Assume that you are considering the purchase of a $1,000 par value bond that pays interest of $70 each six months and has 10 years before maturity. If you purchase this bond, you expect to hold it for 5 years and then to sell it in the market. You (and other investors) currently require a nominal annual rate of 16 percent, but you expect the market to require a nominal rate of only 12 percent when you sell the bond due to a general decline in interest rates. How much should you be willing to pay for this bond today?
A) $952.73
B) $955.51
C) $958.49
D) $961.39
E) $966.99

Question

Quizplus · Accepted Answer

To determine the price you should be willing to pay for the bond today, you need to calculate its present value considering the interest payments and the expected selling price in 5 years. The bond pays $70 every six months, which is a semi-annual payment, and you expect to hold it for 5 years (or 10 periods, since there are two periods per year). The current required nominal annual rate is 16%, but since the bond pays semi-annually, you use half of this rate for each period, which is 8% per period. First, calculate the present value of the interest payments using the formula for the present value of an annuity:$$ PV_{interest} = P \times \left(1 - (1 + r)^{-n}\right) / r $$where $P$ is the payment per period, $r$ is the interest rate per period, and $n$ is the number of periods. Plugging in the values:$$ PV_{interest} = 70 \times \left(1 - (1 + 0.08)^{-10}\right) / 0.08 \approx 472.11 $$Next, calculate the expected selling price of the bond in 5 years. In 5 years, the bond will still have 5 years left until maturity, and you expect the market to require a nominal rate of 12% annually, or 6% per period. The bond will still pay $70 every six months. The present value of the remaining payments and the par value at that time, using the expected rate, gives the bond's selling price:$$ PV_{selling} = 70 \times \left(1 - (1 + 0.06)^{-10}\right) / 0.06 + 1000 / (1 + 0.06)^{10} \approx 837.21 + 558.39 = 1395.60 $$Finally, discount this selling price back to today, using the current rate of 8% per period for 10 periods:$$ PV_{today} = PV_{selling} / (1 + 0.08)^{10} \approx 1395.60 / (1 + 0.08)^{10} \approx 966.99 $$Therefore, you should be willing to pay approximately $966.99 for the bond today.

Assume That You Are Considering the Purchase of a $1,000