Question

Suppose an investor can purchase a 6-year 9% coupon bond with a par value of $100 that
pays interest semi-annually. The yield to maturity for this bond is 10% on a bond-equivalent yield basis.
What is the coupon interest, capital gain/loss and reinvestment income associated with this bond over
its 6-year life? Assume that the reinvestment rate is equal to the yield to maturity.

Answer 1

Price of the bond needs to be calculated first. The price of the bond can be calculated using the PV function of excel. Inputs are:

• Rate = YTM per period = Semi annual YTM = 10%/2 = 5%
• Nper = number of half years in 6years = 2 x 6 = 12
• PMT = semi annual coupon = 9%/2 x 100 = 4.50
• FV = par value = 100

Hence, the price of the bond today = -PV (Rate, Nper, PMT, FV) = - PV (5%, 12, 4.50, 100) = 95.57

The coupon interest associated with this bond over its 6-year life = PMT x Nper = 4.50 x 12 = $ 54.00

The capital gain/loss associated with this bond over its 6-year life = Par value - Price of the bond today = 100 - 95.57 = $ 4.43

The reinvestment income associated with this bond over its 6-year life = FV of all the semi annul coupon payments - sum of all the coupons paid = FV (Rate, Nper, PMT, PV) - 54 = FV (5%, 12, 4.50, 0) - 54 = 71.63 - 54 = $ 17.63