Question

Suppose you purchase a 30-year, zero-coupon bond with a yield to maturity of 6.3%. You hold the bond for five years before selling it.

a. If the bond's yield to maturity is 6.3% when you sell it, what is the internal rate of return of your investment?

b.If the bond's yield to maturity is 7.3% when you sell it, what is the internal rate of return of your investment?

c.If the bond's yield to maturity is 5.3% when you sell it, what is the internal 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.

Answer 1

Face value is not available in the question so we identify the return with purchase and selling YTM rate.

Annual Internal rate of return = ((New YTM rate  - Old YTM rate) / Year ) * 100

New rate is the selling YTM rate, Old rate is the buying rate that is 6.3%

Buy for 30-year coupon but hold till 25-years, So year should take 25

Old rate 6.3% when the time of purchase.

a) If the bond's yield to maturity is 6.3% when you sell it

YTM 6.3% same as while buy and sell, so Internal return rate is 0%

Internal rate of Return = (6.3 - 6.3) / 25 * 100 = 0%

b.If the bond's yield to maturity is 7.3% when you sell it

Internal rate of Return on Investment = (7.3 - 6.3) / 25 * 100

= 1 / 25 * 100 = 0.04 * 100

= 4%

c.If the bond's yield to maturity is 5.3% when you sell it

Internal rate of Return on Investment = (5.3 - 6.3) / 25 * 100

= -1 / 25 * 100 = -0.04 * 100

= -4% Negative Investment return.

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

Zero coupon bond is risk free investment however, If you sell the YTM before the maturity period you have to bare the risk that the YTM may change, even without default.