Question

Valyrian Pharma Inc. has expended a considerable amount of resources in recent years in developing an innovative and thriving​ R&D division that has consistently turned out a range of successful pharmaceutical products. As an analyst working for Macquarie Equities you have been tasked with valuing the growth potential of Valyrian Pharma. Research that you have undertaken leads you to estimate​ that, on​ average, the​ R&D division launches two projects every three years.​ Accordingly, 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 outlay of $ 10.4 million and yield cash flows of $ 1.09 million per year that can grow at one of three possible growth rates in​ perpetuity: 2.7 %​, 0.0 %​, and negative 2.7 %. All three growth rates in the cash flows are equally likely for any given project. These investment projects are always​ "take it or leave​ it" opportunities: If they are not undertaken​ immediately, they disappear forever. Given that the cost of capital will always remain at 11.8 % per​ year, what is the present value of all future growth opportunities Valyrian Pharma will​ produce? ​(​Hint: Make sure to round all intermediate calculations to at least four decimal places.​)​ What is the present value of all future growth​ opportunities?

Answer 1

Step 1: Calculate NPV at Different Growth Rates

The NPV at different growth rates is determined as follows:

NPV = -Initial Investment + Cash Flow/(Cost of Capital - Growth Rate

NPV at 2.7% Growth Rate = -10.4 + 1.09/(11.8% - 2.7%) = $1.5780 million

NPV at 0% Growth Rate = -10.4 + 1.09/(11.8% - 0%) = -$1.1627 million

NPV at -2.7% Growth Rate = -10.4 + 1.09/(11.8% - (-2.7%)) = -$2.8828 million

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Step 2: Calculate Expected Value of Any Opportunity

Since, the NPV is positive only with 2.7% growth rate, the company will select the projects with positive growth rates. The expected value of any opportunity is calculated as below:

Expected Value of Any Opportunity = NPV at 2.7% Growth Rate*1/3 = 1.5780*1/3 = $0.5260 million

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Step 3: Calculate Expected Value of Growth Opportunity

The expected value of growth opportunity is calculated as follows:

Expected Value of Growth Opportunity = Expected Value of Any Opportunity*Probability of a Project Arriving in any Year = 0.5260*2/3 = $0.3507 million

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Step 4: Calculate Present Value of All Future Growth Opportunities

The present value of all future growth opportunities is arrived as below:

Present Value of All Future Growth Opportunities = Expected Value of Growth Opportunity/Cost of Capital = 0.3507/11.8% = $2.972 million (answer)