L29: Sensitivity and Breakeven Analysis ECON 320 Engineering Economics Mahmut Ali GOKCE Industrial Systems Engineering Computer Sciences

Chapter 10 Handling Project Uncertainty Origin of Project Risk Methods of Describing Project Risk Probability Concepts for Investment Decisions Risk-Adjusted Discount Rate Approach

Origins of Project Risk Risk: the potential for loss Project Risk: variability in a project’s NPW Risk Analysis: The assignment of probabilities to the various outcomes of an investment project

Methods of Describing Project Risk Sensitivity Analysis: a means of identifying the project variables which, when varied, have the greatest effect on project acceptability.  What might have greatest effect on NPW, if changed? Break-Even Analysis: a means of identifying the value of a particular project variable that causes the project to exactly break even. Scenario Analysis: a means of comparing a “base case” to one or more additional scenarios, such as best and worst case, to identify the extreme and most likely project outcomes.

Sensitivity Analysis – Example 10.1 Should we or should we not? 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 at the end of project life. Income tax rate = 40% MARR = 15% Depreciation 7-year MACRS (Check out % depreciation from table 8.5) for a 5 year project. Develop a table for after-tax cash flow table! Then we will assess the situation under different scenarios

Example After-tax Cash Flow for BMC’s Transmission- Housings Project – “Base Case” 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

Cash Flow Statement Operating activities Net income 25,28217,63222,88226,63232,655 Depreciation 17,86330,61321,86315,6135,575 Investment activities Investment (125,000) Salvage 40,000 Gains tax (2,611) Net cash flow ($125,500)$43,145$48,245$44,745$42,245$75,619 (Example 10.1, Continued)

Example 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 cost52,23649,21946,20243,18640,16937,15234,13531,11828,101 Fixed cost44,19143,18542,17941,17540,16939,16338,15737,15136,145 Salvage value 37,78238,37838,97439,57340,16940,76541,36141,95742,553 Base Try to understand what will happen if estimates on unit prices, demand, variable and fixed cost, salvage value change?

Sensitivity graph – BMC’s transmission-housings project -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 Base Unit Price Demand Salvage value Fixed cost Variable cost

Example Sensitivity Analysis for Mutually Exclusive Alternatives

Capital (Ownership) Cost  Electrical power: CR(10%) = ($30,000 - $3,000)(A/P, 10%, 7) + (0.10)$3,000 = $5,845  LPG: CR(10%) = ($21,000- $2,000)(A/P, 10%, 7) + (0.10)$2,000 = $4,103  Gasoline: CR(10%) = ($20,000-$2,000)(A/P, 10%, 7) + (0.10) $2,000 = $3,897  Diesel fuel: CR(10%) = ($25,000 -$2,200)(A/P, 10%, 7) +(0.10) $2,200 = $4,903

REMEMBER L 17 FROM CHAPTER 6 ? Annual Equivalent Cost When only costs are involved, the AE method is called the annual equivalent cost. Revenues must cover two kinds of costs: Operating costs and capital costs. Capital costs Operating costs + Annual Equivalent Costs

REMEMBER L 17 FROM CHAPTER 6 ? Capital (Ownership) Costs Def: Owning an equipment is associated with two transactions—(1) its initial cost (I) and (2) its salvage value (S). Capital costs: Taking these items into consideration, we calculate the capital costs as: N 0 N I S CR(i)

Annual O&M Cost Let M be number of shifts per year  Electrical power: $500 + (1.60 + 5)M = $500 + 6.6M  LPG: $1,000 + (12 + 6)M = $1,000 + 18M  Gasoline: $800 + (13.2 + 7)M = $800  M  Diesel fuel: $1,500 + (7.7 + 9)M = $1,500 + 16.7M

Annual Equivalent Cost  Electrical power: AE(10%) = 6,345 + 6.6M  LPG: AE(10%) = 5,103 + 18M  Gasoline: AE(10%) = 4,697  M  Diesel fuel: AE(10%) = 6,403 + 16.7M

Break-Even Analysis  Excel using a Goal Seek function  Analytical Approach

Excel Using a Goal Seek Function NPW Breakeven Value Demand Can we find demand level for which NPW is 0?

Goal Seek Function Parameters

Analytical Approach Unknown Sales Units (X) for BMC transm. housing 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 X + 33,617

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 = X + $44,490

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) = X + $145,113 The NPW: PW (15%) = X + $44,490 - ( X + $145,113) = X - $100,623. Breakeven volume: PW (15%)= X - $100,623 = 0 X b =1,430 units.

Demand PW of inflow PW of OutflowNPW X X - $44, X + $145, X -$100,623 0$44,490$145,113100, ,773160,19865, ,055175,28230, ,197188, ,298188, ,338190,3674, ,620205,45240, ,903220,53775,366

Break-Even Analysis Chart Outflow $350, , , , , ,000 50, , ,000 Profit Loss Break-even Volume X b = 1430 Annual Sales Units (X) PW (15%) Inflow

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