General Weapons, Inc. (Comprehensive time value of money) Mr. Rambo, President o
ID: 2701780 • Letter: G
Question
General Weapons, Inc. (Comprehensive time value of money) Mr. Rambo, President of General 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 10 percent to evaluate each offer.
Offer I
$1,200,000 now plus $625,000 from the end of years 6 through 15. Also if the product goes over $60 million in cumulative sales by the end of year 15, he will receive an additional $3,000,000. Rambo thought there was an 80 percent probability this would happen.
Offer II
Thirty percent of the buyer%u2019s gross margin for the next four years. The buyer in this case is Air Defense, Inc. (ADI). Its gross margin is 60 percent. Sales for year 1 are projected to be $3.5 million and then grow by 35 percent per year. This amount is paid today and is not discounted.
Offer III
A trust fund would be set up for the next four years. At the end of that period, Rambo would receive the proceeds (and discount them back to the present at
10 percent). The trust fund called for semiannual payments for the next four years of $110,000 (a total of $220,000 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 (16 + 1) and subtract 1 from the value in the table. Assume the annual interest rate on this annuity is 10 percent annually (5 percent semiannually). Determine the present value of the trust fund%u2019s final value.
Required: Find the present value of each of the three offers and then indicate which one has the highest present value.
Offer I
$1,200,000 now plus $625,000 from the end of years 6 through 15. Also if the product goes over $60 million in cumulative sales by the end of year 15, he will receive an additional $3,000,000. Rambo thought there was an 80 percent probability this would happen.
Offer II
Thirty percent of the buyer%u2019s gross margin for the next four years. The buyer in this case is Air Defense, Inc. (ADI). Its gross margin is 60 percent. Sales for year 1 are projected to be $3.5 million and then grow by 35 percent per year. This amount is paid today and is not discounted.
Offer III
A trust fund would be set up for the next four years. At the end of that period, Rambo would receive the proceeds (and discount them back to the present at
10 percent). The trust fund called for semiannual payments for the next four years of $110,000 (a total of $220,000 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 (16 + 1) and subtract 1 from the value in the table. Assume the annual interest rate on this annuity is 10 percent annually (5 percent semiannually). Determine the present value of the trust fund%u2019s final value.
Required: Find the present value of each of the three offers and then indicate which one has the highest present value.
Explanation / Answer
offer 1 :
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
offer3 :
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
offer3 has the highest pv
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