Question

Bond X is noncallable and has 20 years to maturity, a 11% annual coupon, and a $1,000 par value. Your required return on Bond X is 11%; 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 12%. 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.

= $

Callaghan Motors' bonds have 9 years remaining to maturity. Interest is paid annually, they have a $1,000 par value, the coupon interest rate is 8%, and the yield to maturity is 9%. What is the bond's current market price? Round your answer to the nearest cent.

=$

Answer 1

Solution to the FIRST QUESTION

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

Face Value = $1,000

Annual Coupon Amount = $110 [$1,000 x 11.00%]

Annual Yield to Maturity = 12.00%

Maturity Period = 15 Years

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

= $110[PVIFA 12.00%, 15 Years] + $1,000[PVIF 12.00%, 15 Years]

= [$110 x 6.81086] + [$1,000 x 0.18270]

= $749.20 + $182.70

= $931.89

Step-2, Calculate the Price of the Bond with 5 years to Maturity with a Face Value of $931.89.

Face Value = $931.89

Annual Coupon Amount = $110 [$1,000 x 11.00%]

Annual Yield to Maturity = 11.00%

Maturity Period = 5 Years

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

= $110[PVIFA 11.00%, 5 Years] + $931.89[PVIF 11.00%, 5 Years]

= [$110 x 3.69590] + [$931.89 x 0.59345]

= $406.55 + $553.03

= $959.58

“Hence, the amount you be willing to pay for Bond X today will be 959.58 “

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.

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