Question

Suppose an investor can purchase a 6-year 9% coupon bond with a par value of \$100...

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.

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

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