4) Suppose a 10-year, $1,000 bond with a 7% coupon rate and semiannual coupons i
ID: 2824669 • Letter: 4
Question
4) Suppose a 10-year, $1,000 bond with a 7% coupon rate and semiannual coupons is trading for a price of S1,104.09 a. what is the bond's YTM (expressed as an APR with semiannual compounding)? b. If the bond's YTM changes to 8% APR, what will the bond's price be? 5) Suppose a 5-year, S1,000 bond with annual coupons has a price of S990 and a yield to maturity of 6%. What is the bond's coupon rate? 6) consider the following bonds Bond Coupon tale (anl payments) Malurity (years 0% Which of the bonds is most sensitive to a 1% drop in interest rate (YTM) and why? Provide an intuitive explanation for your answers.Explanation / Answer
4)
a)
Coupon payment = 0.0 7 * 1000 = 70 / 2 = 35 ( since it is compounded semi annually, we divide by 2)
Number of periods = 10 * 2 = 20
Face value = 1,000
Price = 1,104.09
Yield to maturity using a financial calculator = 5.62%
Keys to use in a financial calculator: 2nd I/Y 2, PV = -1,104.09, FV = 1000, N = 20, PMT = 35, CPT I/Y
b)
Rate = 0.08 / 2 = 0.04 or 4%
Bond price = Copupon payment * [ 1 - 1 / ( 1 + R)n] / R + Face value / ( 1 + R)n
Bond price = 35 * [ 1 - 1 / ( 1 + 0.04)20] / 0.04 + 1000 / ( 1 + 0.04)20
Bond price = 35 * 13.590326 + 456.38695
Bond price = $932.048
5)
Bond price = Copupon payment * [ 1 - 1 / ( 1 + R)n] / R + Face value / ( 1 + R)n
990 = Coupon payment * [ 1 - 1 / ( 1 + 0.06)5] / 0.06 + 1000 / ( 1 + 0.06)5
990 = Coupon payment * 4.212364 + 747.258173
242.741827 = Coupon payment * 4.212364
57.626 = Coupon payment
Coupon rate = ( coupon / face value) * 100
Coupon rate = ( 57.626 / 1000) * 100
Coupon rate = 5.76%
6)
A 0% 15
The cash you receive - just one big payment when the bond matures - is far out in time, so the present value of that cash flow is more sensitive to changes in the discount rate than a regular bond, whose interest payments come before maturity i.e. earlier in time which is why those cash flows are less sensitive to changes in the discount rate.
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