Question

Consider a bond with the following characteristics. Par: $1,000 Two coupon payments per year (i.e., coupons are paid semi-annually) Coupon rate: 7.50% Years to maturity: 40 Bond price: $965 Suppose that the annual market interest rate for this bond drops by 1%. What is the new bond price? Note: recall that the annual yield-to-maturity (YTM) is the market interest rate on the bond. $965.00 $858.33 $1,097.93

Answer 1

Step-1, The Yield to maturity of (YTM) of the Bond

The Yield to maturity of (YTM) of the Bond is calculated using financial calculator as follows (Normally, the YTM is calculated either using EXCEL Functions or by using Financial Calculator)

Variables	Financial Calculator Keys	Figure
Face Value [$1,000]	FV	1,000
Coupon Amount [$1,000 x 7.50% x ½]	PMT	37.50
Yield to Maturity [YTM]	1/Y	?
Time to Maturity [40 Years x 2]	N	80
Bond Price [-$965]	PV	-965

We need to set the above figures into the financial calculator to find out the Yield to Maturity of the Bond. After entering the above keys in the financial calculator, we get the yield to maturity (YTM) on the bond = 3.395%

The semi-annual Yield to maturity = 3.395%

Therefore, the annual Yield to Maturity of the Bond = 7.79% [3.395% x 2]

Step-2, The New price of the Bond

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 7.50% x ½]	PMT	37.50
Market Interest Rate or Required Rate of Return [7.79% x ½]	1/Y	3.395
Time to Maturity [40 Years x 2]	N	80
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 = $1,097.93.

“Therefore, the New Price of the Bond will be $1,097.93”