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 $0.57m now and $197k 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 $1.9m 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 1

Offer 1
Year	Amount	PVF @ 10 %	Present Value
0	570000	1	570000
1		0.9091	0
2		0.8264	0
3		0.7513	0
4		0.683	0
5		0.6209	0
6	197000	0.5645	111206.5
7	197000	0.5132	101100.4
8	197000	0.4655	91703.5
9	197000	0.4241	83547.7
10	197000	0.3855	75943.5
11	197000	0.3505	69048.5
12	197000	0.3186	62764.2
13	197000	0.2897	57070.9
14	197000	0.2633	51870.1
15	2297000	0.2394	549901.8
Total Present Value	1824157.1
Offer 2
Year	Sales	Gross Profit	Amount Received	PVF @10 %	Present Value
	(40% increase from last year)	Sales * 40%	Gross Profit * 30%
0
1	1900000	1140000	342000	0.9091	310912.2
2	2660000	1596000	478800	0.8264	395680.32
3	3724000	2234400	670320	0.7513	503611.416
4	5213600	3128160	938448	0.683	640959.984
	Total present Value	1851163.92
Offer 3
Interest Rate	0.1
Year	Amount	Future Value	Present Value
0
1	206000	449672.1652	2276079.322
2	206000	428259.205
3	206000	407865.9095
4	206000	388443.7233
5	206000	369946.4032
6	206000	352329.9078
7	206000	335552.2931
8	206000	319573.6125
9	206000	304355.8214
10	206000	289862.6871
11	206000	276059.702
12	206000	262914.0019
13	206000	250394.2875
14	206000	238470.75
15	206000	227115
16	206000	216300
17	206000	5117115.469

Percentage Difference between most and least proftable alternatives

2276079 - 1824157 / 1824157 = 24.774 %

Note

Offer 3 - Formula used in excel to calculate Future value and Present value is shown in the image attached below

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