Question

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 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 10%. 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

Solution :

Here, we need that,

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

Face value = 1000

Yield to maturity (i) = 10%

Coupon rate = 7%

Coupon amount = 1000 * 7% = 70

Years to maturity (n) = 15

Now,

Sale price = Coupon amount * [ 1 - ( 1 / (1+i)^n ) / i ] + Face value / ( 1 + i )^n

= 70 * [ 1 - ( 1 / (1+10%)^15 ) / 10% ] + 1000 / ( 1 + 10% )^15

= 771.82

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) = 11%

Coupon rate = 7%

Coupon amount = 1000 * 7% = 70

Yield to held (n) = 5

Now,

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

= 70 * [ 1 - ( 1 / (1+11%)^5 / 11% ] + 771.82 / ( 1 + 11% )^5

= 716.75

Therefore, We will be willing to pay $ 716.75 for bond X today.