Question

Bond valuation

Bond X is noncallable and has 20 years to maturity, a 8% annual coupon, and a $1,000 par value. Your required return on Bond X is 8%; and 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 8%. 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.) 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 = $80 [$1,000 x 8.00%]

Annual Yield to Maturity = 8.00%

Maturity Period = 15 Years

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

= $80[PVIFA 8.00%, 15 Years] + $1,000[PVIF 8.00%, 15 Years]

= [$80 x 8.55948] + [$1,000 x 0.31524]

= $684.76 + $315.24

= $1,000.00

Step-2, Calculate the Price of the Bond with 5 years to Maturity with a Face Value of $1,000.00

Face Value = $1,000.00

Annual Coupon Amount = $80 [$1,000 x 8.00%]

Annual Yield to Maturity = 8.00%

Maturity Period = 5 Years

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

= $80[PVIFA 8.00%, 5 Years] + $1,000[PVIF 8.00%, 5 Years]

= [$80 x 3.99271] + [$1,000 x 0.68058]

= $319.42 + $680.58

= $1,000.00

“Hence, the amount you be willing to pay for Bond X today will be $1,000.00”

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.