Question

You buy a 20-year bond with a coupon rate of 9.6% that has a yield to maturity of 10.6%. (Assume a face value of $1,000 and semiannual coupon payments.) Six months later, the yield to maturity is 11.6%. What is your return over the 6 months?

Answer 1

The Current Price of the Bond if the Yield to Maturity is 10.60%

The Price of the Bond is the Present Value of the Coupon Payments plus the Present Value of the Face Value/Par Value. The Price of the Bond is normally calculated either by using EXCEL Functions or by using Financial Calculator.

Here, the calculation of the Bond Price using financial calculator is as follows

Variables	Financial Calculator Keys	Figures
Face Value [-$1,000]	FV	-1,000
Coupon Amount [$1,000 x 9.60% x ½]	PMT	48
Market Interest Rate or Required Rate of Return [10.60% x ½]	1/Y	5.30
Time to Maturity [20 Years x 2]	N	40
Bond Price	PV	?

Here, we need to set the above key variables into the financial calculator to find out the Price of the Bond. After entering the above keys in the financial calculator, we get the Price of the Bond = $917.62.

The Price of the Bond after 6 months if the Yield to Maturity is 11.60%

The Price of the Bond is the Present Value of the Coupon Payments plus the Present Value of the Face Value/Par Value. The Price of the Bond is normally calculated either by using EXCEL Functions or by using Financial Calculator.

Here, the calculation of the Bond Price using financial calculator is as follows

Variables	Financial Calculator Keys	Figures
Face Value [-$1,000]	FV	-1,000
Coupon Amount [$1,000 x 9.60% x ½]	PMT	48
Market Interest Rate or Required Rate of Return [10.60% x ½]	1/Y	5.80
Time to Maturity [(20 Years – 6 Months) x 2]	N	39
Bond Price	PV	?

Here, we need to set the above key variables into the financial calculator to find out the Price of the Bond. After entering the above keys in the financial calculator, we get the Price of the Bond = $846.71.

The total rate of return over 6 months

The rate of return = [{Coupon payment + (Selling price – Purchase price)} / Purchase price] x 100

= [{$48 + ($846.71 - $917.62)} / $917.62] x 100

= [($48 - $70.91) / $917.62] x 100

= [-$22.91 / $917.62] x 100

= -2.50% (Negative Return)

“Therefore, the rate of return will be -2.50% (Negative Return)”