math Guruu 4

Prob. 1

oupon

																																																																																														$
		C
			Par
			Cash Flows:
	Purchase price
			0.5
				1.0
			1.5
				2.0
			2.5
				3.0
			3.5
				4.0
			4.5
				5.0
			5.5
				6.0
			6.5
				7.0
			7.5
				8.0
			8.5
				9.0
	Yield

Prob. 2

$

Par
Cash Flows:

1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0

Yield

	Coupon
	Start
			10.0
		11.0
		12.0
13.0
14.0
15.0

Prob. 3

C

0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
7.0
7.5
8.0
8.5
9.0

10.0

11.0

12.0

			A				B	D
Market yield	Place text answer in the box below.
Price
		9.5
	10.5
	11.5

Prob. 4

A B

Coupon
Par

Cash Flows:
Start
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
7.0
7.5
8.0
8.5
9.0
9.5
10.0
10.5
11.0
11.5
12.0

	YTM

Prob. 5

A B A B
YTM
Coupon
Par
Cash Flows:
Purchase price
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
7.0
7.5
8.0
8.5
9.0
9.5
10.0

Alfonso Canella: Alfonso Canella:
When interest rates rise, as they do in this example, bond prices fall. Conversely, when rates fall, bond prices rise. The relationship is inverse. Duration is used as a proxy for how exposed your bond is to changes in interest rates. The higher the duration, the more exposed you are to changes in interest rates. So, if you expect rates to rise and bond prices to fall, you will try to reduce the duration of your bonds. If you expect rates to fall and prices to rise, you increase the duration of your bonds. In the first instance, you reduce your losses. In the second instance, you maximize your gains.
Bond portfolio management is ALL about taking a position on future interest rates and, in some cases too, about taking a position on the long term credit quality of the bonds.
Bonds that are tied to mortgages have various risks: interest rates increases or falls, credit quality erosion, and pre-payment (when mortgages are refinanced or homes are sold and the mortgage is paid off). These mortgage-backed bonds were the cause of the 2008 economic crisis. Too many mortgages defaulted (in other words, credit quality collapsed) and the bonds tied to these mortgages defaulted, triggering bank losses and the crisis.

a. Duration	b. Price
New Price is		Alfonso Canella: Alfonso Canella: When interest rates rise, as they do in this example, bond prices fall. Conversely, when rates fall, bond prices rise. The relationship is inverse. Duration is used as a proxy for how exposed your bond is to changes in interest rates. The higher the duration, the more exposed you are to changes in interest rates. So, if you expect rates to rise and bond prices to fall, you will try to reduce the duration of your bonds. If you expect rates to fall and prices to rise, you increase the duration of your bonds. In the first instance, you reduce your losses. In the second instance, you maximize your gains. Bond portfolio management is ALL about taking a position on future interest rates and, in some cases too, about taking a position on the long term credit quality of the bonds. Bonds that are tied to mortgages have various risks: interest rates increases or falls, credit quality erosion, and pre-payment (when mortgages are refinanced or homes are sold and the mortgage is paid off). These mortgage-backed bonds were the cause of the 2008 economic crisis. Too many mortgages defaulted (in other words, credit quality collapsed) and the bonds tied to these mortgages defaulted, triggering bank losses and the crisis.	when rates rise to

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FINE 332
Corporate Finance I

Module 4 Problem Set
Interest Rates and Bond Valuation

1. What is the annual yield of a 9-year, 3.4% semi-annual coupon-paying bond priced today at $666? Par
is $1,000.

2. What is the annual yield of a 15-year, 2.75% annual coupon-paying bond priced today at $785? Par is
$1,000.

3. Show cash flows and prices for these semi-annual bonds, each with par value of $1,000:

# Coupon Rate Years to Maturity Market Yield

A 3.25% 11 4.25%

B 4.6% 12 4.0%

C 4.8% 12 4.35%

D 0.0% 8.5 4.25%

Which would you prefer to hold and why? (Answer in the box provided.)

4. Consider a semi-annual bond with an annual coupon = 4.2%, maturity = 12
years, par value = $1,000, and a market price today = $663:

a. What is its yield to maturity (YTM)?
b. If it can be called at $750 at the end of year 5, what is its yield to call?

5. You have two bonds with the following characteristics:

Characteristics Bond A Bond B
Coupon 4.5% 5.0%

Years to Maturity 10 8
Par Value $1,000 $1,000

Price $880.00 $911.00
a. What are the bond durations?
b. If rates rise to 5.5%, what are the new prices for each bond?