Question

Katie Pairy Fruits Inc. has a $2,300 24-year bond outstanding with a nominal yield of 16 percent (coupon equals 16% × $2,300 = $368 per year). Assume that the current market required interest rate on similar bonds is now only 12 percent. Use Appendix B and Appendix D for an approximate answer but calculate your final answer using the formula and financial calculator methods.

a. Compute the current price of the bond. (Do not round intermediate calculations. Round your final answer to 2 decimal places. Assume interest payments are annual.)

b. Find the present value of 4 percent × $2,300 (or $92) for 24 years at 12 percent. The $92 is assumed to be an annual payment. Add this value to $2,300. (Do not round intermediate calculations. Round your final answer to 2 decimal places. Assume interest payments are annual.)

Answer 1

a)

Coupon = 16% of 2300 = 368

Current Price = Coupon * [1 - 1 / (1 + r)ⁿ] / r + FV / (1 + r)ⁿ

Current Price = 368 * [1 - 1 / (1 + 0.12)²⁴] / 0.12 + 2300 / (1 + 0.12)²⁴

Current Price = 368 * [1 - 0.065882] / 0.12 + 151.528838

Current Price = 368 * 7.784317 + 151.528838

Current Price = $3016.16

b)

Present value = Annuity * [1 - 1 / (1 + r)ⁿ] / r

Present value = 92 * [1 - 1 / (1 + 0.12)²⁴] / 0.12

Present value = 92 * [1 - 0.065882] / 0.12

Present value = 92 * 7.784316

Present value = $716.1571

Adding this value to $2,300

716.1571 + 2,300 = $3,016.16