Question

Question 19 of 20 Check My Work (2 remaining) eBook Problem Walk-Through Bond X is noncallable and has 20 years to maturity, an 11% annual coupon, and a $1,000 par value. Your required return on Bond X is 12%; 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 10.5%. 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. Hide Feedback Incorrect

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Answer 1

BOND coupon rate    11.00%
Face value =   1000
Coupon amount = 1000*11% =   110
  
YTM at time of sale (i)=   10.50%
Years to maturity (n) on sale= 20-5=   15
  
Bond price formula = Coupon amount * (1 - (1/(1+i)^n)/i + face value/(1+i)^n  
(110*(1-(1/(1+10.5%)^15))/10.5%) + (1000/(1+10.5%)^15)  
1036.969123  
So selling price at year 5 is   1,036.97

Today we plans to sell in 5 years  
So time of Coupon received (n)=   5
Required return on Bond X (i)=   12%
  
Bond price formula = Coupon amount * (1 - (1/(1+i)^n)/i + Sale value at year 5/(1+i)^n  
(110*(1-(1/(1+12%)^5))/12%) + (1036.97/(1+12%)^5)  
984.9300088  
  
So we will be willing to pay today for Bond is   $984.93

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