This one really has me confused. I did what I could though. Can youhelp me? Les

Question

This one really has me confused. I did what I could though. Can youhelp me?

Les Moore retired as president of Goodman Snack Foods Company butis currently on a consulting contract for $35,000 per year for thenext 10 years.
a. If Mr. Moore's opportunity cost (potential return) is 10%, whatis the present value of his consulting contract?
b. Assuming Mr. Moore will not retire for two more years and willnot start to receive his 10 payments until the end of the thirdyear, what would be the value of his deferred annuity?

For the a part, I took $35,000 * 6.145 and got $215,075 using thepresent value of an annuity of $1. Did I do that right?

For the b part, I am confused, but tried it anyway. I took $35,000*9.487 (assuming there are 7 time periods at 10%) and got $332,045using the future value of an annuity.

Explanation / Answer

Here N= 10year   Annuity Payment PMT = $35000 Interest =10% =INT We need to find PV of annuity = PVIFA(10%,10)                      N So PVIFA = PMT/(1+INT)^t = PMT*PVIFA(10%,10)                     t=1 ie PVIFA= PMT*[1/Int - 1/(Int*(1+Int)^N)] ie PVIFA = 35000*[1/0.10 - 1/(0.10*(1+0.10)^10)] ie PVIFA = 35000*(10 - 3.8554) ie PVIFA = 35000*6.1445 Ie PVIFA = $215,057.5 So Present value of Consulting contract is $215,057.50 Case B The PV of 10 Yrs contract will remain $215,057.50 at start of3Yr. To adjust for first 2 yrs, we just need to calculate the Presentvalue of $215,057.50 @10% So PV = FV/(1+Int)^N = 215057.50/(1+0.1)^2 = 215057.50 * 0.8264 =177723.52 So If he is to retire after 2 yrs, PV of his defered anuity is$177,723.52 The correct price of Bond is $1156.85. Hence the broker isoverpricing the Bond.

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