Question

Suppose you purchase a

30​-year

​zero-coupon bond with a yield to maturity of

5.5 %

You hold the bond for five years before selling it.a. If the​ bond's yield to maturity is

5.5 %

when you sell​ it, what is the rate of return of your​ investment?

b. If the​ bond's yield to maturity is

6.5 %

when you sell​ it, what is the rate of return of your​ investment?

c. If the​ bond's yield to maturity is

4.5 %

when you sell​ it, what is the rate of return of your​ investment?

d. Even if a bond has no chance of​ default, is your investment risk free if you plan to sell it before it​ matures? Explain.

a. If the​ bond's yield to maturity is

5.5 %

when you sell​ it, what is the rate of return of your​ investment?The rate of return of your investment is

nothing​%.

​(Round to two decimal​ places.)

Answer 1

a. Purchase price = (100 / 1.055)^30 = 20.07. Sale price = (100 / 1.055)^25
= 26.22. Return = (26.22 / 20.07)1/5– 1 = 5.50%.
I.e., since YTM is the same at purchase and sale, IRR = YTM.

b. Purchase price = (100 / 1.065)^30 = 15.11. Sale price = (100 / 1.065)^25 = 20.27.
Return = (20.27 / 15.11)1/5 – 1 = 1.7%. I.e., since YTM rises, IRR < initial YTM.

c. Purchase price = (100 / 1.045)^30 = 26.71. Sale price = (100 / 1.045)^25 = 33.27.
Return = (33.27 / 26.71)1/5– 1 = 10.15%. I.e., since YTM falls, IRR > initial YTM.

d. if you sell prior to maturit then you are exposed to the risk that the YTM may
change in due coarse