This was difficult for me, but I hope I am on the right track. Iworked really ha

Question

This was difficult for me, but I hope I am on the right track. Iworked really hard on this. Can you help me?

Jim Barker calls his broker to inquire about purchasing a bond ofDisk Storage Systems. His broker quotes a price of $1,180. Jim isconcerned that the bond might be overpriced based on the factsinvolved. The $1,000 par value bond pays 14% interest, and it has25 years remaining until maturity. The correct yield to maturity onsimilar bonds is 12%. Compute the new price of the bond and commenton whether you think it is overpriced in the market.

I don't have a solid understanding of this but, I tried. This iswhat I have:

I took 14% of $1,180 and got $165.20 is an annuity. Then took$165.20 at 12% for 25 years. $165.20 * 7.843 and got $1,295.66.Then with the par value of $1,000, I did this, $1,000* 0.059=59.Lastly, I took the $1,295.66 + 59= $1,354.66 as the actual cost ofthe bond or is this how much it will pay out? So, I guess I wouldsay the bond is worth more than he is going to pay for it, so it isnot overpriced.
Am I on the right track?

Explanation / Answer

Here N= 25year   Face value = FV = M= $1,000 Interest =14% coupon rate*FV = 14%*$1000=$140. YTM = 12% = Kd We need to find Vb= value of Bond              N So Vb = INT/(1+kd)^t   +M/(1+Kd)^N    = INT*PVIFA(12%,25) + FV*PVIF(12%,25)             t=1 ie Vb = INT*[1/Kd - 1/(Kd*(1+Kd)^N)] + FV*(1/(1+Kd)^N) ie Vb = 140*[1/0.12 - 1/(0.12*(1+0.12)^25)] + 1000/(1+0.12)^25 ie Vb = 140*(8.3333 - 0.4902) + 1000*0.05882 ie Vb = 1098.034 + 58.82 ie Vb = 1156.85 The correct price of Bond is $1156.85. Hence the broker isoverpricing the Bond. ie Vb = INT(PVIFA kd/2,2N) + M*(PVIF kd/2,2N). ie Vb = 50*(PVIFA 4.5%,22) + 1000*(PVIF 4.5%, 22)

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