You are contemplating the purchase of a 20-year bond that pays R50 in interest each six months.You plan to hold this bond for only 10 years, at which time you will sell it in the marketplace.You require a 12 percent annual return, but you believe the market will require only an 8 percent return when you sell the bond 10 years hence.Assuming you are a rational investor, how much should you be willing to pay for the bond today?

Question

Quizplus · Accepted Answer

Step 1: Calculate the present value of the interest payments
PV of annuity = R50 x [(1 - (1 / (1 + 0.12/2)^20)) / (0.12/2)]

PV of annuity = R50 x 8.059 = R402.94

Step 2: Calculate the present value of the bond at year 10
PV of bond = R50 x [(1 - (1 / (1 + 0.08/2)^20)) / (0.08/2)] + R1,000 / (1 + 0.08/2)^20

PV of bond = R50 x 11.469 + R310.98 = R866.87

Step 3: Calculate the price you should be willing to pay for the bond today
PV of bond at year 10 / (1 + 0.12/2)^20 = PV of bond today + PV of annuity

R866.87 / (1 + 0.12/2)^20 = PV of bond today + R402.94

PV of bond today = R927.68

You Are Contemplating the Purchase of a 20-Year Bond That