Ms. cleanair recived three offers from major automobile companies for her patent
ID: 2708600 • Letter: M
Question
Ms. cleanair recived three offers from major automobile companies for her patent on a new hybrid drive system for medium sized 4 wheel drive trucks. She will use a discount rate of 12% to evaluate each offer.
Offer 1- $500,000 now plus $120,000 for the end of year 6-15. Also if the product goes over $50,000,000. Ms Cleanair thought there was a 75% probability this wouel happen.
Offer 2- 25% of the buyers gross margin for the next four years. The buyer General Cars. (GC) Its gross margin is 65%. Forst sales for one year of the new truck are projected to be $1,000,000 and then grow by 40% per year.
Offer 3- A trust fund would be set up for the next nine years. At the end of that time period, Ms. Cleanair would receive the proceeds ( discount them back to the present at 12%). The trust fund called for semiannual payments for the next nine years of $80,000 ( a total of $160,000 per year). The payments would start immediatly. 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 from the value in the table. Assume the annual intrest rate of 12% Determine the present value of the trust's fund final value.
Required: Find the present value of each of the three offers and then indicate which one has the highest present vlaue.
(Book being used is Foundation of Financial Management 12th edition)
Explanation / Answer
For each payment that would be received in each offer, you need to discount it to the present value. Then you add all the present values of each payment for each offer. To discount each payment to the present value, you divide it by ((1+i)^n.)
i is the interest rate, which in your question would be 12%.
n is the number (which would be years if the interest rate is presented as an annual rate.)
^ means exponent
* means multiply
For example, in offer 1 the present value of the $500,000 that would be received now is the full $500,000. Then the first $120,000 payment gets received in 6 years, so 120,000/(1.12^6) = $60,795.73 which is the present value. That number can be seen as the amount that would have to be invested today to grow to $120,000 in 6 years at a 12% annual rate.
So for each payment that would be received in offer 1, you discount them to the present value and add the present value of each payment. Then you do the same for offers 2 and 3 and find which one is the largest amount.
You also need to consider things like the 75% probability in offer 1. To account for that, you multiply the amount that would be received by the probability rate (1,500,000*.75) to get a net amount. Then you discount that to the present value to include it with the other payments.
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