Question

On the issue date, you bought a 30 year maturity, 5% semiannual coupon bond. The bond then sold at YTM of 6%. Now, seven years later, the similar bond sells at YTM of 4%. If you hold the bond now, what is your realized rate of return for the 7 year holding period?

Answer 1

Purchase price of bond

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

rate = 6%/2 (Semiannual YTM of bonds = annual YTM / 2)

nper = 30 * 2 (30 years remaining until maturity with 2 semiannual coupon payments each year)

pmt = 1000 * 5% / 2 (semiannual coupon payment = face value * coupon rate / 2)

fv = 1000 (face value receivable on maturity)

PV is calculated to be $861.62

Sale price of bond

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

rate = 4%/2 (Semiannual YTM of bonds = annual YTM / 2)

nper = 23 * 2 (23 years remaining until maturity with 2 semiannual coupon payments each year)

pmt = 1000 * 5% / 2 (semiannual coupon payment = face value * coupon rate / 2)

fv = 1000 (face value receivable on maturity)

PV is calculated to be $1,149.46

Realized rate of return is calculated using RATE function in Excel :

nper = 7 * 2 (total number of semiannual coupon payments during holding period = number of years bond is held * 2)

pmt = 1000 * 5% / 2 (semiannual coupon payment = face value * coupon rate / 2)

pv = -861.62 (Purchase price of bond. This is entered with a negative sign because it is a cash outflow)

fv = 1149.46 (Price of bond today. This is entered with a positive sign because it is like a cash inflow)

RATE is calculated to be 4.65%. This is the semiannual realized rate of return. To get annual realized rate of return, we multiply by 2.

Realized rate of return is 9.30%