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 $197k 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 $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 1:

If in year 15, there is a 70% probability to receive an additional $3 million. Thus, value to be included in the calculation = 70%*3 million = 2.1 million

Hence, cash flow for year 15 = 2100000 + 197000 = 2,297,000

The present value is calculated as:

Offer 2:

Sales in year 1 = $2 million

Sales in year 2 = Sales in year 1*(1 + 40%)

= $2 million*(1 + 40%) = 2.8 million

Similarly, Sales for year 3 =  Sales in year 2*(1+ 40%) = 2.8 million *(1+40%) = 3.92 million

Gross Profit Margin = 60%

Gross Profit = Gross Profit Margin*Sales

Gross profit for year 1 = 60%*Sales for year 1 = 60%*$2 million = $1.2 million

Amount received for year 1 = 30%*Gross profit for year 1 = 30%*1.2 million = $0.36 million

The calculations for the rest of the year are shown as below:

Offer 3:

In this offer, the payments are made on semi-annual basis, hence, the rate used is 5% for compounding calculations.

While calculating the present values, the annual compounding is used. Hence, the interest rate of 10% is used while the number of periods is 8.5 years.

The above table is calculated as follows:

Least profitable option is Offer 1 = $1,754,335.97

Most profitable option is Offer 3 = $2,253,981.46

Percentage difference with the least profitable offer as the base = (2,253,981.46 - 1,754,335.97)/1,754,335.97 = 0.2848 = 28.48%