Question

Suppose you purchase a 30-year Treasury bond with a 4% annual coupon, initially trading at par. In 10 years’ time, the bond’s yield to maturity has risen to 7% (EAR). Assume a $110 face value bond. (a) If you sell the bond now, what IRR will you have earned on your investment in the bond?

(b) If you hold the bond to maturity, what IRR will you have earned on your investment in the bond?
(c) Is comparing the IRRs in (a) versus (b) a useful way to evaluate the decision to sell the bond? (Select One)
(i) No, IRR is flawed so you should use NPV instead
(ii) No, the two IRRs represent different returns for different time intervals (iii) Yes, IRR works for bonds, you should pick the choice with the lower IRR because this is effectively a loan
(iv) Yes, IRR works for bonds, you should pick the choice with the higher IRR

Answer 1

The IRR if you sell the bond now can be calculated using the selling price and the present value of cash flows. If you hold the bond to maturity, the IRR will be the coupon rate. Comparing the IRRs in (a) versus (b) is not a useful way to evaluate the decision to sell the bond.

Step-by-step explanation:

When interest rates rise, the value of bonds that were issued at lower interest rates will decrease. In this case, the bond's yield to maturity has risen to 7% after 10 years. To calculate the IRR if you sell the bond now, you need to consider the price at which you sell it. Assuming a face value of $110 and a selling price equal to the bond's value at the new yield to maturity, the IRR can be calculated by finding the discount rate that makes the present value of all cash flows equal to the selling price. This can be done using a financial calculator or spreadsheet software. If you hold the bond to maturity, the IRR will be the same as the coupon rate, which is 4% in this case.

Comparing the IRRs in (a) versus (b) can provide insight into the decision to sell the bond. A higher IRR indicates a higher return on investment, while a lower IRR indicates a lower return. However, it is important to note that the two IRRs represent different returns for different time intervals. The IRR when selling the bond now takes into account the time value of money for the remaining cash flows, while the IRR when holding the bond to maturity does not. Therefore, it is not a useful way to directly compare the two IRRs in order to evaluate the decision to sell the bond.