Question

Kebt Corporation's Class Semi bonds have a 12-year maturity and an 9.25% coupon paid semiannually (4.625% each 6 months), and those bonds sell at their $1,000 par value. The firm's Class Ann bonds have the same risk, maturity, nominal interest rate, and par value, but these bonds pay interest annually. Neither bond is callable. At what price should the annual payment bond sell?

Answer 1

Semi Annual Bond par value = 1000
Coupon rate semi annual = 4.625%, Coupon = Coupon rate = 4.625% * 1000 = 46.25
T ( years) = 12
Number of compoundings per year = 2
Price of Bond = 1000
Hence YTM = (1+ Annual coupon rate/2)^2 -1 = (1+0.04625)² - 1 = 1.0946 -1 =0.0946 or 9.46%
Since The firm's Class Ann bonds have the same risk, maturity, nominal interest rate, and par value so YTM is same = 9.46%
Annual Bond's par value = $1000
Coupon Rate Annually = 9.25%
Coupon = Coupon rate * Par value = 9.25% * 1000 = 92.5
Price = C_t/(1+YTM)^t + Par Value/(1+YTM)^t = 92.5/(1+0.0946)^t + 1000/(1.0946)¹² = 985.30
Price of Bond = 985.30
Best of luck