Cash Investment opportunity (real asset) FirmShareholder Investment opportunities (financial assets) InvestPay dividend to shareholders Shareholders invest for themselves Investment return must exceed the return on investing in a financial asset of equivalent risk to accept the project Investment Decision
Net Present Value Project Market Value - Project Cost Project Market Value - Project Cost 1. Estimate all cash flows, positive and negative 2. Estimate project’s required return 3. Find the present value of the cash flows Discount all future cash flows Discount all future cash flows NPV > 0 : Accept NPV 0 : Accept NPV < 0 : Reject
NPV: Value to Equity Holders Investors: Investors: –You $20,000 & Brother $30,000 Buy a thoroughbred horse $50,000 Buy a thoroughbred horse $50,000 Present value of sale $60,000 Present value of sale $60,000 –NPV = Gain for equity holders Gain for equity holders –Brother’s share = –Your share =
Negative NPV Air Quality Control Act requires a firm to install 3 cleaner ventilation systems Air Quality Control Act requires a firm to install 3 cleaner ventilation systems Cash Flows Cash Flows –Cost: $350,000/unit –Value: Avoid $100,000/unit in fines annually over the 5 year life of the units. At r =14%, NPV = -$20,075 At r =14%, NPV = -$20,075
Project Analysis Alternative analysis of cash flow estimates – –Payback – –Internal Rate of Return Supplements to NPV analysis – –Sensitivity Analysis – –Break-even Analysis – –Monte Carlo Simulation – –Decision Trees
Payback Payback Period Payback Period –Number of years it takes before the cumulative forecasted cash flow equals the initial outlay Payback Rule Payback Rule –Only accept projects that “payback” in the desired time frame
Fixed & Variable Costs Total Costs = Fixed + Variable Costs Total Costs = Fixed + Variable Costs –Total variable costs = quantity * cost per unit –Fixed costs are constant over some time period Ex: Your firm pays $3000 per month in fixed costs. You also pay $15 per unit to produce your product. Ex: Your firm pays $3000 per month in fixed costs. You also pay $15 per unit to produce your product. –What is your total cost if you produce 1000 units? –What if you produce 5000 units?
Example New experimental laser medical treatment New experimental laser medical treatment –Purchase of new laser costs $250,000 –Installation will cost $20,000 –Hourly labor costs are $830 (doctor, nurse, tech) –Charge $3,000 vs. $1,500 for traditional treatment Break-even Calculation Break-even Calculation –Fixed costs = –Variable costs = –Break-even =
Internal Rate of Return IRR is the discount rate that forces PV of the inflows equal to the initial outflow (cost). NPV: IRR: Enter r, solve for NPV. Enter NPV=0, solve for IRR.
IRR Rationale IRR > Opportunity Cost of Capital – –Project’s rate of return is greater than its cost – –Extra return is left after repaying financing to boost stockholders’ returns IRR > r : Accept IRR > r : Accept IRR < r : Reject
Mutually Exclusive Projects Period Project A Project B 0-500-400 1325325 2325200 IRR19.43%22.17% NPV64.0560.74 Req. return for both projects is 10%. Which project should you accept and why? NPV: choose the project with the higher NPV IRR: choose the project with the higher IRR
Relevant Cash Flows Incremental cash flows Incremental cash flows –Any and all changes in cash flows due to accepting a project –“Will this cash flow occur ONLY if we accept the project?” Stand-alone principle Stand-alone principle –Analyze each project in isolation from the firm
Common Cash Flows Sunk costs Sunk costs –Costs that have accrued in the past Opportunity costs Opportunity costs –Costs of lost options Side effects Side effects –Positive: benefits to other projects –Negative: costs to other projects Taxes Taxes
Incremental Cash Flows Luxury Car currently sells Luxury Car currently sells –30,000 cars at $45,000 and 12,000 SUVs at $85,000 Introduces a motorcycle Introduces a motorcycle Expects to sell 21,000 at $12,000 = $252 mil Expects to sell 21,000 at $12,000 = $252 mil Changes brand Changes brand –SUVs decrease: -1,300 * $85,000 = - $110.5 mil –Cars increase: 5,000 * $45,000 = $225 mil –Net sales
Evaluating NPV Estimates NPV estimates are just that – estimates NPV estimates are just that – estimates –NPV ≠ Actual Profitability Forecasting risk Forecasting risk –More sensitive NPV estimates, the greater the forecasting risk –Sources of value
Sensitivity Analysis NPV impact when vary one variable NPV impact when vary one variable Vary inputs separately – –Determines project’s realizations with better/worse outcomes of key variables Shows sensitivity to forecasting errors Scenario Unit Sales Cash Flow NPVIRR Baseline600059,80015,56715.1% Worst case 550053,200-8,22610.3% Best case 650066,40039,35719.7%
Sensitivity Analysis Must identify key variables Must identify key variables –Determines where additional information is needed –Exposes confused forecasts Results are often ambiguous Results are often ambiguous –Difficult to evaluate true probability distribution of outcomes How likely is each state of the world? How likely is each state of the world? –Interactions? Strong demand higher market size / price Strong demand higher market size / price
Scenario Analysis Alternative to sensitivity analysis Alternative to sensitivity analysis Examines outcome given certain events Examines outcome given certain events –Ex: Increased oil prices and car market Consider at least Consider at least –Best case: high revenues, low costs –Worst case: low revenues, high costs –Measure of the range of possible outcomes
Simulation Analysis Managers can consider many possible combinations Generates a probability distribution and estimates probability of positive NPV.
Discounting & Risk High Risk Project with Cost of $125,000 High Risk Project with Cost of $125,000 –If successful, firm will build a $1 million plant which would generate $250,000/yr after taxes –Otherwise, project will be dropped –50% probability of success Expected cash flows: C 0 = -125 C 1 =.5(-1,000) +.5(0) = -500 C t for t=2,3,…=.5(250) +.5(0) = 125
Discounting & Risk High risk so management uses a project discount rate of 25%. NPV – –All: -125 - 500/1.25 +(125/.25)/1.25 2 =negative Problematic approach – –If the test is a failure, then there is no risk at all! – –If successful, there may be normal risk afterwards.
Decision Tree Analysis Low risk if pilot is successful – –Discount rate of 10% Success NPV= -1000 + (250/.1)/1.1 = 1,272 Failure NPV = 0 50% Pilot production and test marketing
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