# Net Present Value and Capacity Planning

**Topics:**Net present value, Real options analysis, Corporate finance

**Pages:**8 (1263 words)

**Published:**October 19, 2012

Real Options Analysis Practice Questions and Solutions

CAPACITY PLANNING

Question 1: PROJECT SABLE Use a 30% per year discount rate to evaluate Project Sable, which has two phases. You may invest in the first, in both or in neither. You may not invest in the second phase without investing in the first. Phase 1 requires an investment of $100. One year later the project delivers on the average $120. At that time, after the phase 1 payout has been received, you may invest an additional $100 for phase 2. One year later, phase 2 pays out on the average $140. However, phase 2`s payout can go up or down by 20%. a. How much would Project Sable be worth if it offered only the phase 1 opportunity? b. How much would Project Sable be worth if you had to choose today, once and for all, whether or not to invest also in Phase 2? c. How much is Project Sable worth if you have access to both phases and can wait to decide whether or not to invest in phase 2?

CAPACITY PLANNING

Phase-1 Year 0 Investment Revenue Use a 30% per year discount rate. a. How much would Project Sable be worth if it offered only the phase 1 opportunity? 100 120 Year 1 100 140 Phase-2 Year 2 Year 3

NPV (Phase 1) = -100 + 120 / (1+0.3) = -7.6

CAPACITY PLANNING

Phase-1 Year 0 Investment Revenue Use a 30% per year discount rate. b. How much would Project Sable be worth if you had to choose today, once and for all, whether or not to invest also in Phase 2? 100 120 Year 1 100 140 Phase-2 Year 2 Year 3

NPV (Phase 1) = -100 + 120 / (1+0.3) = -7.6 NPV (Phase 2) = -100/(1+0.3)2 + 140 / (1+0.3)3 = 4.55 Total NPV = -7.6 + 4.55 = -3.04

CAPACITY PLANNING

Phase-1 Year 0 Investment Revenue 100 120 Year 1 100 140 Phase-2 Year 2 Year 3

Use a 30% per year discount rate. Volatility is 20%. c. How much is Project Sable worth if you have access to both phases and can wait to decide whether or not to invest in phase 2? S = PV(Revenue) X = PV(Investment) A=S/X B = SQRT(T) * sigma Options Value of 2nd Phase = 140/(1+0.3)3 = 63.72 = 100/(1+0.3)2 = 59.17 =1.07 =sqrt(2)*.20 = 0.28 14.6% of S =9.30

Total = -7.6 + 9.30 = 1.70

Question 2: Suppose that you are hired by a company that is evaluating the profitability of a new product. The product launch will require a significant investment: $300 million during the first year for manufacturing capacity, working capital, and marketing and distribution. Revenues are expected to be $10, $12, and $15 million in the following three years of operation, at which point the capacity will be fully utilized, and stay constant afterwards. First Stage Year Revenue Investment Net cash flow 0 -300 -300 1 10 10 2 12 12 3 15 15 4 15 15 5 15 15 6 15 15 7 15 15 8 15 15 9 15 15

CAPACITY PLANNING

There are two alternatives: Alternative-1: After three years, the company can invest $240 million and receive same incremental net cash flows. Alternative-1 Year Revenue Investment Net cash flow 0 1 2 3 -240 -240 4 10 10 5 12 12 6 15 15 7 15 15 8 15 15 9 15 15

Alternative-2: After six years, the company can invest $235 million and receive same incremental net cash flows. Alternative-2 Year Revenue Investment Net cash flow 0 1 2 3 4 5 6 -235 -235 7 10 10 8 12 12 9 15 15

Question 2: Suppose that discount rate is 5% and volatility is 20%. (a) A periodic cash flow that continues indefinitely and pays P dollars each year has a present value of P*(1+1/r) dollars if r is used as discount rate. Using this definition, calculate the revenues at year 10.

CAPACITY PLANNING

First Stage Year Revenue Investment Net cash flow Alternative-1 Year Revenue Investment Net cash flow Alternative-2 Year Revenue Investment Net cash flow -235 -235 10 12 15 0 1 2 3 4 5 6 7 10 8 12 9 15 -240 -240 10 12 15 15 15 15 0 1 2 3 4 10 5 12 6 15 7 15 8 15 9 15 -300 -300 10 12 15 15 15 15 15 15 15 0 1 10 2 12 3 15 4 15 5 15 6 15 7 15 8 15 9 15 Year 10 and later

=15*(1+1/.05) =315

=15*(1+1/.05) =315

=15*(1+1/.05) =315...

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