Finance Help: find present value of each of 3 offers

MBAcandidate

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I can't figure out which formulas I need to use for these problems. There seems to be too much going on for me to get it. :( Please help!

Mr. Rambo, President of Assault Weapons, Inc., was pleased to hear that he had three offers from major defense companies for his latest missile firing automatic ejector. He will use a discount rate of 12 percent to evaluate each offer.

Offer 1: $500,000 now plus $120,000 from the end of year 6 through 15. Also, if the product goes over $50 million in cumulative sales by the end of year 15, he will receive an additional $1,500,000. Rambo thought there was a 75% probability this would happen.

Offer 2: 25% of the buyer’s gross margin for the next four years. The buyer in this case is Air Defense, Inc. (ADI). Its gross margin is 65%. Sales for year 1 are projected to be $1 million and then grow by 40% per year. This amount is paid today and is not discounted.

Offer 3: A trust fund would be set up for the next 9 years. At the end of that period, Rambo would receive the proceeds (and discount them back to the present at 12%). The trust fund called for semiannual payments for the next 9 years of $80,000 (a total of $160,000 per year). The payments would start immediately. Since the payments are coming at the beginning of each period instead of the end, this is an annuity due. To look up the future value of the annuity due in the tables, add 1 to n (18 + 1) and subtract 1 from the value in the table. Assume the annual interest rate on this annuity is 12% annually. Determine the present value of the trust fund’s final value.

Required: Find the present value of each of the three offers and then indicate which one has the highest present value.
 
MBAcandidate said:
Offer 1: $500,000 now plus $120,000 from the end of year 6 through 15. Also, if the product goes over $50 million in cumulative sales by the end of year 15, he will receive an additional $1,500,000. Rambo thought there was a 75% probability this would happen.
Well, I find it easier with these to get the future value, then discount it.

500000(1.12)^15 = 2,736,783

120000(1.12^10 - 1) / .12 = 2,105,848

FV = 2,736,783 + 2,105,848 = 4,842,631

PV = 4842631 / 1.12^15 = 884,731

As far as the possible bonus goes: no comments!
 
MBAcandidate said:
Offer 3: A trust fund would be set up for the next 9 years. At the end of that period, Rambo would receive the proceeds (and discount them back to the present at 12%). The trust fund called for semiannual payments for the next 9 years of $80,000 (a total of $160,000 per year). The payments would start immediately. Since the payments are coming at the beginning of each period instead of the end, this is an annuity due. To look up the future value of the annuity due in the tables, add 1 to n (18 + 1) and subtract 1 from the value in the table. Assume the annual interest rate on this annuity is 12% annually. Determine the present value of the trust fund’s final value.
Problem setters suffer from diarrhea of the mouth...this is really as simple as:
Semiannual payments of $80,000 for the next 9 years, starting immediately, at 12% annually.
Calculate present value.

Really nothing "exotic" about "immediate"; simply add a period to the calculation, then deduct a payment.

Since rate is annual but the periods are semiannual, then the rate must be adjusted in order to be applied
semiannually: (1 + i)^2 = 1.12 ; i = .0583

FV = 80000(1.0583^19 - 1) / .0583 - 80000 = 2,574,852 : the "19" is after 1 period added to 18

PV = 2574852 / 1.0583^18 = 928,526 : beats case#1! : YES, "18" is used here

Can't follow what is meant in case#2: I'm sure Mark or Jonah will come to your rescue :wink:
 
MBAcandidate said:
Thanks, but neither of these answers is correct.
Could be; THEN tell us what is SUPPOSE to be the correct answers,
plus HOW do you know that they're correct.
 
Ask your "professor" if he agrees with this part of my solution to part#3:

"Since rate is annual but the periods are semiannual, then the rate must be adjusted in order to be applied
semiannually: (1 + i)^2 = 1.12 ; i = .0583"

If his answer is lower than mine (by about 10,000), then he is wrong; probably using .06 instead of .0583.
IF that was the intention, then rate MUST be stated as 12@ annually compounded semiannually.
If he's componding at .06, then annual rate becomes 12.36%
 
Yes, he was using 6 percent. I can't remember the answer off hand but it was 908 thousand something. Also, for the first one he said you have to take 120,000 to the power of each year.

So 120,000 to the 6th year, 7th yr., etc.

The last offer answer is $945,094.82.
 
MBAcandidate said:
Yes, he was using 6 percent. I can't remember the answer off hand but it was 908 thousand something. Also, for the first one he said you have to take 120,000 to the power of each year.
So 120,000 to the 6th year, 7th yr., etc.
Sorry, but complete Greek to me...

If .0583 is used, then PV is 928,526 (as I already told you).

IF .06 is used (12% annual compounded semiannally), then PV is 918,181.

Here's how it accumulates, ending with the FV (18 semiannual periods):
Code:
00                                      80,000
01         80,000        4,800         164,800
02         80,000        9,888         254,688
03         80,000       15,281         349,969
....
16         80,000      123,228       2,257,030
17         80,000      135,422       2,472,452
18              0      148,347       2,620,799
The PV of 2,620,799 = 2620799 / 1.06^18 = 918,181
Here's how that accumulates:
Code:
00                           918,181
01           55,091          973,272
02           58,396        1,031,668
03           61,900        1,093,568
....
16          132,028        2,332,502
17          139,950        2,472,452
18          148,347        2,620,799
If your prof is getting something else, then he's doing something "strange" :wink:
 
He could be, but I have to have what he has to get this right.

That's the answer he has for three and the best offer is number two, but I haven't figured out that answer yet. He used Excel to figure this all out.
 
Well, show him my last post, and ask him where he disagrees...
 
MBAcandidate said:
The last offer answer is $945,094.82.
Is that a joke? I didn't sleep much last night so it's not obvious if it is or not.
If it is, a fine jest indeed!
If it isn't, I'm sure I'm not the only one interested in finding out the mathematics behind this seemingly absurd answer. Or is there none?
 
MBAcandidate said:
The last offer answer is $945,094.82.
I guess the magical incantation behind this mystical declaration must really be a closely guarded secret. So much so that the MBAcandidate who posted it can’t even be bothered to share with us mere mortals his or his professor’s mathemagical Excel justification for it (as if Excel is the last resort for such a simple problem). I’m beginning to think that the Excel spreadsheet that his professor used must have been devised by the Mathemagician Merlin himself. After having a good laugh at it, methinks it could give entries at http://uncyclopedia.wikia.com/wiki/Mathematics a run for their money. A slight variation of this site can be found at http://uncyclopedia.wikia.com/wiki/Maths#True_and_falsehood_in_mathematics
 
MBAcandidate said:
… I have to have what he has to get this right.


This reminds me of what the GOP was saying about Bush during most of the past eight years.

Think for yourself.
 
did your professor give you the answers? im pretty sure the first offer is really close i think it might be 9 periods of annuity rather than 10. but if i can get the real answers i can work backwards to try and help out
 
Rockon, this guy's been "quiet" for over a month now;
I get the feeling he was using an "imaginary professor" :wink:
 
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