Question

Consider the following investment offers regarding a product you have recently developed. A 10% interest rate should be used throughout this analysis unless otherwise specified:

Offer (I) – Receive $0.58m now and $192k from year 6 through 15. Also, if your product achieved over $100 million in cumulative sales by the end of year 15, you would receive an additional $3m. Assume that there is a 70% probability this would happen.

Offer (II) – Receive 30% of the buyer’s gross profit on the product for the next 4 years. Assume that the buyer’s gross profit margin is 60%. Sales in year 1 are projected to be $2m and then expected to grow by 40% per year.

Offer (III) – A trust fund would be set up, calling for semiannual payments of $206k for 8 years. On the 17th period, you would receive the compounded proceeds, which would then be discounted over the 8-year period back to the present at the specified annual rate.

Note: The term “k” is used to represent thousands (× $1,000).

Required: Determine the percentage difference between your most and least profitable alternatives, with the least profitable option as the basis for your calculation.

Answer
% Intermediate calculations must be rounded to 3 decimal places (at least). Input your answer as a percent rounded to 2 decimal places (for example: 28.31%).

Answer 1

Offer I
Years	Amount	Disc factor	Present Value
0	$       5,80,000	1	$    5,80,000.00
1	$                   -	0.909090909	$                     -
2	$                   -	0.826446281	$                     -
3	$                   -	0.751314801	$                     -
4	$                   -	0.683013455	$                     -
5	$                   -	0.620921323	$                     -
6	$       1,92,000	0.56447393	$    1,08,378.99
7	$       1,92,000	0.513158118	$       98,526.36
8	$       1,92,000	0.46650738	$       89,569.42
9	$       1,92,000	0.424097618	$       81,426.74
10	$       1,92,000	0.385543289	$       74,024.31
11	$       1,92,000	0.350493899	$       67,294.83
12	$       1,92,000	0.318630818	$       61,177.12
13	$       1,92,000	0.28966438	$       55,615.56
14	$       1,92,000	0.263331254	$       50,559.60
15	$       1,92,000	0.239392049	$       45,963.27
15	$     21,00,000	0.239392049	$    5,02,723.30
	Total		$ 12,35,259.51
Offer II
Years	Sales	Gross Profit Margin	Gross Profit Received	Disc factor	Present Value
1	20,00,000	1200000	360000	0.909090909	327272.7272
2	2800000	1680000	504000	0.826446281	416528.9256
3	3920000	2352000	705600	0.751314801	530127.7236
4	5488000	3292800	987840	0.683013455	674708.0114
	Total				1948637.388
Offer III
Years	Amount	Future Value	Disc factor	Present Value
1	$       2,06,000	449672.1652	$                     -	$                     -
2	$       2,06,000	428259.205	$                     -	$                     -
3	$       2,06,000	407865.9095	$                     -	$                     -
4	$       2,06,000	388443.7233	$                     -	$                     -
5	$       2,06,000	369946.4032	$                     -	$                     -
6	$       2,06,000	352329.9078	$                     -	$                     -
7	$       2,06,000	335552.2931	$                     -	$                     -
8	$       2,06,000	319573.6125	$                     -	$                     -
9	$       2,06,000	304355.8214	$                     -	$                     -
10	$       2,06,000	289862.6871	$                     -	$                     -
11	$       2,06,000	276059.702	$                     -	$                     -
12	$       2,06,000	262914.0019	$                     -	$                     -
13	$       2,06,000	250394.2875	$                     -	$                     -
14	$       2,06,000	238470.75	$                     -	$                     -
15	$       2,06,000	227115	$                     -	$                     -
16	$       2,06,000	216300	$                     -	$                     -
17		5117115.469	0.46650738	2387172.131
Determination of Percentages
The most profitable alternative is the 3rd one and the least profitable alternative is the first one.
Diff in Percentage =	($2387172.31 - $12,35,259.51)/$12,35,259.51*100
Diff in Percentage =	93.25%