5. Bond valuation Bond X is noncallable and has 20 years to maturity, a 8% annua

Question

5. Bond valuation

Bond X is noncallable and has 20 years to maturity, a 8% 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.) Do not round intermediate calculations. Round your answer to the nearest cent.

Explanation / Answer

N= 5year Face value = FV = M= $1,000, INT=8% coupon rate = 8%*1,000=$80
Kd =Reqd rate of return = 10%
We need to find Vb= value of Bond
Vb = INT(PVIFA kd,N) + M*(PVIF kd,N).
ie Vb = INT*[1/Kd - 1/(Kd*(1+Kd)^N)] + M*1/(1+Kd)^N
ie Vb = 80*[1/10% - 1/(10%*(1+10%)^5] + 1,000/(1+10%)^5
ie Vb = 80*3.7908 + $620.92
ie Vb = $924.18.

SO I will be willing to pay $924.18 for this bond today.

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