Chapte What Do Interest kales Mean and What is Their Role in Valuation? 1 3

Solution: The required nominal rate would he:

J

= 2<7< +6<7( = 8%.

At this rate, you would expect to have $ 1 ,000 x 1 .08, or $ 1 ,080 at the end of the year.Can you afford the stereo? In theory, the price of the stereo w i l l increase with the rate ofinflation. So, one year later, the stereo will cost $1,050 x 1.06, or $1,1 13. You will beshort by $33.

* A 1 0-year, 7% coupon bond with a face value of $ 1 ,000 is currently selling for $87 1 .65. Computesour rate of return if you sell the bond next year for $880. 10.

Solution:

7? = -I>,-P 70 + 880.10-871.65P 871.65

-0.09, or 9%.

9. You have paid $980.30 for an 8% coupon bond with a face value of $ 1,000 that mature in five years.You plan on holding the bond for one year. If you want to earn a 9% rate of return on th is investment,\vhat price must you sell the bond for? Is this realistic?

Solution: To find the price, solve

80 + /J..-980.30980.30

= 0.09 for /> ,. 7> =988.53.

Although th is appears possible, the yield to maturity when you purchased the bond was8.5%. At that yield, you only expect the price to be $983.62 next year. In fact, the yieldwould have to drop to 8.35% for the price to be $988.53.

Calculate the duration of a $1,000 6% coupon bond with three years to maturity. Assume that allmarket interest rates are 7%.

solution:

Year

Payments

PV of Payments

Time Weighted 7'Kof Payments

Time Weighted PVof PaymentsDivided by Price

1

60.00

56.07

56.07

0.06

2

60.00

52.41

104.81

0.11

3

1060.00

865.28

2595.83

2.67

Sum

973.76

2.83

This bond has a duration of 2.83 years. Note that the current price of the bond is $973.76,which is the sum of the ind iv idua l 'VKof payments."

r

Consider the bond in the previous question. Calculate the expected price change if interest ratesdrop to 6.75% using the duration approximation. Calculate the actual price change using discountedca>h flow.

Solution: Using the duration approximation, the price change would be:

A/A/> = -DUR x x P = -2.83

l + i 1.07x 973.76 = 6.44.