A4. (Bond valuation) RCA made a coupon payment yesterday on its 6.25% bonds that mature
in 11.5 years. If the required return on these bonds is 9.2% nominal annual, what should
be the market price of these bonds?
n = 11.5 x 2 = 23
r = 9.2%/2 = 4.6%
Present Value = ?
MT = 6.25% x 1000/2 = $31.25
Future Value = $1,000
Present Value = -$793.32
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%?
Starting dividend/(required return - growth rate)
$5.60/(10%-6%) = $5.60/0.04 = $140
Current market value=$140
(Interest-rate risk) A quick look at bond quotes will tell you that GMAC has many different
issues of bonds outstanding. Suppose that four of them have identical coupon rates of
7.25% but mature on four different dates. One matures in 2 years, one in 5 years, one in
10 years, and the last in 20 years. Assume that they all made coupon payments yesterday.
a. If the yield curve were flat and all four bonds had the same yield to maturity of 9%,
what would be the fair price of each bond today?
b. Suppose that during the first hour of operation of the capital markets today, the term
structure shifts and the yield to maturity of all these bonds changes to 10%. What is the
fair price of each bond now?
c. Suppose that in the second hour of trading, the yield to maturity of all these bonds
changes once more to 8%. Now what is the fair price of each bond?
d. Based on the price changes in response to the changes in yield to maturity, how is
interest-rate risk a function of the bond’s maturity? That is, is interest-rate risk the
same for all four bonds, or does it depend on the bond’s maturity?
A: PV= D1/r-g [1- (1+g)n/(1+r)n
n = 2 x 2 = 4... [continues]
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