Nesmith Corporations outstanding bonds have a 1000 par value

Nesmith Corporation\'s outstanding bonds have a $1,000 par value, a 9% semiannual coupon, 15 years to maturity, and an 8% YTM. What is the bond\'s price? Round your answer to the nearest cent.

Solution

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 * 9% * 1/2

= $45

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 = 8/2

r = 4%

n is the remaining maturity

n = 15 * 2

n = 30

(Semi Annual Compounding)

Present Value of Annuity Factor (4% ,30) = 17.2920332979

Present Value of Interest Factor (4% ,30) = 0.30831866787

Therefore

Bond Price =$45* 17.2920332979 + $1,000 * 0.30831866787

Bond Price =$778.141498405 + $308.31866787

Bond Price = $1,086.46016627

Rounding to nearest cent

Bond Price = $1,086.46

Therefore the bond\'s price is $1,086.46.