1. Fundamentals of Corporate Finance, 2/e ROBERT PARRINO, PH.D. DAVID S. KIDWELL, PH.D. THOMAS W. BATES, PH.D.

2. Chapter 12: Evaluating Project Economics and Capital Rationing

3. Learning Objectives 1.EXPLAIN AND DEMONSTRATE HOW VARIABLE COSTS AND FIXED COSTS AFFECT THE VOLATILITY OF PRETAX OPERATING CASH FLOWS AND ACCOUNTING OPERATING PROFITS. 2.CALCULATE AND DISTINGUISH BETWEEN THE DEGREE OF PRETAX CASH FL OW OPERATING LEVERAGE AND THE DEGREE OF ACCOUNTING OPERATING LEVERAGE.

4. Learning Objectives 3.DEFINE AND CALCULATE THE PRETAX OPERATING CASH FLOW AND ACCOUNTING OPERATING PROFIT Break-Even POINTS AND THE CROSSOVER LEVELS OF UNIT SALES FOR A PROJECT. 4.DEFINE SENSITIVITY ANALYSIS, SCENARIO ANALYSIS, AND SIMULATION ANALYSIS AND DESCRIBE HOW THEY ARE USED TO EVALUATE THE RISKS ASSOCIATED WITH A PROJECT.

5. Learning Objectives 5.EXPLAIN HOW THE PROFITABILITY INDEX CAN BE USED TO RANK PROJECTS WHEN A FIRM FACES CAPITAL RATIONING AND DESCRIBE THE LIMITATIONS THAT APPLY TO THE PROFITABILITY INDEX.

6. Variable Costs, Fixed Costs, And Project Risk o Variable costs are costs that vary directly with the number of units sold. o Fixed costs, in contrast, do not vary with unit sales – at least in the short run. o A project with a higher proportion of fixed costs will have cash flows and accounting profits that are more sensitive to changes in revenues.

7. EXHIBIT 12.1: Unit and Annual Costs for Hammock Project

8. Variable Costs, Fixed Costs, And Project Risk o PRETAX OPERATING CASH FLOW EBITDA is often called pretax operating cash flow because it equals the incremental pretax cash operating profits from a project. EBITDA = Revenue – Op Ex where Op Ex = VC + FC

9. Exhibit 12.2: EBITDA Under Alternative Production Technologies

10. Variable Costs, Fixed Costs, And Project Risk o COST STRUCTURE AND SENSITIVITY OF EBITDA TO REVENUE CHANGES Comparing the sensitivity of EBITDA to changes in revenue helps understand the risks and returns of different decision alternatives. Distinguishing between fixed and variable costs enables us to calculate the sensitivity of EBITDA to changes in revenue.

11. Exhibit 12.3: Changes in EBITDA under Alternative Production Technologies

12. Variable Costs, Fixed Costs, And Project Risk o COST STRUCTURE AND SENSITIVITY OF EBITDA TO REVENUE CHANGES Exhibit 12.3 shows how EBITDA is more sensitive to changes in revenue with the automated production process than with the manual process. The reason for the difference is that more of the total costs are fixed with the automated process, making it more difficult to adjust costs when revenue changes.

13. Exhibit 12.4: EBITDA for Different Levels of Unit Sales

14. Variable Costs, Fixed Costs, And Project Risk o COST STRUCTURE AND SENSITIVITY OF EBITDA TO REVENUE CHANGES Exhibit 12.4 shows how EBITDA changes as the number of units sold changes for both the manual and the automated production process. Automated production process produces larger declines in EBITDA when unit sales are lower and larger increases in EBITDA when unit sales are higher.

15. Variable Costs, Fixed Costs, And Project Risk o COST STRUCTURE AND SENSITIVITY OF EBIT TO REVENUE CHANGES The sensitivity of EBIT to changes in revenue is of concern to managers because EBIT is a performance measure that is of interest to investors. EBITDA calculation does not include depreciation and amortization (D&A).

16. Variable Costs, Fixed Costs, And Project Risk o COST STRUCTURE AND SENSITIVITY OF EBIT TO REVENUE CHANGES Depreciation and amortization acts just like a fixed cost, hence included in the EBIT calculation to effectively increase the proportion of costs that are fixed. When D&A is greater than zero, the percentage change in EBIT is greater than the percentage change in EBITDA.

17. Exhibit 12.5: Changes in EBITDA and EBIT

18. Calculating Operating Leverage o OPERATING LEVERAGE Is a measure of the relative amounts of fixed and variable costs in a project’s cost structure; it will be higher with more fixed costs. Two measures of operating Leverage: Degree of pretax cash flow operating leverage Degree of accounting operating leverage

19. Calculating Operating Leverage o DEGREE OF PRETAX CASH FLOW OPERATING LEVERAGE Measures the sensitivity of pretax operating cash flows to changes in revenue. It changes with the level of revenue; the sensitivity of operating cash flows are not the same for all levels of revenue.

20. Calculating Operating Leverage o DEGREE OF PRETAX CASH FLOW OPERATING LEVERAGE Calculate the Cash Flow DOL for the automated production alternative in Exhibit 12.2. EBITDA in the denominator of equation 12.2 varies directly with revenue and will be larger for larger amounts of revenue. The Cash Flow DOL will be smaller as revenue increases.

21. Exhibit 12.6: EBITDA with Unit Sales

22. Calculating Operating Leverage o DEGREE OF ACCOUNTING OPERATING LEVERAGE Measures the sensitivity of accounting operating profits, EBIT, to changes in revenue.

23. Calculating Operating Leverage o DEGREE OF ACCOUNTING OPERATING LEVERAGE EXAMPLE Calculate the Accounting DOL for the automated production alternative in Exhibit 12.5 for expected demand.

24. Break-Even Analysis o Break-Even ANALYSIS Analysis that tells us how many units must be sold in order for a project to Break-Even on a cash flow or accounting profit basis Helps to understand the sensitivity of cash flows and accounting profits to changes in the number of units that will be sold

25. Break-Even Analysis o PRETAX OPERATING CASH FLOW Break-Even Number of units that must be sold for pretax operating cash flow to equal $0

26. Break-Even Analysis o CASH FLOW Break-Even EXAMPLE Calculate the EBITDA Break-Even points for the automated and manual production alternatives in Exhibit 12.2.

27. Exhibit 12.7: EBITDA Break-Even Points

28. Break-Even Analysis o PER-UNIT CONTRIBUTION Dollar amount that is left over from the sale of a single unit after all the variable costs associated with that unit have been paid Amount that is available to help cover fixed costs for the project

29. Break-Even Analysis o CROSSOVER LEVEL OF UNIT SALES (CO) Level of unit sales at which cash flows or profitability for one project alternative switches from being lower than that of another alternative to being higher

30. Break-Even Analysis o THE CROSSOVER LEVEL OF UNIT SALES EXAMPLE Calculate the Crossover level of unit sales for the automated and manual production alternatives in Exhibit 12.2.

31. Break-Even analysis o ACCOUNTING BREAK-EVEN Number of units that must be sold for accounting operating profit to equal $0 EBITBreak-Even= FC+D&A Price-UnitVC.

32. Break-Even Analysis o ACCOUNTING Break-Even In addition to the accounting operating profit Break-even points, we can also calculate the crossover level of unit sales for EBIT.

33. Break-Even Analysis o ACCOUNTING BREAK-EVEN EXAMPLE Calculate the accounting operating profit Break- even point and the crossover level of unit sales for the automated and manual production alternatives in Exhibits 12.1 and 12.2.

34. Risk Analysis o Financial analysts must often resort to different types of risk analysis to obtain a better understanding of how errors in forecasting these factors affect the attractiveness of a project.

35. Risk Analysis o SENSITIVITY ANALYSIS Involves examination of the sensitivity of the results from a financial analysis to changes in individual assumptions An analyst might examine how a project’s NPV changes if there is a decrease in the value of individual cash inflow assumptions or an increase in the value of individual cash outflow assumptions.

36. Using Excel – Sensitivity Analysis

37. Exhibit 12.8: Incremental Free Cash Flows and NPV

38. Risk Analysis o SCENARIO ANALYSIS An analytical method concerned with how the results from a financial analysis will change under alternative scenarios An analyst who wants to examine how the results from a financial analysis will change under alternative scenarios performs a scenario analysis.

39. Exhibit 12.9: NPV Values for Automated Hammock Production

40. Risk Analysis o SIMULATION ANALYSIS An analytical method that uses a computer to quickly examine a large number of scenarios and obtain probability estimates for various values in a financial analysis Rather than selecting individual values for each of the assumptions–such as unit sales, unit price, and unit variable costs–the analyst assumes that those assumptions can be represented by statistical distributions.

41. Risk Analysis o SIMULATION ANALYSIS A computer program repeatedly draws numbers for the distributions for various assumptions, plugs them into the cash flow model, and computes the annual cash flows and NPV. In addition to providing an estimate of the expected cash flows, it also provides information on the distribution of the cash flows that the project is likely to produce in each year.

42. Investment Decisions With Capital Rationing o SELECTING THE BEST PROJECTS What does a firm do when it does not have enough money to invest in all available positive- NPV projects? The process of identifying the bundle of projects that creates the greatest total value and allocating the available capital to these projects is known as capital rationing.

43. Exhibit 12.10: Positive NPV Investments for a Single Year

44. Investment Decisions With Capital Rationing o CAPITAL RATIONING IN A SINGLE PERIOD Involves choosing the set of projects that creates the greatest value in a given period Goal is to select the projects that yield the largest value per dollar invested

45. Investment Decisions With Capital Rationing o CAPITAL RATIONING IN A SINGLE PERIOD Profitability index (PI) is computed for each project Firm chooses the project(s) with the largest profitability indices until it runs out of money. Profitability Index is a measure of the value a project generates for each dollar invested in that project.

46. Investment Decisions With Capital Rationing o CAPITAL RATIONING IN A SINGLE PERIOD Objective is to identify the bundle or combination of positive-NPV projects that creates the greatest total value for stockholders.

47. Investment Decisions With Capital Rationing o PROFITABILITY INDEX EXAMPLE Calculate the profitability index for the lawn mower problem in Chapter 11. The new mower costs $2,000 and brings in net cash flows of $7,000. The discount rate is 10 percent and the NPV is $20,189.

48. Investment Decisions With Capital Rationing o CAPITAL RATIONING IN A SINGLE PERIOD Using PI to choose project(s) that create the most value per dollar invested (4 step procedure): Calculate the PI for each project. Rank the projects from highest PI to lowest PI. Starting at the top of the list (the project with the highest PI) and working your way down (to the project with the lowest PI), select the projects that the firm can afford.

49. Investment Decisions With Capital Rationing o CAPITAL RATIONING IN A SINGLE PERIOD Repeat the third step by starting with the second project on the list, the third project on the list, and so on, to make sure that a more valuable bundle cannot be identified.

50. Investment Decisions With Capital Rationing o CAPITAL RATIONING ACROSS MULTIPLE PERIODS If you are planning to make investments over several years, the investments you choose this year can affect your ability to make investments in future years. This can happen if you plan on reinvesting some or all of the cash flows generated by the projects you invest in this year.

51. Investment Decisions With Capital Rationing o CAPITAL RATIONING ACROSS MULTIPLE PERIODS PI can only be relied upon to identify the projects that the firm should invest in the current year. A limitation of the profitability index is that it does not tell us enough to make informed decisions over multiple periods.

52. Exhibit 12.11: Positive NPV Investments for Two Years Exhibit 12.11: Positive NPV Investments