1. (c) 2001 Contemporary Engineering Economics 1 Chapter 14 Project Risk and Uncertainty Origin of Project Risk Methods of Describing Project Risk

2. (c) 2001 Contemporary Engineering Economics 2 Origins of Project Risk Risk is to describe investment project where cash flows are not known in advance with certainty. 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.

3. (c) 2001 Contemporary Engineering Economics 3 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.

4. (c) 2001 Contemporary Engineering Economics 4 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.

5. (c) 2001 Contemporary Engineering Economics 5 Example 14.2 - After-tax Cash Flow for BMC’s Transmission-Housings Project – “Base Case” (Table 14.1) Income Statement012345 Revenues: Unit Price50 Demand (units)2,000 Sales revenue$100,000 Expenses: Unit variable cost$15 Variable cost30,000 Fixed cost10,000 Depreciation17,86330,61321,86315,6135,575 Taxable Income$42,137$29,387$38,137$44,387$54,425 Income taxes (40%)16,85511,75515,25517,75521,770 Net Income$25,282$17,632$22,882$26,632$32,655

6. (c) 2001 Contemporary Engineering Economics 6 Cash Flow Statement012345 Operating activities Net income25,28217,63222,88226,63232,655 Depreciation17,86330,61321,86315,6135,575 Investment activities Investment125,000 Salvage40,000 Gains tax(2,611) Net cash flow$125,000$43,145$48,245$44,745$42,245$75,619 (Example 14.2, Continued)

7. (c) 2001 Contemporary Engineering Economics 7 Example 14.2 - 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

8. (c) 2001 Contemporary Engineering Economics 8 Sensitivity graph – BMC’s transmission-housings project (Example 14.2) -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

9. (c) 2001 Contemporary Engineering Economics 9 Sensitivity Graph In the graph, we see that the project’s NPW is (1)Very sensitive to changes in product demand and unit price (2)Fairly sensitive to changes in the variable costs, and (3)Relatively insensitive to changes in the fixed cost and the salvage value.

10. (c) 2001 Contemporary Engineering Economics 10 Break-Even Analysis When we perform a sensitivity analysis of a project, we are asking how serious the effect of lower revenues or higher costs will be on the project’s profitability. Break-Even analysis is a technique for studying the effect of variations in output on firm’s NPW. We compute the PW of cash inflows as a function of an unknown variable (say X) – this variable could be annual sales. Break-Even value calculations is similar to that used to calculate the internal rate of return where we want to find the interest rate that makes the NPW equal zero.

11. (c) 2001 Contemporary Engineering Economics 11 Break-Even Analysis with unknown Sales Units (X) [Example 14.4] 012345 Cash Inflows: Net salvage 37,389 Revenue X(1-0.4)($50) 30X Depr.. credit 0.4 (depreciate) 7,14512,2458,7456,2452,230 Cash outflows: Investment -125,000 Variable cost -X(1-0.4)($15) -9X Fixed cost -(0.6)($10,000) -6,000 Net Cash Flow -125,00021X + 1,145 21X + 6,245 21X + 2,745 21X + 245 21X + 33,617

12. (c) 2001 Contemporary Engineering Economics 12 Break-Even Analysis 1. 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 PW(15%) Inflow = 100.5650X + $44,490

13. (c) 2001 Contemporary Engineering Economics 13 2. 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) PW(15%) Outflow = 30.1694X + $145,113 3. The NPW: PW (15%) = 100.5650X + $44,490 - (30.1694X + $145,113) =70.3956X - $100,623. 4. Breakeven volume: PW (15%)= 70.3956X - $100,623 = 0 X BE =1,430 units.

14. (c) 2001 Contemporary Engineering Economics 14 Demand PW of inflow PW of OutflowNPW X100.5650X - $44,490 30.1694X + $145,113 70.3956X -$100,623 0$44,490$145,113-100,623 50094,773160,198-65,425 1000145,055175,282-30,227 1429188,197188,225-28 1430188,298188,25543 1500195,338190,3674,970 2000245,620205,45240,168 2500295,903220,53775,366

15. (c) 2001 Contemporary Engineering Economics 15 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

16. (c) 2001 Contemporary Engineering Economics 16 Scenario Analysis Scenario analysis is a technique that consider considers the sensitivity of PW to changes in both key variables and the range of likely variable values. For example, the decision maker may consider two extreme cases: a worst case scenario (low unit sales, low unit price, high variable cost per unit, high fixed cost, and so on) and a best case scenario. The NPWs under the worst and best conditions are then calculated with the expected, or base-case, NPW.

17. (c) 2001 Contemporary Engineering Economics 17 Scenario Analysis (Example 14.5) 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%)-$5,854$40,169$104,295