Question

Two years ago, you bought a 10-year, 6% annual coupon payment bond when its yield-to-maturity was 8%. Right after you purchased this bond, the yield-to-maturity on this bond increased to 9% and stayed at the same level in the next two years. You reinvested the coupon payments at the market rate of 9%. You just sold the bond at 9% yield-to-maturity. 1) What is your annualized holding period return? 2) What is your capital gain/loss?

Answer 1

Purchase price of bond

Purchase price of bond is calculated using PV function in Excel :

rate = 8% (YTM of bond)

nper = 10 (Years remaining until maturity with 1 coupon payment each year)

pmt = 1000 * 6% (annual coupon payment = face value * coupon rate)

fv = 1000 (face value receivable on maturity)

PV is calculated to be $865.80

Sale price of bond

Sale price of bond is calculated using PV function in Excel :

rate = 9% (YTM of bond)

nper = 8 (Years remaining until maturity with 1 coupon payment each year)

pmt = 1000 * 6% (annual coupon payment = face value * coupon rate)

fv = 1000 (face value receivable on maturity)

PV is calculated to be $833.96

a]

Annualized holding period return (HPR) is calculated using IRR function in Excel :

Cash outflow in year 0 = purchase price = $865.80

Cash inflow in year 1 = annual coupon payment = 1000 * 6% = $60

Cash inflow in year 2 = annual coupon payment + sale price = $60 + $833.96 = $893.96

Annualized holding period return (HPR) is 5.14%

b]

Capital loss = purchase price - sale price

Capital loss = $865.80 - $833.96 = $31.84