Question

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 division launches two projects every three​ years, so you estimate that there is a 60 % chance that a project will be produced every year.​ Typically, the investment opportunities the​ R&D division produces require an initial investment of $ 9.9 million and yield profits of $ 1.09 million per year that grow at one of three possible growth rates in​ perpetuity: 2.6 %​, 0.0 %​, and negative 2.6 %. 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 11.8 % per year. What is the present value of all future growth opportunities Big Industries will​ produce? ​(​Hint: Make sure to round all intermediate calculations to at least four decimal places.​)

Answer 1

Initial investment - $9.9 Million

Profit per year - $1.09 Million

Perpetuity growth rate

Scenario 1 = 2.6%

Scenario 2 = 0%

Scenario 3 = -2.6%

Cost of capital = 11.8%

Present Value of a growing perpetuity = Profit at period 1 / (Cost of capital - growth rate)

Thus, Present Value of a growing perpetuity (scenario 1) = $1.09 Million / (11.8%-2.6%) = $11.8478 Million

Present Value of a growing perpetuity (scenario 2) = $1.09 Million / (11.8%-0%) = $9.2373 Million

Present Value of a growing perpetuity (scenario 3) = $1.09 Million / (11.8%-(-2.6%)) = $7.5694 Million

All three growth rates are equally likely for any given project. Thus, each of the growth scenario has a probability of 33.3%. Thus, present value of all future growth opportunities will be the weighted average of present value of each of the growth scenarios with the probability.

Present value of all future growth opportunities = ($11.8478*33.3%)+($9.2373*33.3%)+($7.5694*33.3%) = $3.9453+$3.0760+$2.5206 = $9.5420 Million

Additional recommendation

Initial investment is $9.9 Million which is higher than the present value of all future growth of $9.5420 Million. Hence, at this probability of growth rates, this project shouldn't be implemented.