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MGMT 332 Corporate Finance I

Module 4: Interest Rates and Bond Valuation

Problem Set 4 – Interest Rates and Bond Valuation

1. What is the annual yield of a 5-year, 3.25% semi-annual coupon-paying bond priced today at $1,075? Par is $1,000.

2. What is the annual yield of a 15-year, 5.25% annual coupon-paying bond priced today at $799? Par is $1,000.

3. Show the cash flows and prices for the following four bonds, each with a par value of $1,000 and paying interest semi-annually:

# Coupon Rate Years to Maturity Market Yield

A 1.5% 10 4.15 B 4.4% 6 5.0 C 6.2% 5 4.2 D 0.0% 9 5.1

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

4. Consider a semi-annual bond with an annual coupon = 3.0%, maturity = 5 years, par value = $1,000, and a market price today = 0:

a. What is its yield to maturity (YTM)? b. Suppose the bond can be called at $900 at the end of year 3, what is its

yield to call?

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5. You have two (2) bonds with the following characteristics:

Characteristics Bond A Bond B

Coupon 2.0% 3.0% Yield to Maturity 4. % 4. % Years to Maturity 8 9

Par Value $1,000 $1,000 Price $845.00 $880.00

a. What are the bond durations? b. If rates rise to 5.00%, what are the new prices for each bond?

Prob. 1

CF$
Coupon
Par
Start
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
Yield

Prob. 2

CF$
Coupon
Par
Start
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
10.0
11.0
12.0
13.0
14.0
15.0
Yield

Prob. 3

ABCD
Yield
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

Prob. 4

ab
Coupon
Par
YTM
Start
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0

Prob. 5

a. Durationb. Price at 5.0%
ABAB
YTM4.3114%4.6467%
Coupon2.000%3.000%
Par1,000.001,000.00
Start(845.00)(880.00)
4.907.330.510.0015.00
9.5914.331.010.0015.00
14.0821.021.510.0015.00
18.3827.392.010.0015.00
22.5033.472.510.0015.00
26.4339.273.010.0015.00
30.1944.783.510.0015.00
33.7950.034.010.0015.00
37.2255.024.510.0015.00
40.4959.765.010.0015.00
43.6164.265.510.0015.00
46.5868.536.010.0015.00
49.4072.586.510.0015.00
52.0976.407.010.0015.00
54.6580.027.510.0015.00
5,764.4483.448.01,010.0015.00
86.668.515.00
6,069.859.01,015.00
7.397.90Price @5.0%804.1750856.4664

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.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.