Question

Bond X is noncallable and has 20 years to maturity, a 10% annual coupon, and a $1,000 par value. Your required return on Bond X is 11%; if you buy it, you plan to hold it for 5 years. You (and the market) have expectations that in 5 years, the yield to maturity on a 15-year bond with similar risk will be 9.5%. How much should you be willing to pay for Bond X today? (Hint: You will need to know how much the bond will be worth at the end of 5 years.) Do not round intermediate calculations. Round your answer to the nearest cent.

Answer 1

Step-1, Calculate the Price of the Bond with 15 years to Maturity

Face Value = $1,000

Annual Coupon Amount = $100 [$1,000 x 10%]

Annual Yield to Maturity = 9.50%

Maturity Period = 15 Years

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

= $100[PVIFA 9.50%, 15 Years] + $1,000[PVIF 9.50%, 15 Years]

= [$100 x 7.82818] + [$1,000 x 0.25632]

= $782.82 + $286.32

= $1,039.14

Step-2, Calculate the Price of the Bond with 5 years to Maturity with a Face Value of $1,124.56

Face Value = $1,039.14

Annual Coupon Amount = $100 [$1,000 x 10%]

Annual Yield to Maturity = 11%

Maturity Period = 5 Years

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

= $100[PVIFA 11%, 5 Years] + $1,039.14[PVIF 11%, 5 Years]

= [$100 x 3.69590] + [$1,039.14 x 0.59345]

= $369.59 + $616.68

= $986.27

“Therefore, the amount you be willing to pay for Bond X today will be $986.27”

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.