1. © 2012 McGrawHill Ryerson Ltd.Chapter 10 -1 ..and Possible Solutions ◦ 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 LO2, LO3

2. © 2012 McGrawHill Ryerson Ltd.Chapter 10 -2  Sensitivity Analysis: The analysis of effects of changes in sales, costs, and so on, on the project profitability  Example: Given the expected cash flow forecasts listed on the next slide, determine the NPV of the project given changes in the cash flow components using an 8% cost of capital. Assume that all variables remain constant, except the one you are changing. LO2, LO3

3. © 2012 McGrawHill Ryerson Ltd.Chapter 10 -3 LO2, LO3

4. © 2012 McGrawHill Ryerson Ltd.Chapter 10 -4 Using the information in the previous page and assuming the following, one at a time, calculate the NPV and show effects of the changes LO2, LO3

5. © 2012 McGrawHill Ryerson Ltd.Chapter 10-5 For the pessimistic scenario, the NPV is: NPV= -($322) LO2, LO3

6. © 2012 McGrawHill Ryerson Ltd.Chapter 10-6  The terms “optimistic” and “pessimistic” are completely subjective  Variables are often inter-related and it may be difficult to identify all of the consequences associated with a change in one of them  Scenario Analysis: A way of project analysis using different but consistent combinations of variables Example: Presence of a competing store is expected to reduce sales in your store by 15%. Also, prices might be reduced to the point that variable costs equal 82% of revenue. What is the effect of this lower sales-smaller margin scenario on your NPV analysis? LO2, LO3

7. © 2012 McGrawHill Ryerson Ltd.Chapter 10-7 Lower sales – smaller margin ratio LO2, LO3

8. © 2012 McGrawHill Ryerson Ltd.Chapter 10-8  An accounting break-even occurs where total revenues equal total costs (profits equal zero)  A NPV break-even occurs when the NPV of the project equals zero  Revisit the cash flow analysis on Slide #9: ◦ 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 LO2

9. © 2012 McGrawHill Ryerson Ltd.Chapter 10 -9 In this example, the accounting break-even happens, if Break-Even Revenues= Fixed Costs + Depreciation Profit per $1 of Sales = $2,000 + $450 $1 - $0.8125 = $2,450 $0.1875 = $13.067 million LO2

10. © 2012 McGrawHill Ryerson Ltd.Chapter 10 -10 A project which simply breaks even on an accounting basis will always have a negative NPV! NPV= PV of Cash Flows – C 0 = [$450,000 * (12 year Annuity Factor)] - $5.4 m  $0 Note: the 12 year Annuity Factor  12 for all discount rates! CFO= profit after tax + depreciation = $0 + $450,000 = $450,000 LO2

11. © 2012 McGrawHill Ryerson Ltd.Chapter 10 -11 The NPV break-even will occur, if:  Pretax Profit (0.1875 Sales) - 2.45 m Note: Cash flow = Depreciation + After Tax Profit Variable Costs81.25% of Sales + Fixed Costs + Depreciation$2.45 m - Tax @ 40%0.40 x [(0.1875 Sales) - 2.45 m]  After Tax Profit 0.60 x [(0.1875 Sales) - 2.45 m]  Cash flow $0.45 m + 0.60 x [(0.1875 Sales) - 2.45 m] = 0.1125 * Sales - $1.02 m LO2

12. © 2012 McGrawHill Ryerson Ltd.Chapter 10 -12 NPV break-even sales is equal to: But: NPV = 0 if PV (cash flows) = C 0  NPV = 0 if (0.1125 x Sales – 1.02 m) x 7.536 = 5.4 m  Sales = $15.4 m  PV(cash flows) = Cash Flows x Annuity Factor = (0.1125 x Sales - 1.02 m) x 12 year Annuity Factor = (0.1125 x Sales - 1.02 m) x 7.536 LO2

13. © 2012 McGrawHill Ryerson Ltd.Chapter 10 -13 Economic Value Added and Break Even Analysis Break-even EVA  0.60  (0.1875  Sales – 2.45m) – 266,553 = 0  Sales = 15.4m LO2

14. © 2012 McGrawHill Ryerson Ltd.Chapter 10-14 LO2

15. © 2012 McGrawHill Ryerson Ltd.Chapter 10-15  Operating Leverage: The degree to which a firm’s operating costs are fixed  Degree of Operating Leverage: The percentage change in operating profits when sales changes by 1 percent  Example: A company has sales outcomes that range from $16mil 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? DOL = % ∆ in profit/ % ∆ in sales = 102.2/18.75 = 5.45 LO2, LO3