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 $0.54m now and $193k 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:

Present value of $ 193000 receivable from year 6 to 15

Year	Amount	Disc @ 10%	Discounting factor	Discounted Cash flows
6	$193,000	( 1/1.10)^6	0.5645	$108,943.47
7	$193,000	( 1/1.10)^7	0.5132	$99,039.52
8	$193,000	( 1/1.10)^8	0.4665	$90,035.92
9	$193,000	( 1/1.10)^9	0.4241	$81,850.84
10	$193,000	( 1/1.10)^10	0.3855	$74,409.85
11	$193,000	( 1/1.10)^11	0.3505	$67,645.32
12	$193,000	( 1/1.10)^12	0.3186	$61,495.75
13	$193,000	( 1/1.10)^13	0.2897	$55,905.23
14	$193,000	( 1/1.10)^14	0.2633	$50,822.93
15	$193,000	( 1/1.10)^15	0.2394	$46,202.67
		Total		$736,351.50

Present value of receiving Additional $ 30,00000 if we achieve the Targeted sales = ($ 3 M * 0.70 + $ 0*0.30)/( 1.10)^15

= $ 2100000/( 1.10)^15

= $ 2100000/4.177248

= $ 502723.32

Note: If we will not achieve the Targeted sales we get nothing..

Calculating the present value of amount to be received.

Particulars	Amount
Receive $ 0.54 M now	$540,000
PV of $ 193000 from year 6 to 15	$736,351.50
PV of $ 30,00000	$502,723.32
Total amount	$1,779,075

Hence the Present value of the Future cash inflows is $ 17,79075 under Option I

Option II:

Year	Sales	Gross profit ( sales * 60%)	Amount ( 30% GP)
1	$2,000,000	$1,200,000.00	$ 1200000*0.30=$ 360000
2	$ 20,00000*1.4=$ 2800000	$1,680,000.00	$ 1680000*0.30=$ 504000
3	$ 2800000*1.4=$ 3920000	$2,352,000.00	$ 2352000*0.3=$ 705600
4	$ 3920000*1.4=$ 5488000	$3,292,800.00	$ 3292800*0.3=$ 987840
	Total	$8,524,800.00	$2,557,440

Computation of the Present value of the Future cash inflows

Year	Cash inflow	Disc @ 10%	Discounted Cash flows
1	$360,000.00	0.9091	$327,272.73
2	$504,000.00	0.8264	$416,528.93
3	$705,600.00	0.7513	$530,127.72
4	$987,840.00	0.6830	$674,708.01
		Total	$1,948,637.39

Hence the Present value of the Future amount is $ 19,48637.39 Under Option II

Option III:

Annual Interest rate = 10%

Interest rate for 6 months = 10% /2 = 5%

S.No	Amount	Future value factor @ 5%	Future Value factor	Future Cash flows
1	$206,000	(1.05)^15	2.0789	$428,259.20
2	$206,000	( 1.05)^14	1.9799	$407,865.91
3	$206,000	( 1.05)^13	1.8856	$388,443.72
4	$206,000	( 1.05)^12	1.7959	$369,946.40
5	$206,000	( 1.05)^11	1.7103	$352,329.91
6	$206,000	( 1.05)^10	1.6289	$335,552.29
7	$206,000	( 1.05)^9	1.5513	$319,573.61
8	$206,000	( 1.05)^8	1.4775	$304,355.82
9	$206,000	( 1.05)^7	1.4071	$289,862.69
10	$206,000	( 1.05)^6	1.3401	$276,059.70
11	$206,000	( 1.05)^5	1.2763	$262,914.00
12	$206,000	( 1.05)^4	1.2155	$250,394.29
13	$206,000	( 1.05)^3	1.1576	$238,470.75
14	$206,000	( 1.05)^2	1.1025	$227,115.00
15	$206,000	( 1.05)^1	1.0500	$216,300.00
16	$206,000	( 1.05)^0	1.0000	$206,000.00
		Total		$4,873,443.30

It is assumed that funds are reinvested after every cash flow

It is also assumed that semi Annual payments occur at the end of Six months

Present value of $ 48,73443.3 is $ 4873443.30/( 1.10)^8

= $ 48,73443.30/( 1.10)^8

= $ 2273497.27

Present Value under Option III is $ 22,73497.27

Particulars	Amount	Status
Option 1 Present value	$1,779,075	Least Profitable Alternative
Option II Present value	$1,948,637.39
Option III Present value	$2,273,497.27	Most profitablr Alternative

% Difference between Most profitable Alternative and least profitable alternative is ( $ 2273497.27-$ 1779075)/$ 1779075

= $ 494422.44/$ 1779075*100

= 27.7909

Hence there is 27.80 % diffeerence between most Profitable and least profitable alternative.

Option III is preferable.