Project Analysis Chapter 10 PDF

CH. 10: Project Analysis 2025-02-07 1  Some “What if” Questions “What-if” questions ask what will happen to a project in various circumstances. – What if your market share turns out to be higher or lower than you forecast? – What if interest rates r...

CH. 10: Project Analysis 2025-02-07 1  Some “What if” Questions “What-if” questions ask what will happen to a project in various circumstances. – What if your market share turns out to be higher or lower than you forecast? – What if interest rates rise during the life of the project? – What if costs turn out to be higher than anticipated? – ……… 2025-02-07 2  Sensitivity Analysis Sensitivity analysis is the analysis of the effects of changes in a single, specific variable (i.e., sales, costs) on project profitability. – Sensitivity analysis examines how sensitive a particular NPV calculation is when underlying assumptions are varied one at a time. – NPV=f(initial investment, sales, costs, interest rate). If sales are higher or lower than you forecast, what happens 3 2025-02-07  Sensitivity analysis: an example Year 0 years 1-12 Investment -$5,400,000 Sales $16,000,000 Variable costs $13,000,000 Fixed costs 2,000,000 Depreciation 450,000 Pretax profit 550,000 Tax (at 40%) 220,000 Profit after tax 330,000 CFs -5,400,000 780,000 2025-02-07 4  Variable costs and fixed costs Variable costs change as the level of output changes and they are zero when production is zero. – It is common to assume that variable costs are proportional to production. – In the example, the financial manager estimates that the variable costs are at 81.25% of sales. – variable costs = 81.25% × 16 =$13 million. Fixed costs are not dependent on the level of output (rent per month). – In our example, the fixed costs are forecast to be $2 million per year. 2025-02-07 5  Sensitivity analysis: an example PV = 780,000 ×A(8%, 12) = 780,000 × 7.5361 = $5.878 million NPV = 5.878 – 5.4 = $478,000 2025-02-07 6  Sensitivity analysis: an example For the purpose of comparison, the firm’s analysts prepared both the optimistic and pessimistic forecasts for the different variables. Variables pessimistic optimistic expected Investment -6,200,000 -5,000,000 -5,400,000 Sales 14,000,000 18,000,000 16,000,000 Variable cost (%) 83 80 81.25 Fixed cost 2,100,000 1,900,000 2,000,000 2025-02-07 7  Sensitivity analysis: an example For the pessimistic scenario, other things being equal, if investment is $6.2 million, the NPV is: Year 0 years 1-12 Investment -$6,200,000 Sales $16,000,000 Variable costs $13,000,000 Fixed costs 2,000,000 Depreciation 516666.67 Pretax profit 483,333.33 Tax (at 40%) 193,333.33 Profit after tax 290,000 CFs -6,200,000 806666.67 NPV = -121,000 2025-02-07 8  Sensitivity analysis NPV calculations Variable pessimistic (NPVs) expected (NPVs) optimistic (NPVs) Investment -121,000 478,000 778,000 Sales -1,218,000 478,000 2,174,000 Variable cost -788,000 478,000 1,382,000 Fixed cost 26,000 478,000 930,000 the pessimistic forecast for sales or investment leads to a negative NPV of $1.218 million or $121,000. an error in fixed cost estimate appears to be relatively unimportant because even under the pessimistic forecast for this variable, the NPV is still positive. 2025-02-07 9  Sensitivity analysis: limitations The terms “optimistic” and “pessimistic” are completely subjective. – What exactly do optimistic and pessimistic mean? – It gives somewhat ambiguous results. Sensitivity analysis treats each variable in isolation. – In reality, the underlying variables are likely to be inter-related. – For example, if wages are higher than your forecast, both variable costs and fixed costs are likely to be at the upper end of your range. 2025-02-07 10  Scenario analysis In a scenario analysis, financial managers look at what happens to NPVs under different scenarios, where each scenario involves a particular combination of assumptions. – A way of project analysis using different but consistent combinations of variables. NPV = f(I, S, VC, FC). – Scenario 0 (normal case): I = I0, S=S0, VC=VC0; FC=FC0, NPV=NPV0 – Scenario 1 : I = I1, S=S1, VC=VC0; FC=FC0, then, NPV=NPV1 – Scenario 2 : I = I2, S=S1, VC=VC1; FC=FC0, then NPV=NPV2 2025-02-07 11  Scenario analysis: an example Because of the strong competition (Presence of a competing store), the opening of a new plant may not be as attractive as expected. If the competition causes 15% reduction in sales and variable costs to increase to 82% of sales, what 1. Sales happens $13,600,000 to NPV under this scenario? 2. VC $11,152,000 3. FC 2,000,000 4. Depreciation 450,000 5. Pre-tax profit -2,000 6. Taxes 0 7. Profit after tax -2,000 Cash flows 448,000 2025-02-07 12  Scenario analysis: an example NPV at 8%= 448,000 × 7.536 – 5,400,000 = - $2,023,872. Sensitivity analysis vs scenario analysis: Both analyses calculate how NPV depends on input estimates. Sensitivity analysis changes inputs one at a time, whereas scenario analysis changes several variables at once. 2025-02-07 13  Break-even analysis Break-even analysis is the analysis of the level of sales at which the company breaks even.  Accounting break-even analysis: This is the break-even point in terms of accounting profits.  Economic break-even analysis: The Economic break-even point is the level of sales at which the EVA=0. Revisit the cash flow analysis on Slide #4: – Sales were estimated to be $16 million. – Variable costs were 81.25% of sales ($0.8125 of variable costs per $1 of sales). – Fixed costs were $2 million, and depreciation was $450,000. 2025-02-07 14 Accounting break-even analysis: an example Pre-tax profits = sales – 81.25% × sales – 2 – 0.45 =0  Sales = $13.067 million. Pre-tax profits = sales – VC – FC – depreciation= sales – sales × ratio of VC to sales – FC – depreciation = 0  Sales = (FC + depreciation)/(1 – ratio of VC to sales) 2025-02-07 15  Accounting break-even and NPV Using the accounting break-even, the project had to generate sales of $13.067 million to have a zero profit. If a project breaks even in accounting terms, is it an acceptable investment? NO. – A project which simply breaks even on an accounting basis will always have a negative NPV. 2025-02-07 16  Accounting break-even and NPV A project which simply breaks even on an accounting basis will always have a negative NPV! Proof: CF = profit after tax + depreciation = $0 + $450,000 = $450,000 NPV = PV of Cash Flows – C0 = [$450,000 * (12-year Annuity Factor)] - $5.4 m  $0 Note: the 12-year Annuity Factor  12 for all discount rates! 2025-02-07 17  Economic break-even analysis Accounting profit is calculated after the deduction of all costs except the opportunity cost of the capital that is invested in the project. Economic profit (economic value added or EVA) is the income that is measured after deduction of the cost of capital. – A project that has a positive EVA adds to firm value; one with a negative EVA reduces firm value. 2025-02-07 18  Economic break-even point Economic break-even point: The level of sales at which EVA=0 The minimum level of sales needed to cover all costs including the cost of capital. 2025-02-07 19  Economic break-even point Equivalent annual cost (EAC): The level of cash flow the investment returns over its life such that the NPV=0. EVA = accounting profit – (EAC – depreciation) =accounting profit –additional cost of capital 2025-02-07 20  Economic value added and break- even analysis: EAC For our example, EAC=(initial investment)/(12-year annuity factor at 8%) =5.4/7.536=$716,553 EAC is higher than the annual depreciation of $450,000, and the difference = 716,553 – 450,000=$266,553 EVA=accounting profit – 266,553 2025-02-07 21  Economic break-even point 1. Variable costs 81.25 percent of sales 2. Fixed costs $2 million 3. Depreciation $450,000 4. Pretax profit (.1875 x sales) - $2.45 million 5. Tax (as 40%).40 x (.1875 x sales - $2.45 millions) 6. After - tax accounting profit.60 x (.1875 x sales - $2.45 millions) 7. Cost of capital over and above $266,553 allowed depreciation 8. Economic Value Added (line 6 - line 7).60 x (.1875 x sales - $2.45 millions) - $266,553 Break-even EVA  0.60 (0.1875 Sales – 2.45m) – 266,553 = 0  Sales = 15.4m  Economic break-even and NPV EVA = accounting profit – (EAC – depreciation) =after-tax cash flows – EAC At the economic break-even point, NPV=0 The economic break-even point: The level of sales needed before the project adds value for shareholders 2025-02-07 23 Economic break-even Taxes and break-even points Will an increase in tax rate affect – Accounting break-even point? Accounting break-even is unaffected since taxes paid are zero when pretax profit is zero, regardless of the tax rate. – Economic break-even point? Economic break-even increases since the after-tax cash flow corresponding to any level of sales falls when the tax rate increases. 2025-02-07 25  Operating leverage Total costs = VC + FC + depreciation = sales × VC ratio + FC + depreciation The degree to which costs are fixed is called operating leverage. A business’s operating leverage is usually measured by the degree of operating leverage, which is defined as percentage change in profits fixed costs  depreciation DOL  1  percentage change in sales profits For a profitable firm (profit >0), what is lowest possible value for DOL? 2025-02-07 26  Example A company has sales outcomes that range from $16 mil to $19 mil, depending on the economy. The same conditions can produce profits in the range from $550,000 to $1,112,000. What is the DOL? % ∆ in profit = (1,112,000-550,000)/550,000=102.2% % ∆ in sales = (19-16)/16=18.75% DOL = % ∆ in profit/ % ∆ in sales = 102.2/18.75 = 5.45 2025-02-07 27  Operating leverage: an example High FC High VC Slump Normal Boom Slump Normal Boom Sales 13,000 16,000 19,000 13,000 16,000 19,000 -VC 10,563 13,000 15,438 10,920 13,440 15,960 -FC 2,000 2,000 2,000 1,560 1,560 1,560 -Depreciation 450 450 450 450 450 450 =Pretax profits -13 550 1,112 70 550 1,030 In the first case, the firm has a higher operating leverage fixed costs  depreciation 2,000  450 DOL 1  1  5.45 profits 550 In the second case, the firm has a lower operating leverage fixed costs  depreciation 1,560  450 DOL 1  1  4.65 profits 550 2025-02-07 28  Decision trees Imagine you are a financial manager of a big firm. The firm has recently developed a new product and is ready to go ahead with full-scale production and test marketing. The project involves two stages. The first stage is to test marketing. This stage will take a year and will cost $100 million. Furthermore, you believe there is a 75% chance that the marketing tests will prove successful. If the initial marketing tests are successful, the firm can acquire some land, build a new plant, and go ahead with full-scale production. This is the second stage. This stage will cost $1,500 million. Production will occur over the next five years. The forecast cash flow is $900 million per year. If the firm decides to go ahead with investments and produce the new product, the5NPV at a cost of capital of 15% is 900 NPV  1500   $1,517 t 1 1  15%t This NPV is calculated at the end of year 1. 2025-02-07 29  Decision trees A decision tree is a diagram of sequential decisions and the possible outcomes of such decisions. Decision process with decision trees  Second stage: – If the tests are successful, it is obvious that your firm should invest, because $1,517 is positive. – If the tests are unsuccessful, don’t invest.  First stage: – Should the firm invest $100 million now to obtain a 75% chance of $ 1,517 million one year later? The expected payoff evaluated at the end of the first year is: Expected payoff = 75%×1,517 +25% × 0 =$1,138 – The NPV of testing now is NPV = 1138/(1+15%) – 100 =$890 2025-02-07 30  Real options and the value of flexibility A corporation typically has the following four options regarding an investment project it has decided to undertake: The option to expand The option to abandon Investment timing options Flexible production facilities Value of the project = NPV without options + value of the options 2025-02-07 31