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 $0.51m 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 $207k 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

Discount Rate

10%

Offer 1

Year	Amount (Thousand $)	Present Value
0	510	510.000
6	197	111.201
7	197	101.092
8	197	91.902
9	197	83.547
10	197	75.952
11	197	69.047
12	197	62.770
13	197	57.064
14	197	51.876
15	197	47.160
15	2100	502.723
Present Value of Offer 1	1764.336

Offer 2

Years (a)	Sales (b)	Gross Margin ( c = b*60%)	Amount Received (d = c*30%)(Thousand $)	Present Value (d/((1+10%)^a)
1	1900	1140	342.00	310.909
2	2660	1596	478.80	395.702
3	3724	2234.4	670.32	503.621
4	5213.6	3128.16	938.45	640.973
Present Value of Offer 2	1851.206

Offer 3

Period	Payment
1	207
2	207
3	207
4	207
5	207
6	207
7	207
8	207
9	207
10	207
11	207
12	207
13	207
14	207
15	207
16	207
	3312

Present Value of Offer 3 (1545/1.1^8)    = 1545.072

Present Value of Offer 1                 1764.336K $

Present Value of Offer 2                 1851.206K $

Present Value of Offer 3                 1545.072K $

Percentage difference between your most and least profitable alternatives

Percentage difference between Offer 2 and Offer 3 (Offer 2 PV - Offer 3 PV)/Offer 3 PV   = 19.81%

Percentage difference between Offer 1 and Offer 3 (Offer 1 PV - Offer 3 PV)/Offer 3 PV   = 14.19%

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