Principles of Corporate Finance Brealey and Myers Sixth Edition A Project Is Not a Black Box Slides by Matthew Will Irwin/McGraw Hill Chapter 10 ©The McGraw-Hill Companies, Inc., 200 10- Topics Covered Sensitivity Analysis Break Even Analysis Monte Carlo Simulation Decision Trees Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 10- How To Handle Uncertainty Sensitivity Analysis - Analysis of the effects of changes in sales, costs, etc on a project Scenario Analysis - Project analysis given a particular combination of assumptions Simulation Analysis - Estimation of the probabilities of different possible outcomes Break Even Analysis - Analysis of the level of sales (or other variable) at which the company breaks even Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 10- Sensitivity Analysis Example Given the expected cash flow forecasts for Otoban Company’s Motor Scooter project, listed on the next slide, determine the NPV of the project given changes in the cash flow components using a 10% cost of capital Assume that all variables remain constant, except the one you are changing Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 10- Sensitivity Analysis Example - continued Investment Sales Variable Costs Fixed Costs Depreciation Pretax profit Taxes @ 50% Profit after tax Operating cash flow Net Cash Flow Year - 15 - 15 Years - 10 37.5 30 1.5 1.5 1.5 3.0 NPV= 3.43 billion Yen Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 10- Sensitivity Analysis Example - continued Possible Outcomes Variable Range Pessimistic Expected Optimistic Market Size mil 51 mil 1.1 mil Market Share 04 16 Unit price Unit Var Cost 350,000 360,000 375,000 300,000 380,000 275,000 Fixed Cost bil bil bil Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 10- Sensitivity Analysis Example - continued NPV Calculations for Pessimistic Market Size Scenario Year Investment Years - 10 - 15 Sales 41.25 Variable Costs 33 Fixed Costs Depreciation 1.5 Pretax profit 3.75 Taxes @ 50% 1.88 Profit after tax 1.88 Operating cash flow 3.38 Net Cash Flow Irwin/McGraw Hill - 15 + 3.38 NPV= +5.7 bil yen ©The McGraw-Hill Companies, Inc., 200 10- Sensitivity Analysis Example - continued NPV Possibilities (Billions Yen) Variable Range Pessimistic Expected Optimistic Market Size 1.1 3.4 5.7 Market Share - 10.4 3.4 17.3 Unit price Unit Var Cost - 4.2 - 15.0 3.4 3.4 5.0 11.1 Fixed Cost 0.4 3.4 6.5 Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 10- Break Even Analysis Point at which the NPV=0 is the break even point Otoban Motors has a breakeven point of 8,000 units sold PV Inflows Break even 400 NPV=9 PV (Yen) Billions PV Outflows 200 19.6 85 Irwin/McGraw Hill 200 Sales, 000’s ©The McGraw-Hill Companies, Inc., 200 10- 10 Monte Carlo Simulation Modeling Process Step 1: Modeling the Project Step 2: Specifying Probabilities Step 3: Simulate the Cash Flows Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 10- 11 Decision Trees Turboprop -550 NPV= ? 960 (.8) +150(.6) 220(.2) 930(.4) +30(.4) 140(.6) -150 +100(.6) or Piston -250 NPV= ? Irwin/McGraw Hill +50(.4) 800(.8) 100(.2) 410(.8) 180(.2) 220(.4) 100(.6) ©The McGraw-Hill Companies, Inc., 200 10- 12 Decision Trees Turboprop -550 NPV= ? 960 (.8) +150(.6) 220(.2) 930(.4) +30(.4) 140(.6) -150 +100(.6) or Piston -250 NPV= ? Irwin/McGraw Hill +50(.4) 800(.8) 100(.2) 410(.8) 180(.2) 220(.4) 100(.6) 812 456 660 364 148 ©The McGraw-Hill Companies, Inc., 200 10- 13 Decision Trees Turboprop -550 NPV= ? 960 (.8) +150(.6) 220(.2) 930(.4) +30(.4) 140(.6) -150 +100(.6) or Piston -250 NPV= ? Irwin/McGraw Hill 800(.8) 100(.2) 410(.8) 180(.2) 220(.4) ( 960 × 80)+50(.4) + ( 220 × 20 ) = 812 100(.6) 812 456 660 364 148 ©The McGraw-Hill Companies, Inc., 200 10- 14 Decision Trees Turboprop -550 NPV= ? 960 (.8) 660 660 − 150 +150(.6) − 150 == 450 450 11 10 10 220(.2) 930(.4) +30(.4) 140(.6) *450 -150 +100(.6) or Piston 331 -250 NPV= ? Irwin/McGraw Hill +50(.4) 800(.8) 100(.2) 410(.8) 180(.2) 220(.4) 100(.6) 812 456 660 364 148 ©The McGraw-Hill Companies, Inc., 200 10- 15 Decision Trees NPV=888.18 Turboprop -550 NPV= ? NPV=444.55 +150(.6) Piston 930(.4) 140(.6) *450 +50(.4) NPV=184.55 -150 or 331 -250 Irwin/McGraw Hill 220(.2) +30(.4) 812 812 + 150 NPV=550.00 18 + 150 == 888 888 18 +100(.6) 11 10 10 NPV= ? 960 (.8) 800(.8) 100(.2) 410(.8) 180(.2) 220(.4) 100(.6) 812 456 660 364 148 ©The McGraw-Hill Companies, Inc., 200 10- 16 Decision Trees NPV=888.18 Turboprop -550 NPV= ? 960 (.8) +150(.6) 220(.2) 710.73 NPV=444.55 930(.4) +30(.4) 140(.6) *450 NPV=550.00 -150 +100(.6) or -250 NPV= ? Irwin/McGraw Hill 100(.2) 410(.8) 456 660 180(.2) )) ++ ((444 == ((888 18 55 331 888403.82 18×× 60 60 444 55×× 40 40)) Piston 800(.8) 812 +50(.4) NPV=184.55 220(.4) 100(.6) 364 148 ©The McGraw-Hill Companies, Inc., 200 10- 17 Decision Trees NPV=888.18 Turboprop -550 NPV=96.12 960 (.8) +150(.6) 220(.2) 710.73 NPV=444.55 930(.4) +30(.4) 140(.6) *450 NPV=550.00 Piston -250 NPV=117.00 Irwin/McGraw Hill +100(.6) or -150 800(.8) 100(.2) 410(.8) 710 73 710.73 − 550331= 96.12180(.2) 403.82− 550 = 96.12 11 10 220(.4) 10 +50(.4) NPV=184.55 100(.6) 812 456 660 364 148 ©The McGraw-Hill Companies, Inc., 200 10- 18 Decision Trees NPV=888.18 Turboprop -550 NPV=96.12 960 (.8) +150(.6) 220(.2) 710.73 NPV=444.55 930(.4) +30(.4) 140(.6) *450 NPV=550.00 -150 +100(.6) or Piston -250 403.82 NPV=117.00 +50(.4) Irwin/McGraw Hill NPV=184.55 331 800(.8) 100(.2) 410(.8) 180(.2) 220(.4) 100(.6) 812 456 660 364 148 ©The McGraw-Hill Companies, Inc., 200 ... NPV=117.00 Irwin/McGraw Hill +100 (.6) or -150 800(.8) 100 (.2) 410( .8) 710 73 710. 73 − 550331= 96.12180(.2) 403.82− 550 = 96.12 11 10 220(.4) 10 +50(.4) NPV=184.55 100 (.6) 812 456 660 364 148 ©The... NPV=550.00 18 + 150 == 888 888 18 +100 (.6) 11 10 10 NPV= ? 960 (.8) 800(.8) 100 (.2) 410( .8) 180(.2) 220(.4) 100 (.6) 812 456 660 364 148 ©The McGraw-Hill Companies, Inc., 200 10- 16 Decision Trees NPV=888.18... -250 NPV= ? Irwin/McGraw Hill +50(.4) 800(.8) 100 (.2) 410( .8) 180(.2) 220(.4) 100 (.6) 812 456 660 364 148 ©The McGraw-Hill Companies, Inc., 200 10- 13 Decision Trees Turboprop -550 NPV= ? 960