Question

You are considering investing in a​ zero-coupon bond that will pay you its face value of $ 100 in eight years. If the bond is currently selling for $ 58.20​, then the internal rate of return​ (IRR) for investing in this bond is closest​ to:

A. 8.1​%

B. 7.0​%

C. 9.2​%

D. 6.0​%

Answer 1

Face value of the bond = FV = $100

Present value of the bond = PV = $58.20

Time period = n = 8 years

YTM is the IRR for the zero-coupon bond when the bond is held till maturity.

Since Zero-coupon bonds do not pay any coupons. Hence, the price of the bond is calculated using the formula:

PV = FV/(1+YTM)ⁿ

58.20 = 100/(1+YTM)⁸

(1+YTM)⁸ = 100/58.20

1+YTM = (100/58.2)^1/8

1+YTM = 1.07000209231484

YTM = 1.07000209231484 - 1 = 0.07000209231484 ~ 7%

YTM = IRR = 7%

Answer -> 7% (Option B)