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Week 4 Exam

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A1. (Bond valuation) A $1,000 face value bond has a remaining maturity of 10 years and a required return of 9%. The bond’s coupon rate is 7.4%. What is the fair value of this bond?

Solution:

Coupon Payment = $1,000 × 3.7% = $37 ((10 years × 2) = 20 periods[pic]

P = [pic][pic]

= $481.29 + $414.64

= $895.94

Answer: $895.94

A10. (Dividend discount model) Assume RHM is expected to pay a total cash dividend of $5.60 next year and its dividends are expected to grow at a rate of 6% per year forever. Assuming annual dividend payments, what is the current market value of a share of RHM stock if the required return on RHM common stock is 10%?

Solution:

P0 = D1 / (r - g) = (5.60 / (.10 -.06)) ( $140.00

Answer: $140

B16. (Interest-rate risk) Philadelphia Electric has many bonds trading on the New York Stock

Exchange. Suppose PhilEl’s bonds have identical coupon rates of 9.125% but that one issue matures in 1 year, one in 7 years, and the third in 15 years. Assume that a coupon payment was made yesterday.

a. If the yield to maturity for all three bonds is 8%, what is the fair price of each bond?

Solution:

(9.125% x 1,000)/2 = $45.625 fv = $1,000 ( -$1,010.61
(9.125% x 1,000)/2 = $45.625 fv = $1,000 ( -$1,059.42
(9.125% x 1,000)/2 = $45.625 fv = $1,000 ( -$1,097.27

Answer: -$1,010.61, -$1,059.42, -$1,097.27

b. Suppose that the yield to maturity for all of these bonds changed instantaneously to 7%.
What is the fair price of each bond now?

Solution:

(9.125% x 1,000)/2 = $45.625 fv = $1,000 ( -$1,020.18
(9.125% x 1,000)/2 = $45.625 fv = $1,000 (-$1,116.03
(9.125% x 1,000)/2 = $45.625 fv = $1,000 (-$1,195.42

Answer: -$1,020.18, -$1,116.03, -$1,195.42

c. Suppose that the yield to maturity for all of these bonds changed instantaneously again, this time to 9%. Now what is the fair price

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