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 $0.53m now and $192k 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 $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 % 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

Option i)

Year (i)	Cashflow (ii)	Present value factor (iii)	Discounted cashflow (iv)=(ii)*(iii)
0	530,000	1.00	$530,000.00
6	192,000	1/(1.1^6) = 0.5645	$108,384.00
7	192,000	1/(1.1^7) = 0.5132	$98,534.40
8	192,000	1/(1.1^8) = 0.4665	$89,568.00
9	192,000	1/(1.1^9) = 0.4241	$81,427.20
10	192,000	1/(1.1^10) = 0.3855	$74,016.00
11	192,000	1/(1.1^11) = 0.3505	$67,296.00
12	192,000	1/(1.1^12) = 0.3186	$61,171.20
13	192,000	1/(1.1^13) = 0.2897	$55,622.40
14	192,000	1/(1.1^14) = 0.2633	$50,553.60
15	192,000	1/(1.1^15) = 0.2394	$45,964.80
15	3,000,000*70% = 2,100,000	1/(1.1^15) = 0.2394	$502,740.00
			$1,765,277.60

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	$1,900,000	$1,140,000	$342,000	0.9091	$310,909.09
2	1,900,000*140% = $2,660,000	$1,596,000	$478,800	0.8264	$395,702.48
3	2,660,000*140% = $3,724,000	$2,234,400	$670,320	0.7513	$503,621.34
4	3,724,000*140% = $5,213,600	$3,128,160	$938,448	0.6830	$640,972.61
					$1,851,205.52

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

Note: Assumed accumulated amount doesnot earn any interest. And the amount will be paid at the initial of 17th period.

Most profitable alternative = option ii = $1,851,205.52

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

Percentage difference between most & least profitable alternative = ($1,851,205.52-$1,560,000)*100/$1,560,000

= $291,205.52*100/$1,560,000

= $29,120,552/$1,560,000

= 18.67%