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posted by  lazar on 8/19/2009 9:42:04 AM  |  status: Live  |  Earned Karma: 25

corporate finance

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  1. (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?

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?

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 of each bond?

d. Based on the fair prices at the various yields to maturity, is interest-rate risk the same, higher, or lower for longer-versus shorter-maturity bonds?

 
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posted by Domokun on 8/19/2009 8:58:34 PM  |  status: Live
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Response Details:
Since bonds pay coupons biannually, a coupon rate of 9.125% means a payment of $45.6 every 6 months on a nominal $1000 bond.
a. If the YTM is 8%, the price of the first bond is:
45.6/(1.04) + 1045.6/(1.04^2) = 1010.56
The 8% must be divided by 2 in order to find the relevant interest for every 6 months.
The price of second bond that matures in 7 years can be calculated with the following formula:

45.6 * [1-(1/1.04)^14] / 0.04 + 1000 / (1.04)^14 = 1059.15
Similarly, the price of the third bond that matures in 15 years is calculated as:
45.6 * [1-(1/1.04)^30] / 0.04 + 1000 / (1.04)^30 = 1096.84

b. Similarly, at a YTM of 7%, the prices are:
1 year: 1020.14
7 years: 1115.76
15 years: 1194.96

c. At a YTM of 9%, the prices are:
1 year: 1001.12
7 years: 1006.13
15 years: 1009.77

d. The interest-rate risk is higher for longer-term bonds as the variation in prices is much more pronounced.
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