| Price of Bonds Did I answer this question correctly?
Johnson Company has issued bonds which have a 9% coupon rate,
payable semiannually. The bonds mature in 8 years, have a face value of $1,000 and a yield to maturity of 8.5%. What is the price of the bonds?
Although some bonds pay interest annually, the vast majority actually pay interest semiannually. To evaluate semiannual payment bonds, we must do the following:
Divide the annual coupon interest payment by 2 to determine the dollars of interest paid each six months.
Multiply the years to maturity, N, by 2 to determine the number of semiannual periods.
Divide the nominal (quoted) interest rate, Kd, by 2 to determine the periodic (semi-annual) interest rate.
By doing the previous steps, we obtain the following formula:
Vb = INT/2 + M
(1+Kd/2)^t (1 + Kd/2)^2N
Coupon rate = (0.09)/2 = 0.045
Years of Maturity (N) = (8)2 = 16
Nominal Interest Rate (Kd) = (0.085)/2 = 0.0425
INT = (0.09)(1000) = $90 or $45 semiannually
M (value of the bond) = $1,000
Vb = 90/2 + 1000
(1 + .085/2)^8 (1 + 0.085/2)^2*8
= 45 + 1000
(1.0425)^8 (1.0425)^16
= 45 + 1000
1.39511 1.946332
= 32.255521 + 513.78695
= 546.04247 or 1092.09 / year |