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 65 % chance that a project will be produced every year.​ Typically, the investment opportunities the​ R&D division produces require an initial investment of $ 9.8 million and yield profits of $ 1.04 million per year that grow at one of three possible growth rates in​ perpetuity: 3.3 %​, 0.0 %​, and negative 3.3 %. 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 11.9 % 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

Expected Present Value of Inflows = Sum of (Probability of each possibility*PV of each possibility)

PV of each possibility = Perpetuity/(Required Rate of Return-Growth Rate), Probability = 1/3

= [{1/3}*{1.04/(11.9%-3.3%)}]+[{1/3}*{1.04/(11.9%)}]+[{1/3}*{1.04/(11.9%+3.3%)}]

= 4.031 + 2.9131 + 2.2807

= $9.2248 Million

NPV = Expected PV of Inflows-Initial Investment = 9.2248-9.8 = $-0.5752 Million

Expected PV of Growth Opportunity = NPV*Probability that Project will be produced = -0.5752*65% = $-0.3739