4 Suppose a 10year 1000 bond with a 7 coupon rate and semian

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.

Solution

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.