Question

Ch 7 #14

Bond X is noncallable and has 20 years to maturity, a 7% annual coupon, and a $1,000 par value. Your required return on Bond X is 8%; 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 5.5%. 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.

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Answer 1

Answer :

Calculation of sale price or value at the end of 5th year

Face value = 1000

Yield to maturity (i) = 5.5%

Coupon rate = 7%

Coupon amount = 1000 * 7% = 70

Years to maturity (n) = 15

Bond price formula = Coupon amount * [ 1 - ( 1 / (1 + i )^n ) / i ] + face value / ( 1 + i )^n

= 70 * [ 1 - ( 1 / ( 1 + 5.5% )^15 ) / 5.5% ] + 1000 / ( 1 + 5.5% )^15

= 1150.56

Calculation of Today's price ( price after 1 year )

Today's price or worth for us will be present value of coupons for 5 years and present value of sale value at end of 5th year

Face value = 1000

Yield to maturity (i) = 8%

Coupon rate = 7%

Coupon amount = 1000 * 7% = 70

Yield to held (n) = 5

Bond price formula = Coupon amount * [ 1 - ( 1 / ( 1 + i )^n ) / i ] + sale value / ( 1 + i )^n

= 70 * [ 1 - ( 1 / ( 1 + 8% )^5 ) / 8% ] + 1150.56 / ( 1 + 8% )^5

= 1062.54

So, we will be willing to pay $1062.54 for bond X today.