Here is my question I need to answer. Jim Busby calls his broker to inquire abou

Question

Here is my question I need to answer.
Jim Busby calls his broker to inquire about purchasing a bondof Disk Storage Systems. His broker quotes a price of$1,180. Jim is concerned that the bond might be overpricedbased on the facts involved. The $1,000 par value bond pays14 percent interest, and it has 25 years remaining untilmaturity. The current yield to maturity on similar bonds is12 percent. Compute the new price of the bond and comment onwhether you think it is overpriced in the marketplace. Here is my question I need to answer.
Jim Busby calls his broker to inquire about purchasing a bondof Disk Storage Systems. His broker quotes a price of$1,180. Jim is concerned that the bond might be overpricedbased on the facts involved. The $1,000 par value bond pays14 percent interest, and it has 25 years remaining untilmaturity. The current yield to maturity on similar bonds is12 percent. Compute the new price of the bond and comment onwhether you think it is overpriced in the marketplace.

Explanation / Answer

We have N=25yrs, M=Maturity value of bond = 1000, Couponrate = 14%. So INT = 14%xM = 14%*1000 = 140, & Current yieldrate Kd=12%
Value of Bond Vb = INT(PVIFA Kd,N) + M(PVIF Kd,N) Putting values we get Vb=140(PVIFA 12%,25) + 1000(PVIF 12%,25) ie Vb = 140*[1/Kd - 1/{Kd(1+Kd)^N}] +1000*(1/(1+Kd)^N ie Vb = 140*[1/12% - 1/{12%*(1+12%)^25}] +1000*(1/(1+12%)^25) ie Vb = 140*(1/12% - 0.49) + 1000*0.06 ie Vb = 140*7.84 + 60 ie Vb= 1098.04+ 60 = 1158.04 So value of Bond is 1158.04
SO the Broker is selling the Bond way over the ActualValue of Bond by $21.96

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