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 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 11%. 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

Calculation of sale price or value at end of 5th year
face value =	1000
Yield to maturity(i)=	11%
Coupon rate =	7%
Coupon Amount = 1000*9%=	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+11%)^15))/11% + 1000/(1+11%)^15
712.37
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*9%=	70
Years 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% + 712.37/(1+8%)^5
764.31
So, we will be willing to pay $764.31 for bond X today.