Write a consultation report to advise your corporate client on their estimated cost of equity capital
Client: Air New Zealand
School of Accounting and Commercial Law
MMPA 504: Finance
Trimester Three 202
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Assignment: Company Report
1. Write a consultation report to advise your corporate client on their estimated cost of equity capital. Include in your report:
Your client: Air New Zealand (One of Top 50 listed Companies on New Zealand Stock Exchange (by market capitalisation)
Data: collected from public resources, and sufficient for your estimation (e.g., 24-60 historical monthly returns)
Technique: Regression using Capital Asset Pricing Model (CAPM)
Structure: Intro – Data and Method – Results – Limitations – Recommendations
2. This assignment has a word limit of 1,000, accounts for 15% of your final grade, is due to submit by 5 p.m. Thursday 10 February 2022 (Week 10) to Blackboard and will be marked out of 100.
3. Please ensure name, student number and company name are clearly printed on the first page of the report.
4. Report must be typed, using Times New Roman, 12 font size, 1.5 spacing.
5. Visual aids (e.g., tables, graphs, diagrams, formulas) are encouraged to illustrate your points/ results.
6. The work you submit must be entirely your work. Also, do not plagiarise. Copying the work of others is cheating and will earn “0” marks and disciplinary action.
7. The extension request and penalties policy can be found in the course outline on Blackboard.
8. Sources should be accurately cited. You may use APA referencing or legal citation (footnotes) for this assignment. A link with guidance on the APA referencing style is available on the MPA Student Information organisation on Blackboard.
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MMPA 504
Corporate Finance
Week 8: Cost of Capital
Reading:
Berk and DeMarzo Chapter
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2
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Week 2a
Advanced Financial Accounting
Week 6 & 7 Recap
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Overview Week 8
The Equity Cost of Capital
Market Risk Premium
Beta Estimation
The Debt Cost of Capital
Weighted Average Cost of Capital (WACC)
A Project’s Cost of Capital
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1.The Equity Cost of Capital
The Capital Asset Pricing Model (C A P M) is a practical way to estimate cost of equity.
The cost of capital of any investment opportunity equals the expected return of available investments with the same beta.
The estimate is provided by the Security Market Line equation:
Advanced Financial Accounting
Week 2a
4
Example 1: Computing the Equity Cost of Capital
Problem
Suppose you estimate that Walmart’s stock has a volatility of 16.1% and a beta of 0.20.
A similar process for Johnson & Johnson yields a volatility of 13.7% and a beta of 0.54.
Which stock carries more total risk? Which has more market risk?
If the risk-free interest rate is 4% and you estimate the market’s expected return to be 12%, calculate the equity cost of capital for Walmart and Johnson & Johnson.
Which company has a higher cost of equity capital?
Example 1: Computing the Equity Cost of Capital
Solution
Total risk is measured by volatility; therefore, Walmart stock has more total risk than Johnson & Johnson.
Systematic risk is measured by beta. Johnson & Johnson has a higher beta, so it has more market risk than Walmart.
Given Johnson & Johnson’s estimated beta of 0.54, we expect the price for Johnson & Johnson’s stock to move by 0.54% for every 1% move of the market.
Example 1: Computing the Equity Cost of Capital
Solution
Therefore, Johnson & Johnson’s risk premium will be 0.54 times the risk premium of the market, and Johnson & Johnson’s equity cost of capital is
Example 1: Computing the Equity Cost of Capital
Solution
Walmart has a lower beta of 0.20. The equity cost of capital for Walmart is
Because market risk cannot be diversified, it is market risk that determines the cost of capital; thus, Johnson & Johnson has a higher cost of equity capital than Walmart, even though it is less volatile.
2. Market Risk Premium
Most practitioners use the S&P 500 as the market proxy, even though it is not actually the market portfolio
Determining the Risk-Free Rate
The yield on U.S. Treasury securities
Surveys suggest most practitioners use 10- to 30-year treasuries
The Historical Risk Premium
Estimate the risk premium (E[RMkt] − rf) using the historical average excess return of the market over the risk-free interest rate
Advanced Financial Accounting
Week 2a
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Risk-free rate
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Table 1.Historical Excess Returns of the S&P 500 Compared to One-Year and Ten-Year U.S. Treasury Securities
*Based on a comparison of compounded returns over a ten-year holding period.
Advanced Financial Accounting
Week 2a
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2. Market Risk Premium (Cont.)
A Fundamental Approach – Gordon Growth Model
Using historical data has two drawbacks:
Standard errors of the estimates are large
Backward looking, so may not represent current expectations
One alternative is to solve for the discount rate that is consistent with the current level of the index
Advanced Financial Accounting
Week 2a
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3. Beta Estimation
Estimating Beta from Historical Returns
Recall, beta is the expected percent change in the excess return of the security for a 1% change in the excess return of the market portfolio.
Advanced Financial Accounting
Week 2a
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Beta on Yahoo! Finance
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Figure 1. Monthly Returns for Cisco Stock and for the S&P 500, 2000-2017
Advanced Financial Accounting
Week 2a
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Figure 2. Scatterplot of Monthly Excess Returns for Cisco Versus the S&P 500, 2000-2017
Advanced Financial Accounting
Week 2a
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3. Beta Estimation (Cont.)
Estimating Beta from Historical Returns
As the scatter plot on the previous slide shows, Cisco tends to be up when the market is up, and vice versa.
Beta corresponds to the slope of the best-fitting line in the plot of the security’s excess returns versus the market excess return
Linear Regression
Given data for rf, Ri, and RMkt, statistical packages for linear regression can estimate βi.
A regression for Cisco using the monthly returns for 2000–2017 indicates the estimated beta is 1.56.
Advanced Financial Accounting
Week 2a
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3. Beta Estimation in Excel (Cont.)
Calculate beta using 3 different methods in Excel:
Formula Method: (Beta of Portfolio i with Portfolio P)
Regression Method
Slope Method
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Cov
Example 2: Using Regression Estimates to Estimate the Equity Cost of Capital
Problem
Suppose you have estimated Tikyberd’s beta to be 0.8 with a 95% confidence interval of 0.65 to 0.95.
Assuming the risk-free rate is 2% and the market is expected to return 12%, what range would you estimate for Tikyberd’s equity cost of capital?
Advanced Financial Accounting
Week 2a
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Example 2: Using Regression Estimates to Estimate the Equity Cost of Capital
Solution
Based on the 95% confidence interval for Tikyberd’s beta, the equity cost of capital is expected to fall between 8.5% and 11.5%.
4. The Debt Cost of Capital
Debt Yields Versus Returns
Yield to maturity is the I R R an investor will earn from holding the bond to maturity and receiving its promised payments.
If there is little risk the firm will default, yield to maturity is a reasonable estimate of investors’ expected rate of return.
If there is significant risk of default, yield to maturity will overstate investors’ expected return.
Advanced Financial Accounting
Week 2a
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4. The Debt Cost of Capital (Cont.)
Consider a one-year bond with Y T M of y. For each $1 invested in the bond today, the issuer promises to pay $(1 + y) in one year.
Suppose the bond will default with probability p, in which case bond holders receive only $(1 + y − L), where L is the expected loss per $1 of debt in the event of default.
So the expected return of the bond is
The importance of the adjustment depends on the riskiness of the bond.
Table 2. Annual Default Rates by Debt Rating (1983–2011)
Rating: AAA AA A BBB BB B CCC CC−C
Default Rate: Average 0.0% 0.1% 0.2% 0.5% 2.2% 5.5% 12.2% 14.1%
In Recessions 0.0% 1.0% 3.0% 3.0% 8.0% 16.0% 48.0% 79.0%
Source: “Corporate Defaults and Recovery Rates, 1920-2011,” Moody’s Global Credit Policy, February 2012.
4. The Debt Cost of Capital (Cont.)
The average loss rate for unsecured debt is 60%.
According to Table 2, during average times the annual default rate for B-rated bonds is 5.5%.
So the expected return to B-rated bondholders during average times is 0.055 × 0.60 = 3.3% below the bond’s quoted yield.
4. The Debt Cost of Capital (Cont.)
Debt Betas
Alternatively, we can estimate the debt cost of capital using the C A P M .
Debt betas are difficult to estimate because corporate bonds are traded infrequently.
Berk Chapter 21 shows a method for estimating debt betas
One approximation is to use estimates of betas of bond indices by rating category.
Table 3. Average Debt Betas by Rating
and Maturity*
By Rating A and above BBB BB B CCC
Avg. Beta <0.05 0.10 0.17 0.26 0.31
By Maturity (BBB and above) 1-5 year 5-10 year 10-15 year >15 year
Avg. Beta Blank 0.01 0.06 0.07 0.14
Source: S. Schaefer and I. Strebulaev, “Risk in Capital Structure Arbitrage, “Stanford GSB working paper, 2009.
*Note that these are average debt betas across industries. We would expect debt beats to be lower (higher) for industries that are less (more) exposed to market risk. One simply way to approximate this difference is to scale the debt betas in Table 3 by the relative asset beta for the industry (see Figure 4 on page 425).
Example 3: Estimating the Debt Cost of Capital
Problem
In early 2013, auto parts retailer Autozone had outstanding 10-year bonds with a yield to maturity of 3% and a B B B rating.
If corresponding risk-free rates were 1.5% and the market risk premium is 8%, estimate the expected return of Autozone’s debt.
Example 3: Estimating the Debt Cost of Capital
Solution
Using the average estimates in Table 2 and an expected loss rate of 60%, we have
Alternatively, we can estimate the bond’s expected return using the C A P M and an estimated beta of 0.10 from Table 3. In that case, rd = 1.5% + 0.10(8%) = 2.3%.
Both estimates are rough approximations and they both suggest that the expected return of Autozone’s debt is below its yield-to-maturity of 3%.
5. Weighted Average Cost of Capital
Asset (unlevered) cost of capital
Expected return required by investors to hold the firm’s underlying assets
The Weighted Average Cost of Capital (WACC)
Advanced Financial Accounting
Week 2a
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Weighted Average Cost of Capital (Cont.)
Taxes
When interest payments on debt are tax deductible, the net cost to the firm is given by
Weighted Average Cost of Capital (WACC):
Or:
Advanced Financial Accounting
Week 2a
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The Weighted Average Cost of Capital (Cont.)
How does rwacc compared with rU?
Unlevered cost of capital (or pretax W A C C)
Expected return investors will earn by holding the firm’s assets
In a world with taxes, it can be used to evaluate an all-equity project with the same risk as the firm
In a world with taxes, W A C C is less than the expected return of the firm’s assets.
With taxes, W A C C can be used to evaluate a project with the same risk and the same financing as the firm.
Example 4: Estimating the WACC
Problem
Cavo Corp’s equity cost of capital is 15%, and its debt cost of capital is 7%.
The corporate tax rate is 34%.
The firm has $100 million in debt outstanding and a market capitalization of $250 million.
What is Cavo’s unlevered cost of capital?
What is Cavo’s weighted average cost of capital?
Example 4: Estimating the WACC
Solution
Cavo’s unlevered cost of capital is
Example 4: Estimating the WACC
Solution
Cavo’s W A C C is
Or
Advanced Financial Accounting
Week 2a
34
6. A Project’s Cost of Capital
All-Equity Comparables
Find an all-equity financed firm in a single line of business that is comparable to the project.
Use the comparable firm’s equity beta and cost of capital as estimates.
Levered Firms as Comparable
Advanced Financial Accounting
Week 2a
35
Example 5: Estimating the Beta of a Project from a Single-Product Firm
Problem
You have just graduated with an M B A, and decide to pursue your dream of starting a line of designer clothes and accessories. You are working on your business plan, and believe your firm will face similar market risk to Lululemon (L U L U). To develop your financial plan, estimate the cost of capital of this opportunity assuming a risk-free rate of 3% and a market risk premium of 5%
Example 5: Estimating the Beta of a Project from a Single-Product Firm
Solution
Checking Yahoo! Finance, you find that Lululemon has no debt. Using five years of weekly data, you estimate their beta to be 0.80. Using L U L U’s beta as the estimate of the project beta,
Thus, assuming your business has a similar sensitivity to market risk as Lululemon, you can estimate the appropriate cost of capital as 7%.
In other words, rather than investing in the new business, you could invest in the fashion industry simply by buying L U L U stock.
Given this alternative, to be attractive, the new investment must have an expected return at least equal to that of L U L U, which from the C A P M is 7%.
Example 6: Unlevering the
Cost of Capital
Problem
Your firm is considering expanding its household products division. You identify Procter & Gamble (PG) as a firm with comparable investments. Suppose PG’s equity has a market capitalization of $144 billion and a beta of 0.55. PG also has $37 billion of AA-rated debt outstanding, with an average yield of 3.1%. Estimate the cost of capital of your firm’s investment given a risk-free rate of 3% and a market risk-premium of 5%.
Example 6: Unlevering the
Cost of Capital
Solution
Because investing in the division is like investing in PG’s assets by holding its debt and equity, we can estimate our cost of capital based on PG’s unlevered cost of capital.
First, we estimate PG’s equity cost of capital based on PG’s unlevered cost of capital.
PG’s equity cost of capital using the C A P M as Re = 3% + 0.55(5%) = 5.75%. Because PG’s debt is highly rated, we approximate its debt cost of capital using the debt yield of 3.1%. Thus, PG’s unlevered cost of capital is
Alternative, we can estimate PG’s unlevered beta. Given its high rating, if we assume PG’s debt is zero we have
Example 6: Unlevering the
Cost of Capital
Taking this result as an estimate of the beta of our project, we can compute our project’s cost of capital from the C A P M as rU = 3% + 0.438(5%) = 5.19%.
The slight difference in rU using the two methods arises because in the first case, we assumed the expected return of PG’s debt is equal to its promised yield of 3.1% (which overestimates the cost of debt), while in the second case, we assumed the debt has a beta of zero, which implies an expected return equal to the risk-free rate of 3% according to the C A P M (which underestimates the cost of debt, because PG’s debt is not risk free). The truth is somewhere between the two results.
Cash and Net Debt
Some firms maintain high cash balances
Cash is a risk-free asset that reduces the average risk of the firm’s assets.
Because the risk of the firm’s enterprise value is what we’re concerned with, leverage should be measured in terms of net debt
Example 7: Cash and Beta
Problem
Apple’s market capitalization in mid-2016 was $484 billion, and its beta was 1.03. At that same time, the company had $25 billion in cash and $69 billion in debt.
Based on this data, estimate the beta of Apple’s underlying business enterprise.
Example 7: Cash and Beta
Solution
Industry Asset Betas
We can combine estimates of asset betas for multiple firms in the same industry.
Doing this will reduce the estimation error of the estimated beta for the project.
Example 8: Estimate and Industry Asset Beta
Problem
Consider the following data for U.S. department stories in mid-2009, showing the equity beta, ratio of net debt to enterprise value (D/V), and debt rating for each firm. Estimate the average and median asset beta for the industry.
Company Ticker Equity Beta D/V Debt Rating
Dillard’s DDS 2.38 0.59 B
JCPenney JCP 1.60 0.17 BB
Kohl’s KSS 1.37 0.08 BBB
Macy’s M 2.16 0.62 BB
Nordstrom JWN 1.94 0.35 BBB
Saks SKS 1.85 0.50 CCC
Sears Holding SHLD 1.36 0.23 BB
Example 8: Estimate and Industry Asset Beta
Solution
Note that D/V provides the fraction of debt financing, and(1−D/V) the fraction of equity financing, for each firm. Debt beta for each firm is calculated as:
Doing this calculation for each firm, we obtain the following estimates:
Example 8: Estimate and Industry Asset Beta
The large difference in the firms’ equity beta are mainly due to differences in leverage. The firms’ asset beta are much more similar, suggesting that the underlying business in this industry have similar market risk. By combining estimates from several closely related firms in this way can get a more accurate estimate of the beta for investments in the industry.
Review Questions
What inputs do we need to estimate a firm’s equity cost of capital using the C A P M ?
How can you estimate the market risk premium?
How can you estimate a stock’s beta from historical returns?
Why does the yield to maturity of a firm’s debt generally overestimate its debt cost of capital?
Review Questions
Describe two methods that can be used to estimate a firm’s debt cost of capital.
What data can we use to estimate the beta of a project?
Why does the equity beta of a levered firm differ from the beta of its assets?
Why might projects within the same firm have different costs of capital?
Next: Week 9
Capital Structure: Reading Chapter 14
50
Advanced Financial Accounting
Week 2a
50
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