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**

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