Question

b) You are an analyst working for Goldman Sachs, and you are trying to value the growth potential of a large established company Big Industries. Big Industries has a thriving R&D division that has consistently turned out successful products. You estimate that, on average, the R&D division generates two new product proposals every three years, so that there is a 66% chance that a project will be proposed every year. Typically, the investment opportunities the R&D division produces require an initial investment of £10 million and yield profits of £1 million per year that grow at one of three possible growth rates in perpetuity: 3%, 0%, and −3%. All three growth rates are equally likely for any given project. These opportunities are always “take it or leave it” opportunities: If they are not undertaken immediately, they disappear forever. Assume that the cost of capital will always remain at 12% per year. What is the present value of all future growth opportunities Big Industries will produce?

[15 marks]

Answer 1

Using the discounting model we can calculate the PV of yields in perpetuity

as

Below is the PV of all 3 scenarios 3%, 0% and -3% respectively

Growth rate Possibility	Initial Investment	Yield in 1 year	Discounting in Perpetuity
33%	$     1,000,000.00	$     1,030,000.00	$   11,444,444.44
33%	$     1,000,000.00	$     1,000,000.00	$     8,333,333.33
33%	$     1,000,000.00	$         970,000.00	$     6,466,666.67

Since all have equal possibility we can calculate the expected value as

33% * 11,444,444.44 + 33% * 8,333,333.33 + 33% * 6,466,666.67 = $8,660,666.67

The chance of a project proposal is 66% so the PV of future growth opportunities is 0.66 * 8,660,666.67 = $5,716,040