Question

Suppose your investment horizon is 5 years. You today buy a 10- year coupon bond with coupon rate 7%, paid once a year. The term structure today is flat at 4%.

a. What is the bond’s price?

b. Suppose you expect that the term structure will remain flat at 4% for the next six years. What is your expected realized yield?

c. Now suppose that immediately after you bought the bond, the term structure falls to 3% and you expect it to stay at 3% for the next six years. How did this change affect your expected realized yield?

Answer 1

Hello Sir/ Mam

(a) Bond price today = $1,243.33

n = 10, coupon = 70, future value = 1000, YTM = 4%

Using excel function,"=PV(4%,10,-70,-1000,0)", we get that the Present Value = $1,243.33

(b) Realised Yield = 4%

n = 5, coupon = 70, future value = 1000, YTM = 4%

Using excel function,"=PV(4%,5,-70,-1000,0)", we get that the Present Value = $1,133.55

Hence,

PMT = 70, future value = 1133.55, n = 5, pv = 1243.33

Using excel function,"=RATE(5,70,-1243.33,1133.55,0)", we can get that the Yield = 4%

(c) Realised Yield = 4.75%

n = 5, coupon = 70, future value = 1000, YTM = 3%

Using excel function,"=PV(3%,5,-70,-1000,0)", we get that the Present Value = $1,183.19

Hence,

PMT = 70, future value = 1183.19, n = 5, pv = 1243.33

Using excel function,"=RATE(5,70,-1243.33,1183.19,0)", we can get that the Yield = 4.75%

I hope this solves your doubt.

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