Question

A bond with a $1,000 par, 7 years to maturity, a coupon rate of 6%, and annual payments has a yield to maturity of 3.9%. What will be the actual percentage change in the bond price if the yield changes instantaneously to 5.4%?

Answer 1

Price of the Bond if the Yield to maturity is 3.90%

• 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
Par Value/Face Value of the Bond [$1,000]	FV	1,000
Coupon Amount [$1,000 x 6.00%]	PMT	60
Market Interest Rate or Yield to maturity on the Bond [3.90%]	1/Y	3.90
Maturity Period/Time to Maturity [7 Years]	N	7
Bond Price/Current market price of the Bond	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 (PV) = $1,126.51.

Price of the Bond if the Yield to maturity increases to 5.40%

Variables	Financial Calculator Keys	Figures
Par Value/Face Value of the Bond [$1,000]	FV	1,000
Coupon Amount [$1,000 x 6.00%]	PMT	60
Market Interest Rate or Yield to maturity on the Bond [5.40%]	1/Y	5.40
Maturity Period/Time to Maturity [7 Years]	N	7
Bond Price/Current market price of the Bond	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 (PV) = $1,034.22.

Percentage change in the price of the Bond

Percentage change in the price of the Bond = [(Price at 5.40% YTM - Price at 3.90% YTM) / Price at 3.90% YTM] x 100

= [($1,034.22 - $1,126.51) / $1,126.51] x 100

= [-$92.29 / $1,126.51] x 100

= -8.19% (Negative)

“Here, the Percentage change in the price of the Bond will be -8.19% (Negative)”