Question

5. A 20-year bond with $1,000 face amount and 7% annual coupons was issued twenty years ago. You bought the bond six years ago, immediately after a coupon was paid, when the market interest rate on such bonds was 6%, and you sold it two years ago, immediately after a coupon was paid, when the market interest rate was 5%. What rate of return did you earn over the period when you held the bond? (Hint: You must figure out what you paid to buy the bond, what you received when you sold the bond, and what other payments you received. Then use the FV, PV, PMT and N keys in your calculator.)

Answer 1

First, we calculate the purchase price of the bond.

Price of a bond is the present value of its cash flows. The cash flows are the coupon payments and the face value receivable on maturity

Purchase price of bond is calculated using financial calculator with these inputs :

I/Y = 6 (YTM of bond = market interest rate)

N = 14 (Years remaining until maturity with 1 coupon payment each year)

PMT = 70 (annual coupon payment = face value * coupon rate = $1000 * 7% = $70)

FV = 1000 (face value receivable on maturity)

CPT --> PV

PV is calculated to be -$1,092.95

Purchase price of bond is $1,092.95

Next, we calculate the sale price of the bond.

Price of a bond is the present value of its cash flows. The cash flows are the coupon payments and the face value receivable on maturity

Sale price of bond is calculated using financial calculator with these inputs :

I/Y = 5 (YTM of bond = market interest rate)

N = 12 (Years remaining until maturity with 1 coupon payment each year)

PMT = 70 (annual coupon payment = face value * coupon rate = $1000 * 7% = $70)

FV = 1000 (face value receivable on maturity)

CPT --> PV

PV is calculated to be -$1,177.27

Sale price of bond is $1,177.27

Rate of return earned is calculated using financial calculator with these inputs :

N = 2 (Number of years for which the bond is held)

PMT = 70 (annual coupon payment = face value * coupon rate = $1000 * 7% = $70)

PV = -1092.95 (Purchase price of bond. This is entered with a negative sign because it is a cash outflow to buy the bond)

FV = 1177.27 (Sale price of bond)

CPT --> I/Y

I/Y is calculated to be 10.08%

Rate of return earned is 10.08%