will be
So the premium is
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47
Alternative Example 6.5 (3 of 3)
Solution:
At a market rate of 6%, the price of the bond will be
So the discount is
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Time and Bond Prices
Holding all other things constant, a bond’s yield to maturity will not change over time.
Holding all other things constant, the price of discount or premium bond will move toward par value over time.
If a bond’s yield to maturity has not changed, then the I R R of an investment in the bond equals its yield to maturity even if you sell the bond early.
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Textbook Example 6.6 (1 of 4)
The Effect of Time on the Price of a Coupon Bond
Problem
Consider a 30-year bond with a 10% coupon rate (annual payments) and a $100 face value. What is the initial price of this bond if it has a 5% yield to maturity? If the yield to maturity is unchanged, what will the price be immediately before and after the first coupon is paid?
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Textbook Example 6.6 (2 of 4)
Solution
We computed the price of this bond with 30 years to maturity in Example 6.5:
Now consider the cash flows of this bond in one year, immediately before the first coupon is paid. The bond now has 29 years until it matures, and the timeline is as follows:
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Textbook Example 6.6 (3 of 4)
Again, we compute the price by discounting the cash flows by the yield to maturity. Note that there is a cash flow of $10 at date zero, the coupon that is about to be paid. In this case, we can treat the first coupon separately and value the remaining cash flows as in Eq. 6.5:
Note that the bond price is higher than it was initially. It will make the same total number of coupon payments, but an investor does not need to wait as long to receive the first one. We could also compute the price by noting that because the yield to maturity remains at 5% for the bond, investors in the bond should earn a
return of 5% over the year:
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Textbook Example 6.6 (4 of 4)
What happens to the price of the bond just after the first coupon is paid? The timeline is the same as that given earlier, except the new owner of the bond will not receive the coupon at date zero. Thus, just after the coupon is paid, the price of the bond (given the same yield to maturity) will be
The price of the bond will drop by the amount of the coupon ($10) immediately after the coupon is paid, reflecting the fact that the owner will no longer receive the coupon. In this case, the price is lower than the initial price of the bond. Because there are fewer coupon payments remaining, the premium investors will pay for the bond declines. Still, an investor who buys the bond initially, receives the first coupon, and then sells it earns a 5% return if the bond’s yield does not change:
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Financial Calculator Solution (6 of 9)
Initial Price
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Financial Calculator Solution (7 of 9)
Price just after first coupon
Price just before first coupon
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Alternative Example 6.6 (1 of 3)
Problem
Suppose that W M T issued a bond that has ten years remaining until maturity, a $1000 face value, and a 3% coupon rate with annual coupon payments. If the current market interest rate is 5%, what is the current price of the bond? What will the price be in 4 years, assuming the current market rate remains unchanged?
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Alternative Example 6.6 (2 of 3)
Solution:
At a market rate of 5%, the price of the bond will be:
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Alternative Example 6.6 (3 of 3)
Solution:
At a market rate of 5% and 6 years left to maturity, the price of the bond will be:
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Figure 6.1 The Effect of Time on Bond Prices
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The graph contains four plots, for 10% coupon rate, 5% coupon rate, 3% coupon rate, and zero coupon. The plot for 10% coupon rate is a sawtooth curve that falls from (0, 178) to (30, 100). The plot for 5% coupon rate is a sawtooth curve that extends from (0, 100) to (30, 100). The plot for 3% coupon rate is a sawtooth curve that rises from (0, 70) to (30, 100). The plot for zero coupon is a curve that rises from (0, 22) to (30, 100). All values estimated.
59
Interest Rate Changes and Bond Prices (1 of 2)
There is an inverse relationship between interest rates and bond prices.
As interest rates and bond yields rise, bond prices fall.
As interest rates and bond yields fall, bond prices rise.
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Interest Rate Changes and Bond Prices (2 of 2)
The sensitivity of a bond’s price to changes in interest rates is measured by the bond’s duration.
Bonds with high durations are highly sensitive to interest rate changes.
Bonds with low durations are less sensitive to interest rate changes.
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Textbook Example 6.7 (1 of 3)
The Interest Rate Sensitivity of Bonds
Problem
Consider a 15-year zero-coupon bond and a 30-year coupon bond with 10% annual coupons. By what percentage will the price of each bond change if its yield to maturity increases from 5% to 6%?
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Textbook Example 6.7 (2 of 3)
Solution
First, we compute the price of each bond for each yield to maturity:
Yield to Maturity 15-Year, Zero-Coupon Bond 30-Year, 10% Annual Coupon Bond
5% start fraction 100 over 1.05 to the power of 15 end fraction = $48.10 10 times start fraction 1 over 0.05 end fraction left parenthesis 1 minus start fraction 1 over 1.05 to the power of 30 end fraction right parenthesis + start fraction 100 over 1.05 to the power of 30 end fraction = $176.86
6% start fraction 100 over 1.06 to the power of 15 end fraction = $41.73 10 times start fraction 1 over 0.06 end fraction left parenthesis 1 minus start fraction 1 over 1.06 to the power of 30 end fraction right parenthesis + start fraction 100 over 1.06 to the power of 30 end fraction = $155.06
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Textbook Example 6.7 (3 of 3)
The price of the 15-year zero-coupon bond changes by
if its yield to maturity increases from
5% to 6%. For the 30-year bond with 10% annual coupons,
the price change is
Even though the 30-year bond has a longer maturity, because of its high coupon rate, its sensitivity to a change in yield is actually less than that of the 15-year zero coupon bond.
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Alternative Example 6.7 (1 of 3)
Problem
The University of Pennsylvania sold $300 million of 100-year bonds with a yield to maturity of 4.67%. Assuming the bonds were sold at par and pay an annual coupon, by what percentage will the price of the bond change if its yield to maturity decreases by 1%? Increases by 2%?
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Alternative Example 6.7 (2 of 3)
Solution
Yield decreases by 1%
Price increases by 26.5%
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Alternative Example 6.7 (3 of 3)
Solution
Yield increases by 2%
Price decreases by 29.9%
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Figure 6.2 Yield to Maturity and Bond Price Fluctuations over Time
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The plot has numerous fluctuations in Y T M over 30 years, but tends to stay between extremes of Y T M = 4.0% and Y T M = 6.0%. The graph in panel b shows bond price in percentage of face value, versus year, and has four plots. The plot for price with 4% yield is a broken orange line that rises in a curve from (0, 31) through (15, 59) to (30, 100) The plot for price with 5% yield is a green line that rises in a curve from (0, 24) through (15, 48) to (30, 100). The plot for price with 6% yield is a broken purple line that rises in a curve from (0, 31) through (15, 55) to (30, 100) The plot for actual bond price is a blue line with numerous fluctuations, but it remains almost entirely between the plots for 4% yield and for 6% yield.
68
6.3 The Yield Curve and Bond Arbitrage
Using the Law of One Price and the yields of default-free zero-coupon bonds, one can determine the price and yield of any other default-free bond.
The yield curve provides sufficient information to evaluate all such bonds.
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Replicating a Coupon Bond (1 of 3)
Replicating a three-year $1000 bond that pays 10% annual coupon using three zero-coupon bonds:
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The timeline is from 0 to 3 increments of 1.
Coupon bond. First year. $100, Second year. $100. Year 3. $1100
First year zero. First year. $100. Second year zero. Year 2. $100. Third year zero. Year 3. $1100. Zero coupon bond portfolio. Year 1 $100, year 2, $100, and Year 3. $1100
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Replicating a Coupon Bond (2 of 3)
Table 6.2 Yields and Prices (per $100 Face Value) for Zero-Coupon Bonds
Maturity 1 year 2years 3 years 4 years
Y T M 3.50% 4.00% 4.50% 4.75%
Price $96.62 $92.45 $87.63 $83.06%
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Replicating a Coupon Bond (3 of 3)
By the Law of One Price, the three-year coupon bond must trade for a price of $1153.
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• Zero Coupon Bond, 1 year.
Face Value Required, 100.
Cost, 96.62.
• Zero Coupon Bond, 2 years.
Face Value Required, 100.
Cost, 92.45.
• Zero Coupon Bond, 3 years.
Face Value Required, 1100.
Cost, 11 multiplied by 87.63 = 963.93.
• Total cost, $1153.00.
72
Valuing a Coupon Bond Using Zero-Coupon Yields
The price of a coupon bond must equal the present value of its coupon payments and face value.
Price of a Coupon Bond
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Coupon Bond Yields
Given the yields for zero-coupon bonds, we can price a coupon bond
Blank N P E R R A T E P V P M T F V Excel Formula
Given 3 blank −1,153 100 1,000 blank
Solve for Rate blank 4.44% blank blank blank = RATE(3, 100, −1153, 1000)
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Financial Calculator Solution (8 of 9)
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In order, they are as follows: Gold, P forward slash Y R, 1. A series of calculator keys and corresponding values are displayed. In order, they are as follows: N, 3; I forward slash Y R, 4.44; P V, negative 1,153; P M T, 100; F V, 1,000.
75
Textbook Example 6.8 (1 of 3)
Yields on Bonds with the Same Maturity
Problem
Given the following zero-coupon yields, compare the yield to maturity for a three-year, zero-coupon bond; a three-year coupon bond with 4% annual coupons; and a three-year coupon bond with 10% annual coupons. All of these bonds are default free.
Maturity 1 year 2 years 3 years 4 years
Zero- coupon Y T M 3.50% 4.00% 4.50% 4.75%
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Textbook Example 6.8 (2 of 3)
Solution
From the information provided, the yield to maturity of the three-year, zero-coupon bond is 4.50%. Also, because the yields match those in Table 6.2, we already calculated the yield to maturity for the 10% coupon bond as 4.44%. To compute the yield for the 4% coupon bond, we first need to calculate its price. Using Eq. 6.6, we have
The price of the bond with a 4% coupon is $986.98. From Eq. 6.5, its yield to maturity solves the following equation:
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Textbook Example 6.8 (3 of 3)
We can calculate the yield to maturity using the annuity spreadsheet:
N P E R R A T E P V P M T F V Excel Formula
Given 3 negative 986.98 100 1,000
Solve for Rate 4.47% Blank = RATE(3, 40, −986.98, 1000)
To summarize, for the three-year bonds considered
Coupon rate 0% 4% 10%
Y T M 4.50% 4.47% 4.44%
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Financial Calculator Solution (9 of 9)
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In order, they are as follows: Gold, P forward slash Y R, 1. A series of calculator keys and corresponding values are displayed. In order, they are as follows: N, 3; I forward slash Y R, 4.47; P V, negative 986.98; P M T, 40; F V, 1,000.
79
Treasury Yield Curves
Treasury Coupon-Paying Yield Curve
Often referred to as “the yield curve”
On-the-Run Bonds
Most recently issued bonds
The yield curve is often a plot of the yields on these bonds.
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6.4 Corporate Bonds
Corporate Bonds
Issued by corporations
Credit Risk
Risk of default
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Corporate Bond Yields (1 of 9)
Investors pay less for bonds with credit risk than they would for an otherwise identical default-free bond.
The yield of bonds with credit risk will be higher than that of otherwise identical default-free bonds.
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Corporate Bond Yields (2 of 9)
No Default
Consider a one-year, zero-coupon Treasury Bill with a Y T M of 4%.
What is the price?
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Corporate Bond Yields (3 of 9)
Certain Default
Suppose now bond issuer will pay 90% of the obligation.
What is the price?
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Corporate Bond Yields (4 of 9)
Certain Default
When computing the yield to maturity for a bond with certain default, the promised rather than the actual cash flows are used.
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Corporate Bond Yields (5 of 9)
Certain Default
The yield to maturity of a certain default bond is not equal to the expected return of investing in the bond.
The yield to maturity will always be higher than the expected return of investing in the bond.
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Corporate Bond Yields (6 of 9)
Risk of Default
Consider a one-year, $1000, zero-coupon bond issued.
Assume that the bond payoffs are uncertain.
There is a 50% chance that the bond will repay its face value in full and a 50% chance that the bond will default and you will receive $900.
Thus, you would expect to receive $950.
Because of the uncertainty, the discount rate is 5.1%.
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Corporate Bond Yields (7 of 9)
Risk of Default
The price of the bond will be
The yield to maturity will be
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Corporate Bond Yields (8 of 9)
Risk of Default
A bond’s expected return will be less than the yield to maturity if there is a risk of default.
A higher yield to maturity does not necessarily imply that a bond’s expected return is higher.
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Corporate Bond Yields (9 of 9)
Table 6.3 Price, Expected Return, and Yield to Maturity of a One-Year, Zero-Coupon Avant Bond with Different Likelihoods of Default
Avant Bond (1-year, zero-coupon) Bond Price Yield to Maturity Expected Return
Default Free $961.54 4.00% 4%
50% Chance of Default $903.90 10.63% 5.1%
Certain Default $865.38 15.56% 4%
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Bond Ratings
Investment Grade Bonds
Speculative Bonds
Also known as Junk Bonds or High-Yield Bonds
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Table 6.4 Bond Ratings (1 of 2)
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Investment Grade Debt
• A lower case a a slash A A A: Judged to be of the best quality. They carry the smallest degree of investment risk and are generally referred to as “gilt edged.” Interest payments are protected by a large or an exceptionally stable margin and principal is secure. While the various protective elements are likely to change, such changes as can be visualized are most unlikely to impair the fundamentally strong position of such issues.
• A lowercase a slash A A: Judged to be of high quality by all standards. Together with the A a a group, they constitute what are generally known as high-grade bonds. They are rated lower than the best bonds because margins of protection may not be as large as in A a a securities or fluctuation of protective elements may be of greater amplitude or there may be other elements present that make the long-term risk appear somewhat larger than the A a a securities.
• A slash A: Possess many favorable investment attributes and are considered as upper-medium-grade obligations. Factors giving security to principal and interest are considered adequate, but elements may be present that suggest a susceptibility to impairment sometime in the future.
• B lowercase a a slash B B B: Are considered as medium-grade obligations (i.e., they are neither highly protected nor poorly secured). Interest payments and principal security appear adequate for the present but certain protective elements may be lacking or may be characteristically unreliable over any great length of time. Such bonds lack outstanding investment characteristics and, in fact, have speculative characteristics as well.
92
Table 6.4 Bond Ratings (2 of 2)
[Table 6.4 continued]
*Ratings: Moody’s/Standard & Poor’s
Source:
www.moodys.com
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Speculative Bonds
• B a slash B B Judged to have speculative elements; their future cannot be considered as well assured. Often the protection of interest and principal payments may be very moderate, and thereby not well safeguarded during both good and bad times over the future. Uncertainty of position characterizes bonds in this class.
• B slash B: Generally, lack characteristics of the desirable investment. Assurance of interest and principal payments of maintenance of other terms of the contract over any long period of time may be small.
• C lowercase a a slash C C C: Are of poor standing. Such issues may be in default or there may be present elements of danger with respect to principal or interest.
• C a slash C C: Are speculative in a high degree. Such issues are often in default or have other marked shortcomings.
• C slash C, D: Lowest-rated class of bonds, and issues so rated can be regarded as having extremely poor prospects of ever attaining any real investment standing.
93
Corporate Yield Curves
Default Spread
Also known as Credit Spread
The difference between the yield on corporate bonds and Treasury yields
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Figure 6.3 Corporate Yield Curves for Various Ratings, February 2018
Source: Bloomberg
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The U S Treasury’s yield curve is blue, and it rises at a decreasing rate from (0.25, 2.3%) through (10, 2.8%) to (30, 3,2%). The U S Industrials, Ay Ay Ay curve is yellow, and it rises at a decreasing rate from (0.25, 2.5%) through (10, 3.5%) to (30, 3.9%). The U S Industrials, Ay curve is green, and it rises at a decreasing rate from (0.25, 2.7%) through (10, 3.7) and (20, 4.2) to (30, 4.5%). All values estimated.
95
Figure 6.4 Yield Spreads and the Financial Crisis
Source:
Bloomberg.com
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The graph has three plots with similar fluctuations. The plot for Ay ay ay is blue, and begins at (2005, 0.6), peaks at (2009, 2.5) and (2012, 1) and ends at (2018, 0.7). The plot for Ay is red, and begins at (2005, 1), peaks at (2009, 4) and (2012, 1.5) and ends at (2018, 1.0). The plot for B ay ay is green, and begins at (2005, 1.5), peaks at (2009, 6.7) and (2012, 2.4) and ends at (2018, 1.3). The graph in panel b shows yield spread of short-term loans to major international banks, L I B O R, versus U S treasury bonds, with spread in percentage versus time, measured on January fourth of each year from 2005 to 2018. The plot remains below 1% until mid-2007, then begins fluctuating between 1% and 2.5% until mid-2007. The plot then spikes steeply to 4.6% in late 2008, but drops below 1% in mid-2009, remaining below 1% through 2018. All values estimated.
96
6.5 Sovereign Bonds
Bonds issued by national governments
U.S. Treasury securities are generally considered to be default free.
All sovereign bonds are not default-free,
e.g., Greece defaulted on its outstanding debt in 2012.
Importance of inflation expectations.
Potential to “inflate away” the debt.
European sovereign debt, the E M U, and the E C B
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Figure 6.5 Percent of Debtor Countries in Default or Restructuring Debt, 1800–2006
Source: Data from This Time Is Different, Carmen Reinhart and Kenneth Rogoff, Princeton University Press, 2009.
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The data depicted is as follows:
• 1800 to 1830: 1 to 15 percent
• 1840 to 1880: 15 to 50 percent
• 1890 to 1930: 10 to 20 percent
• 1940 to 1950: 20 to 45 percent
• 1960 to 1980: 5 to 10 percent
• 1990 to 2000: 10 to 35 percent
98
Figure 6.6 European Government Bond Yields, 1976–2018
Source: Federal Reserve Economic Data,
research.stlouisfed.org/fred2
.
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The graph has six plots representing Germany, Ireland, Spain, France, Portugal, and Italy. The plot for Germany begins at (1976, 8.2); peaks at (1982, 19), (2012, 11.8); (1995, 7.5) and ends at (2016, 0.5). The plot for France begins at (1976, 10.1); peaks at (1982, 17), (1991, 10.5); (1995, 8.1) and ends at (2016, 1). The plot for Ireland begins at (1976, 14); peaks at (1982, 19), (1987, 13.5); (1993, 10.5); (2012, 12) and ends at (2016, 1). The plot for Spain begins at (1980, 15.5); peaks at (1984, 18), (1987, 13.5); (1991, 15); (1995, 12); (2012, 7) and ends at (2016, 2). The plot for Italy begins at (1991, 13.8); peaks at (1992, 14.4), (1995, 13.5); (2012, 7) and ends at (2016, 1.8). All values estimated.
99
Chapter Quiz
What is the relationship between a bond’s price and its yield to maturity?
If a bond’s yield to maturity does not change, how does its cash price change between coupon payments?
How does a bond’s coupon rate affect its duration—the bond price’s sensitivity to interest rate changes?
Explain why two coupon bonds with the same maturity may each have a different yield to maturity.
There are two reasons the yield of a defaultable bond exceeds the yield of an otherwise identical default-free bond. What are they?
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Corporate Finance
Fifth Edition
Chapter 6
Appendix
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101
Forward Interest Rates
6A.1 Computing Forward Rates
A forward interest rate (or forward rate) is an interest rate that we can guarantee today for a loan or investment that will occur in the future.
In this chapter, we consider interest rate forward contracts for one-year investments, so the forward rate for year 5 means the rate available today on a one-year investment that begins four years from today.
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Computing Forward Rates (1 of 5)
By the Law of One price, the forward rate for year 1 is equivalent to an investment in a one-year, zero-coupon bond.
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Computing Forward Rates (2 of 5)
Consider a two-year forward rate.
Suppose the one-year, zero-coupon yield is 5.5% and the two-year, zero-coupon yield is 7.0%.
We can invest in the two-year, zero-coupon bond at 7.0%
and earn
after two years.
Or, we can invest in the one-year bond and earn $1.055 at the end of the year.
We can simultaneously enter into a one-year interest
rate forward contract for year 2 at a rate of
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Computing Forward Rates (3 of 5)
At then end of two years, we will have
Since both strategies are risk free, by the Law of One Price, they should have the same return:
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Computing Forward Rates (4 of 5)
Rearranging, we have
The forward rate for year 2 is
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Computing Forward Rates (5 of 5)
In general,
Rearranging, we get the general formula for the forward interest rate:
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Textbook Example 6A.1 (1 of 2)
Computing Forward Rates
Problem
Calculate the forward rates for years 1 through 5 from the following zero-coupon yields:
Maturity 1 2 3 4
Y T M 5.00% 6.00% 6.00% 5.75%
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Textbook Example 6A.1 (2 of 2)
Solution
Using Eqs. 6A.1 and 6A.2:
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Alternative Example 6.A1 (1 of 2)
Problem
At the end of 2015, yields on Canadian government bonds were
Maturity 1 Year 2 Years 3 Years 4 Years 5 Years 6 Years 7 Years 8 Years 9 Years 10 Years
Yield 0.51% 0.47% 0.54% 0.67% 0.82% 0.97% 1.13% 1.28% 1.42% 1.55%
Based on this yield curve, what is
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Alternative Example 6.A1 (2 of 2)
Solution
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6A.2 Computing Bond Yields from Forward Rates
It is also possible to compute the zero-coupon yields from the forward interest rates:
For example, using the forward rates from Example 8A.1, the four-year zero-coupon, yield is
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6A.3 Forward Rates and Future Interest Rates (1 of 2)
How does the forward rate compare to the interest rate that will actually prevail in the future?
It is a good predictor only when investors do not care about risk.
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Textbook Example 6A.2 (1 of 2)
Forward Rates and Future Spot Rates
Problem
JoAnne Wilford is corporate treasurer for Wafer Thin Semiconductor. She must invest some of the cash on hand for two years in risk-free bonds. The current one-year, zero-coupon yield is 5%. The one-year forward rate is 6%. She is trying to decide between three possible strategies: (1) buy a two-year bond, (2) buy a one-year bond and enter into an interest rate forward contract to guarantee the rate in the second year, or (3) buy a one-year bond and forgo the forward contract, reinvesting at whatever rate prevails next year. Under what scenarios would she be better off following the risky strategy?
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Textbook Example 6A.2 (2 of 2)
Solution
From Eq. 6A.3, both strategies (1) and (2) lead to the same
risk-free return of
The third strategy returns
where r is the one-
year interest rate next year. If the future interest rate turns out to be 6%, then the two strategies will offer the same return. Otherwise Wafer Thin Semiconductor is better off with strategy (3) if the interest rate next year is greater than the forward rate—6%—and worse off if the interest rate is lower than 6%.
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Forward Rates and Future Interest Rates (2 of 2)
We can think of the forward rate as a break-even rate.
Since investors do care about risk,
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Copyright
This work is protected by United States copyright laws and is provided solely for the use of instructors in teaching their courses and assessing student learning. Dissemination or sale of any part of this work (including on the World Wide Web) will destroy the integrity of the work and is not permitted. The work and materials from it should never be made available to students except by instructors using the accompanying text in their classes. All recipients of this work are expected to abide by these restrictions and to honor the intended pedagogical purposes and the needs of other instructors who rely on these materials.
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117
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ward Interest Rate + Risk Premium
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