Question

Apple Company’s bonds have maturity period of five years. The bonds have a $1000 face value, the coupon rate is 18% per year paid monthly. Suppose you purchased the bond for $920. Three years after from the date of purchase, the market interest rate on such bonds decreases to 12%.

(a) At what price will the bonds sell after these three years?

(b) If you want to make a 24% return on this investment, three years after the date of purchase, what would be your selling price?

(c) Would you be able to sell the bond with the price you found in part (b)? Explain your reasoning.

Answer 1

To determine the sale price of the bonds after three years, calculate the present value of the remaining cash flows. If you want to make a 24% return on your investment, use the same present value formula but with a desired rate of return of 24%. To determine if you can sell the bond with the price found in part (b), compare it to the price calculated in part (a).

Step-by-step explanation:

To determine the sale price of the bonds after three years, we need to calculate the present value of the remaining cash flows. The coupon rate is 18% per year, paid monthly, so the monthly coupon payment is $150 ([$1000 * 18%] / 12). Assuming the market interest rate is now 12%, we can use the present value formula to calculate the present value of the remaining coupon payments for the next two years, as well as the present value of the face value repaid at maturity:

Present value of remaining coupon payments = $150 * [(1 - (1 + 0.12/12)^(-12 * 2)) / (0.12/12)]

Present value of face value = $1000 / (1 + 0.12/12)^(12 * 2)

Adding these two present values will give us the sale price of the bonds after three years.

To calculate the selling price required to make a 24% return on the investment, we can use the same present value formula but with a desired rate of return of 24% instead of 12%.

Finally, to determine if you would be able to sell the bond with the price found in part (b), you need to compare it to the selling price calculated in part (a). If the price found in part (b) is higher than the price calculated in part (a), you would be able to sell the bond. Otherwise, you would not be able to sell the bond.