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 $0.5m now and $190k 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 $207k 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 the offer = 500000+ 190000/1.10^6+190000/1.10^7+....+190000/1.10^15+3000000*0.7/1.1^15

=500000+ 1/1.1^5* 190000/0.1*(1-1/1.1^10)+2100000/1.1^15

=$1727628.92

Offer II

Amount received after one year = $2000000*60%*30% =$360000

Present value of the offer = 360000/1.1+360000*1.4/1.1^2+360000*1.4^2/1.1^3+360000*1.4^3/1.1^4

   =$1948637.39

Offer III

Present value of the offer = 207000/1.1^0.5+207000/1.1+......+207000/1.1^8

   =207000/1.1^0.5*(1-1/1.1^8)/(1-1/1.1^0.5)

=$2262560.51

The most profitable option is Option IIII and the least one is Option I

% difference = (2262560.51-1727628.92)/1727628.92 = 0.3096334 or 30.96%