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 $191k 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 $202k 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.

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 I:

Present value of $ 191000 receivable from year 6 to 15

Year	Amount	Disc @ 10%	Discounting factor	Discounted Cash flows
6	$191,000	( 1/1.10)^6	0.5645	$107,814.52
7	$191,000	( 1/1.10)^7	0.5132	$98,013.20
8	$191,000	( 1/1.10)^8	0.4665	$89,102.91
9	$191,000	( 1/1.10)^9	0.4241	$81,002.65
10	$191,000	( 1/1.10)^10	0.3855	$73,638.77
11	$191,000	( 1/1.10)^11	0.3505	$66,944.33
12	$191,000	( 1/1.10)^12	0.3186	$60,858.49
13	$191,000	( 1/1.10)^13	0.2897	$55,325.90
14	$191,000	( 1/1.10)^14	0.2633	$50,296.27
15	$191,000	( 1/1.10)^15	0.2394	$45,723.88
		Total		$728,720.91

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 $ 0.57 M now	$570,000
PV of $ 191000 from year 6 to 15	$728,720.91
PV of $ 30,00000	$502,723.32
Total amount	$1,801,444

Hence the Present value of the Future cash inflows is $ 1801444

Offer 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	$202,000	(1.05)^15	2.0789	$419,943.49
2	$202,000	( 1.05)^14	1.9799	$399,946.18
3	$202,000	( 1.05)^13	1.8856	$380,901.13
4	$202,000	( 1.05)^12	1.7959	$362,762.98
5	$202,000	( 1.05)^11	1.7103	$345,488.55
6	$202,000	( 1.05)^10	1.6289	$329,036.71
7	$202,000	( 1.05)^9	1.5513	$313,368.30
8	$202,000	( 1.05)^8	1.4775	$298,446.00
9	$202,000	( 1.05)^7	1.4071	$284,234.29
10	$202,000	( 1.05)^6	1.3401	$270,699.32
11	$202,000	( 1.05)^5	1.2763	$257,808.88
12	$202,000	( 1.05)^4	1.2155	$245,532.26
13	$202,000	( 1.05)^3	1.1576	$233,840.25
14	$202,000	( 1.05)^2	1.1025	$222,705.00
15	$202,000	( 1.05)^1	1.0500	$212,100.00
16	$202,000	( 1.05)^0	1.0000	$202,000.00
		Total		$4,778,813.34

It is assumed that funds are reinvested after every cash flow

It is also assumed that semi Annual payments occur at the end of 6 months

Present value of $ 47,78813.34 is $ 4778813.34/( 1.10)^8

= $ 47,78813.34/( 1.10)^8

= $ 22,29351.69

Hence the Present value of the amount under option III is $ 2229351.69

Particulars	Amount	Status
Option 1 Present value	$1,801,444	Least Profitable Alternative
Option II Present value	$1,948,637.39
Option III Present value	$2,229,351.69	Most profitablr Alternative

% Difference between Most profitable Alternative and least profitable alternative is ( $ 2229351.69-$ 1801444)/$ 1801444

= $ 427907.69/$ 1801444*100

= 23.7536%

Hence there is 23.75 % diffeerence between most Profitable and least profitable alternative.

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