Question

BOND VALUATION

You are considering a 20-year, $1,000 par value bond. Its coupon rate is 10%, and interest is paid semiannually. If you require an "effective" annual interest rate (not a nominal rate) of 8.47%, how much should you be willing to pay for the bond? Do not round intermediate steps. Round your answer to the nearest cent.

Answer 1

Effective Annual Rate = 8.47%
(1 + Semiannual Interest Rate)^2 - 1 = 0.0847
(1 + Semiannual Interest Rate)^2 = 1.0847
1 + Semiannual Interest Rate = 1.04149
Semiannual Interest Rate = 0.04149 or 4.149%

Face Value = $1,000

Annual Coupon Rate = 10.00%
Semiannual Coupon Rate = 5.00%
Semiannual Coupon = 5.00% * $1,000
Semiannual Coupon = $50

Time to Maturity = 20 years
Semiannual Period = 40

Current Price = $50 * PVIFA(4.149%, 40) + $1,000 * PVIF(4.149%, 40)
Current Price = $50 * (1 - (1/1.04149)^40) / 0.04149 + $1,000 / 1.04149^40
Current Price = $1,164.77

So, you should pay a maximum sum of $1,164.77 for this bond.