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 $0.55m now and $194k 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 $2.1m and then expected to grow by 40% per year.

Offer (III) – A trust fund would be set up, calling for semiannual payments of $204k 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 I:

Present value of $ 194000 receivable from year 6 to 15

Year	Amount	Disc @ 10%	Discounting factor	Discounted Cash flows
6	$194,000	( 1/1.10)^6	0.5645	$109,507.94
7	$194,000	( 1/1.10)^7	0.5132	$99,552.67
8	$194,000	( 1/1.10)^8	0.4665	$90,502.43
9	$194,000	( 1/1.10)^9	0.4241	$82,274.94
10	$194,000	( 1/1.10)^10	0.3855	$74,795.40
11	$194,000	( 1/1.10)^11	0.3505	$67,995.82
12	$194,000	( 1/1.10)^12	0.3186	$61,814.38
13	$194,000	( 1/1.10)^13	0.2897	$56,194.89
14	$194,000	( 1/1.10)^14	0.2633	$51,086.26
15	$194,000	( 1/1.10)^15	0.2394	$46,442.06
		Total		$740,166.79

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 $ 194000 from year 6 to 15	$740,166.79
PV of $ 30,00000	$502,723.32
Total amount	$1,812,890

Hence the Present value of the Future cash inflows is $ 18,12890 under optionI.

Option II:

Year	Sales	Gross profit ( sales * 60%)	Amount ( 30% GP)
1	$2,100,000	$1,260,000.00	$ 1260000*0.30= $ 378000
2	$ 2100000*1.40= $ 2940000	$1,764,000.00	$ 1764000*0.30=$ 529200
3	$ 2940000*1.40=$ 4116000	$2,469,600.00	$ 2469600*0.30=$ 740880
4	$ 4116000*1.40=$ 57,62400	$3,457,440.00	$ 3457440*0.30=$ 10,37232
		Total	$2,685,312

Computation of the Present value of the Future cash inflows

Year	Cash inflow	Disc @ 10%	Discounted Cash flows
1	$378,000.00	0.9091	$343,636.36
2	$529,200.00	0.8264	$437,355.37
3	$740,880.00	0.7513	$556,634.11
4	$1,037,232.00	0.6830	$708,443.41
		Total	$2,046,069.26

Hence the Present value of the Future amount is $ 20,46069.26 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	$204000	(1.05)^15	2.0789	$424101.35
2	$204000	( 1.05)^14	1.9799	$403906.05
3	$204000	( 1.05)^13	1.8856	$384672.43
4	$204000	( 1.05)^12	1.7959	$366354.69
5	$204000	( 1.05)^11	1.7103	$348909.23
6	$204000	( 1.05)^10	1.6289	$332294.5
7	$204000	( 1.05)^9	1.5513	$316470.96
8	$204000	( 1.05)^8	1.4775	$301400.91
9	$204000	( 1.05)^7	1.4071	$287048.49
10	$204000	( 1.05)^6	1.3401	$ 273379.51
11	$204000	( 1.05)^5	1.2763	$ 260361.44
12	$204000	( 1.05)^4	1.2155	$247963.28
13	$204000	( 1.05)^3	1.1576	$236155.50
14	$204000	( 1.05)^2	1.1025	$ 224910
15	$204000	( 1.05)^1	1.0500	$214200
16	$204000	( 1.05)^0	1.0000	$204000
		Total		$4826128.32

It is assumed that funds are reinvested after every cash flow

It is assumed that semi Annual payments occur at the end of each year.

Present value of $ 4826128.32is $ 4826128.32/( 1.10)^8

=$ 4826128.32/( 1.10)^8

= $ 2251424.479

Present value under option III is $ 2251424.79

Particulars	Amount	Status
Option 1 Present value	$1,812,890	Least Profitable Alternative
Option II Present value	$2,046,069.26
Option III Present value	$2251424.79	Most profitable Alternative

% Difference between Most profitable Alternative and least profitable alternative is ( $ 2251424.79-$ 1812890)/$ 1812890

= $ 438534.79/$ 1812890*100

= 24.1898%

Hence there is 24.1898% diffeerence between most Profitable and least profitable alternative.