Question

Renfro Rentals has issued bonds that have a 7% coupon rate, payable semiannually. The bonds mature in 17 years, have a face value of $1,000, and a yield to maturity of 9.5%. What is the price of the bonds? Round your answer to the nearest cent.

Answer 1

Price of Bond = Cupon Amount * Present Value of Annuity Factor (r,n) + Redemption Amount * Present Value of Interest Factor (r,n)

Where Cupon Amount = $1,000 * 7% * 1/2

= $35

Why did we multiply 1/2?

- Since compounding is Semi Annual

Redemption Amount = $1,000

r is the Yield to Maturity (YTM)

Yield for 6 months = 9.5/2

r = 4.75%

n is the remaining maturity

n = 17 * 2

n = 34

(Semi Annual Compounding)

Present Value of Annuity Factor (4.75% ,34) = 16.7068357878

Present Value of Interest Factor (4.75% ,34) = 0.20642529984

Therefore Bond Price =$35* 16.7068357878 + $1,000 * 0.20642529984

Bond Price =$584.739252573 + $206.42529984

Bond Price = $791.164552413

Rounding to nearest cent

Bond Price = $791.16

Therefore the bond's price is $791.16