I can't figure out which formulas I need to use for these problems but I have the answers to it thought. And some steps that was told.

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.

[spoiler=:39omy8n8]Step 1: convert annual cashflow of $120,000 to one single payment at year 5

Step 2: convert single payment year 5 to year 0

Step 3: Find PV for 1.125 million at Year 5 (Ans: $205875)

Step 4: Add all PV from Step 1 to Step 3 (Ans: 1290301)[/spoiler:39omy8n8]

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.

[spoiler=:39omy8n8]18 payments

i = 12% /2 = 6%

FV[sub:39omy8n8]IFA[/sub:39omy8n8]= 33.76 - 1

Year 19 = FV[sub:39omy8n8]a[/sub:39omy8n8] = 80000 x FU[sub:39omy8n8]IFA[/sub:39omy8n8]

PV = FU x PV[sub:39omy8n8]IF[/sub:39omy8n8] = 12% = (Ans: $946.11)[/spoiler:39omy8n8]

Required: Find the present value of each of the three offers and then indicate which one has the highest present value.

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