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 10%; 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 7%. 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.

Answer 1

Calcultion of sale price      
BOND coupon rate    7.00%   or 0.07
Face value =   1000  
Coupon amount = 1000*7% =   70  
YTM on sale (i)=   7.00%   or 0.07
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      
(70*(1-(1/(1+0.07)^15))/0.07) + (1000/(1+0.07)^15)      
1000      
  

Calcultion of Purchase price

Today we plans to sell in 5 years      

So time of Coupon received (n)=   5  
Required return on Bond X (i)=   10%   or 0.10
      
Bond price formula = Coupon amount * (1 - (1/(1+i)^n)/i + Sale value at year 5/(1+i)^n      
(70*(1-(1/(1+0.1)^5))/0.1) + (1000/(1+0.1)^5)      
=886.2763969      
      
So we will be willing to pay today for Bond is   $886.28  

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