Net Present Value and Capacity Planning

CAPACITY PLANNING

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