Question

Fix-It Inc. recently issued 10-year, $1000 par value bonds at an 9% coupon rate. Assume bond coupons are paid semiannually. Round PVFA and PVF values in intermediate calculations to four decimal places. Do not round other intermediate calculations.

a. Two years later, similar bonds are yielding investors 6%. At what price are Fix-Its bonds selling? Round the answer to the nearest cent. $

b. What would the bonds be selling for if yields had risen to 12%? Round the answer to the nearest cent. $

Answer 1

a)

Coupon = (9% of 1000) / 2 = 45

Rate = 6%/ 2= 3%

Number of periods = (10 - 2) * 2 = 16

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

Price = 45 * [1 - 1 / (1 + 0.03)^16] / 0.03 + 1000 / (1 + 0.03)^16

Price = 45 * [1 - 0.623167] / 0.03 + 623.166939

Price = 45 * 12.5611 + 623.166939

Price = $1,188.42

b)

Rate -= 12%/ 2 = 6%

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

Price = 45 * [1 - 1 / (1 + 0.06)^16] / 0.06 + 1000 / (1 + 0.06)^16

Price = 45 * [1 - 0.393646] / 0.06 + 393.466284

Price = 45 * 10.105895 + 393.646284

Price = $848.41