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 $199k 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 $209k 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

Option i)

Year (i)	Cashflow (ii)	Present value factor (iii)	Discounted cashflow (iv)=(ii)*(iii)
0	540,000	1.00	$540,000.00
6	199,000	1/(1.1^6) = 0.56	$112,330.31
7	199,000	1/(1.1^7) = 0.51	$102,118.47
8	199,000	1/(1.1^8) = 0.47	$92,834.97
9	199,000	1/(1.1^9) = 0.42	$84,395.43
10	199,000	1/(1.1^10) = 0.39	$76,723.11
11	199,000	1/(1.1^11) = 0.35	$69,748.29
12	199,000	1/(1.1^12) = 0.32	$63,407.53
13	199,000	1/(1.1^13) = 0.29	$57,643.21
14	199,000	1/(1.1^14) = 0.26	$52,402.92
15	199,000	1/(1.1^15) = 0.24	$47,639.02
15	3,000,000*70% = 2,100,000	1/(1.1^15) = 0.24	$502,723.30
			$1,801,966.56

Option ii)

Year (i)	Sales (ii)	Gross profit (iii)=(ii)*60%	Share of gross profit (iv)=(iii)*30%	Present value factor @10% (v)	Discounted cashflow (vi)=(iv)*(v)
1	$2,000,000	$1,200,000	$360,000	0.91	$327,272.73
2	2,000,000*140% = $2,800,000	$1,680,000	$504,000	0.83	$416,528.93
3	2,800,000*140% = $3,920,000	$2,352,000	$705,600	0.75	$530,127.72
4	3,920,000*140% = $5,488,000	$3,292,800	$987,840	0.68	$674,708.01
					$1,948,637.39

Option iii)

Compounded proceed = $209,000*16periods = $3,344,000

Discounted cashflow = $3,344,000/(1.1^8) = $3,344,000/2.14358881 = $1,560,000

Most profitable alternative = option ii = $1,948,637.39

Least profitable alternative = option iii = $1,560,000

Percentage difference between most & least profitable alternative = ($1,948,637.39-$1,560,000)*100/$1,560,000

= $388,637.39*100/$1,560,000

= $38,863,739/$1,560,000

= 24.91%