Question

A bond has a face value of $1,000, coupon rate of 8%, and matures in 6 years. Imagine that the market interest rate is 6%, but immediately after you buy the bond the rate drops to 5%. What is the immediate effect on the bond price?

Hint: the effect is the price of the bond after the change minus the price of the bond before the change.

Answer 1

The current market price of these bond if the market rate is 6%

The Current Market Price of the Bond is the Present Value of the Coupon Payments plus the Present Value of the face Value

Face Value of the bond = $1,000

Annual Coupon Amount = $80 [$1,000 x 8%]

Annual Yield to Maturity = 6%

Maturity Period = 6 Years

The current market price of these bonds = Present Value of the Coupon Payments + Present Value of the face Value

= $80[PVIFA 6%, 6 Years] + $1,000[PVIF 6%, 6 Years]

= [$80 x 4.91732] + [$1,000 x 0.70496]

= $393.39 + $704.96

= $1,098.35

The current market price of these bond if the market rate drops to 5%

Face Value of the bond = $1,000

Annual Coupon Amount = $80 [$1,000 x 8%]

Annual Yield to Maturity = 5%

Maturity Period = 6 Years

The current market price of these bonds = Present Value of the Coupon Payments + Present Value of the face Value

= $80[PVIFA 5%, 6 Years] + $1,000[PVIF 5%, 6 Years]

= [$80 x 5.07569] + [$1,000 x 0.74622]

= $406.05 + $746.22

= $1,152.27

Therefore, the immediate effect on the bond price will be $53.92 [i.e.. $1,152.27 - $1,098.35]

NOTE

-The formula for calculating the Present Value Annuity Inflow Factor (PVIFA) is [{1 - (1 / (1 + r)ⁿ} / r], where “r” is the Yield to Maturity of the Bond and “n” is the number of maturity periods of the Bond.

-The formula for calculating the Present Value Inflow Factor (PVIF) is [1 / (1 + r)ⁿ], where “r” is the Yield to Maturity of the Bond and “n” is the number of maturity periods of the Bond.