Question

A revenue bond matures in 15 year, pays a 5.5 percent coupon rate every 6 months, and has a face value of $5,000. The market interest rate for similar risk and maturity municipal bonds is 4 percent. What is the current price of the bond? What would the price be if the market was 6 percent?

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 = $5,000 * 5.5% * 1/2

= $137.5

Redemption Amount = $5,000

r is the yield in the market on similar bonds

Yield for 6 months = 4/2

r = 2%

n is the remaining maturity

n = 15 * 2

n = 30

(Semi Annual Compounding)

Present Value of Annuity Factor (2% ,30) = 22.3965

Present Value of Interest Factor (2% ,30) = 0.5521

Therefore

Bond Price =$137.5* 22.3965 + $5,000 * 0.5521

Bond Price =$3079.5188 + $2760.5

Bond Price = $5840.0188

Therefore the current price of the bond is $5840.0188.

Calculation of the price be if the market was 6 percent

This means that the Yield for 6 months would be 6/2

r = 3%

All other inputs will be same

Present Value of Annuity Factor (3% ,30) = 19.6004

Present Value of Interest Factor  (3% ,30) = 0.4120

Bond Price = $137.5* 19.6004 + $5,000 * 0.4120

Bond Price = $2695.055 + $2060

Bond Price = $4755.055

Therefore the price of the bond when market is 6% will be $4755.055.