1. Chapter 10 Sensitivity and Breakeven Analysis

2. Handling Project Uncertainty Origin of Project Risk Methods of Describing Project Risk

3. Origins of Project Risk Risk is to describe investment project where cash flows are not known in advance with certainty. Project risk on the other hand refer to variability in a project’s PW. In essence, we can see that risk is the potential for loss. Risk Analysis is the assignment of probabilities to the various outcomes of an investment project.

4. Origins of Project Risk continue…. The decision to make a major capital investment such as introducing a new product requires cash flow information over the life of a project. The profitability estimate of an investment depends on cash flow estimations, which are generally uncertain. The factors to be estimated include  the total market for the product;  the market share that the firm can attain;  the growth in the market;  the cost of producing the product, including labor and materials;  the selling price;  the life of a product;  the cost and the life of equipment needed; and  the effective tax rates. Many of these factors are subject to uncertainty.

5. Methods of Describing Project Risk Fist, begin analyzing project risk by determining the uncertainty inbuilt in a project cash flows. We can do this analysis in a number of ways such as the following; Sensitivity Analysis (SA): Determines the effect on the PW of variations in the input variables (revenues, operating cost, and salvage value). SA is sometimes called “what if analysis” because it answers questions such as,  What if incremental sales are only 1,000 units, rather than 2,00 units? Then  what will be the NPW be?.  SA begins with a base-case situation, which is developed using most-likely values for each input. A useful way to present results of sensitivity analysis is to plot sensitivity graphs. Break-Even Analysis is a technique for studying the effect of variations in output on a firm’s NPW. Scenario Analysis is a technique that does consider the sensitivity of NPW to both changes in key variables and to the range of likely variable values. The decision maker may consider two extreme cases, a  “worst-case” scenario (low unit sales, high variable cost per unit, high fixed cost, and so on) and a  “best-case” scenario to identify the extreme and most likely project outcomes.

6. Sensitivity Analysis – Example 10.1 Transmission-Housing Project by Boston Metal Company New investment = $125,000 Number of units = 2,000 units Unit Price = $50 per unit Unit variable cost = $15 per unit Fixed cost = $10,000/Yr Project Life = 5 years Salvage value = $40,000 Income tax rate = 40% MARR = 15%

7. Example 10.1 - After-tax Cash Flow for BMC’s Transmission Housings Project – “Base Case” 012345 Revenues: Unit Price50 Demand (units)2,000 Sales revenue$100,000 Expenses: Unit variable cost$15 Variable cost30,000 Fixed cost10,000 Depreciation17,86330,61321,86315,6135,581 Taxable Income$42,137$29,387$38,137$44,387$54,419 Income taxes (40%)16,85511,75515,25517,75521,768 Net Income$25,282$17,632$22,882$26,632$32,651

8. 8 Depreciation Calculation –Cost Base = $125,000 –Recovery Period = 7-year MACRS N MACRS Rate Depreciation Amount Allowed Depreciation Amount 114.29 %$17,863 224.49 %$30,613 317.49 %$21,863 412.49 %$15,613 58.93 %$11,150$ 5,581 68.92 %$11,1500 78.93 %$11,1500 84.46 %$5,5750

9. 9 Gains (Losses) associated with Asset Disposal Salvage value = $40,000 Book Value (year 5) = Cost Base – Total Depreciation = $125,000 - $ 91,533 = $ 33,467 Taxable gains = Salvage Value – Book Value = $40,000 - $ 33,467 = $6,533 Gains taxes = (Taxable Gains) (Tax Rate) = $6,533 x (0.40) = $2,613

10. Cash Flow Statement012345 Operating activities Net income25,28217,63222,88226,63232,651 Depreciation17,86330,61321,86315,6135,581 Investment activities Investment(125,000) Salvage40,000 Gains tax(2,613) Net cash flow($125,500)$43,145$48,245$44,745$42,245$75,619 (Example 10.1, Continued)

12. 12 Is this investment justifiable at a MARR of 15%? PW(15%) = -$125,000 + +$43,145(P/F, 15%, 1) +.... +$75,619(P/F, 15%, 5) = $40,169 > 0  Yes, Accept the Project 0 12345 $125,000 $43,145 $48,245 $44,745 $42,245 $75,619 Years

13. Example 10.2 - Sensitivity Analysis for Five Key Input Variables Deviation-20%-15%-10%-5%0%5%10%15%20% Unit price$57$9,999$20,055$30,111$40,169$50,225$60,281$70,337$80,393 Demand12,01019,04926,08833,13040,16947,20854,24761,28668,325 Variable cost 52,23649,21946,20243,18640,16937,15234,13531,11828,101 Fixed cost44,19143,18542,17941,17540,16939,16338,15737,15136,145 Salvage value 37,78238,37838,97439,57340,16940,76541,36141,95742,553 Base

14. Sensitivity graph – BMC’s transmission-housings project (Example 10.2) -20% -15%-10%-5% 0%5%10%15%20% $100,000 90,000 80,000 70,000 60,000 50,000 40,000 30,000 20,000 10,000 0 -10,000 Base Unit Price Demand Salvage value Fixed cost Variable cost

15. Analytical Approach Unknown Sales Units (X) 012345 Cash Inflows : Net salvage 37,389 X(1-0.4)($50) 30X 0.4 (dep) 7,14512,2458,7456,2452,230 Cash outflows: Investment -125,000 -X(1-0.4)($15) -9X -(0.6)($10,000) -6,000 Net Cash Flow -125,00021X + 1,145 21X + 6,245 21X + 2,745 21X + 245 21X + 33,617

16. PW of cash inflows PW(15%) Inflow = (PW of after-tax net revenue) + (PW of net salvage value) + (PW of tax savings from depreciation = 30X(P/A, 15%, 5) + $37,389(P/F, 15%, 5) + $7,145(P/F, 15%,1) + $12,245(P/F, 15%, 2) + $8,745(P/F, 15%, 3) + $6,245(P/F, 15%, 4) + $2,230(P/F, 15%,5) = 30X(P/A, 15%, 5) + $44,490 = 100.5650X + $44,490

17. PW of cash outflows: PW(15%) Outflow = (PW of capital expenditure) + (PW) of after-tax expenses = $125,000 + (9X+$6,000)(P/A, 15%, 5) = 30.1694X + $145,113 The NPW: PW (15%) = 100.5650X + $44,490 - (30.1694X + $145,113) = 70.3956X - $100,623. Breakeven volume: PW (15%)= 70.3956X - $100,623 = 0 X b = 1,430 units.

18. Demand PW of inflow PW of OutflowNPW X100.5650X - $44,490 30.1694X + $145,113 70.3956X -$100,623 0$44,490$145,113100,623 50094,773160,19865,425 1000145,055175,28230,227 1429188,197188,22528 1430188,298188,25543 1500195,338190,3674,970 2000245,620205,45240,168 2500295,903220,53775,366

19. Outflow Break-Even Analysis Chart 0 300 600 900 1200 1500 1800 2100 2400 $350,000 300,000 250,000 200,000 150,000 100,000 50,000 0 -50,000 -100,000 Profit Loss Break-even Volume X b = 1430 Annual Sales Units (X) PW (15%) Inflow

20. Scenario Analysis Variable Considered Worst- Case Scenario Most-Likely- Case Scenario Best-Case Scenario Unit demand1,6002,0002,400 Unit price ($)485053 Variable cost ($)171512 Fixed Cost ($)11,00010,0008,000 Salvage value ($)30,00040,00050,000 PW (15%)-$5,856$40,169$104,295