Question

The Beta Co. bonds have a maturity of 13 years, a face value of $1,000, a coupon rate of 6.5 percent, and pay interest annually. What is the percentage change in the price of these bonds if the market yield rises to 6.9 percent from its current level of 6.5 percent?

Answer 1

Price of the Bond at Current Yield to Maturity of 6.50%

Face Value of the bond = $1,700

Annual Coupon Amount = $65 [$1,000 x 6.50%]

Yield to Maturity = 6.50%

Maturity Period = 13 Years

Price of the Bond = Present Value of the Coupon Payments + Present Value of the face Value

= $65[PVIFA 6.50%, 13 Years] + $1,000[PVIF 6.50%, 13 Years]

= [$65 x 8.59974] + [$1,000 x 0.44102]

= $558.98 + $441.02

= $1,000.00

Price of the Bond if the Yield to Maturity rise to 6.90%

Face Value of the bond = $1,700

Annual Coupon Amount = $65 [$1,000 x 6.50%]

Yield to Maturity = 6.90%

Maturity Period = 13 Years

Price of the Bond = Present Value of the Coupon Payments + Present Value of the face Value

= $65[PVIFA 6.90%, 13 Years] + $1,000[PVIF 6.90%, 13 Years]

= [$65 x 8.40523] + [$1,000 x 0.42004]

= $546.34 + $420.04

= $966.38

Change in the bond’s price in dollars = -33.62 [$996.38 - $1,000.00]

Therefore, The Percentage Change in the bond’s price

= [Change in the bond’s price in dollars / Bond Price at 6.50% YTM]

= -$33.62 / $1,000] x 100

= -3.36% (Negative)

“The Percentage Change in the bond’s price = -3.36% (Negative)”

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.