Question

Primrose Corporation issued a 5 year, $500,000 bond with a 10% coupon rate. Interest is payable every 6 months. The market discount rate is 12% annually.

1. What is the price the bonds will sell for? Show your work.

Can you please show how you do the formula and explain how to do this because I do not understand fully.

Answer 1

Interest are payable every 6 months. Therefore, there are 2 payments in a year.

Face value = $500,000

Semi annual coupon = (Coupon rate * face value) / 2

Semi annual coupon = (0.1 * 500,000) / 2 = 25,000

Total number of periods = Number of years * number of periods in a year

Total number of periods = 5 * 2 = 10

Semi annual rate = 12% / 2 = 6%

Price of bond = Coupon * [1 - 1 / (1 + r)^n] / r + FV / (1 + r)^n

Price of bond = 25,000 * [1 - 1 / (1 + 0.06)^10] / 0.06 + 500,000 / (1 + 0.06)^10

Price of bond = 25,000 * [1 - 0.558395] / 0.06 + 279,197.3885

Price of bond = 25,000 * 7.360087 + 279,197.3885

Price of bond = $463,199.56