Ch11. Project Analysis and Evaluation

1) Scenario and other what-if analyses

• Actual cash flows and projected cash flows.• Forecasting risks (estimation risks): errors in

projected cash flows will lead to incorrect decisions.

• (1) Scenario analysis.• In order to handle the possible errors in

estimating cash flows, re-estimate cash flows or others under various circumstances/economic scenario.

• Ex) The project costs $200,000 and has a 5-year life. It does not have salvage value. Straight-line depreciation is applied. The required rate is 12% and tax rate is 34%

Base Worst BestUnit Sales 6,000 5500 6500Price per Unit 80 75 85Variable costs per unit 60 62 58Fixed costs per year 50,000 55000 45000

Sales 480,000 412,500 552,500Total variable costs 360,000 341,000 377,000Fixed costs per year 50,000 55,000 45,000Depreciation 40,000 40,000 40,000EBIT 30,000 (23,500) 90,500Tax (34%) 10,200 0 30,770Net Income 19,800 (23,500) 59,730

Operating cash flow 59,800 16,500 99,730Project cost 200,000 200,000 200,000NPV $15,565.62 ($140,521.19) $159,504.33

• 2) Sensitivity analysis• Analysis to figure out a key determinant to estimates in

analysis, assuming other variables are constant.• Among the variables, sale is usually found more

significant than others.Base Worst Best

Sales 480,000 412,500 552,500Operating cash flow 59,800 32,500 87,850Project cost 200,000 200,000 200,000NPV $15,565.62 ($82,844.77) $116,679.59

Base Worst BestFixed costs per year 50,000 55,000 45,000Operating cash flow 59,800 56,500 63,100Project cost 200,000 200,000 200,000NPV $15,565.62 $3,669.86 $27,461.38

3) Simulation analysis:

• A combination of scenario and sensitivity analyses.

4) Break-Even Analysis

• Variable costs (VC): costs that change when the quantity of output changes. Ex) direct labor costs and raw material costs.

• VC = v × Q

• Fixed costs (FC): costs that do not change when the quantity of output changes during a particular time period.

• Total costs = VC + FC = v × Q + FC• Marginal or incremental costs: change in costs

that occurs when there is a small change in output.

5) Accounting Break-Even• A tool for analyzing the relationship between

sales volume and profitability.• Sales or quantity making EBIT (or Net Income

without considering interest) equal to zero.

• EBIT = Sale – VC – FC – D

• Net Income = (Sale – VC – FC – D) × (1-t)

• If EBIT or Net Income =0, then Sale –VC –FC-D = s × q - v × q – FC – D = 0.

• q = (FC + D) / (s - v).

• 6) Operating cash flow, sales volume and break-even.

• Ex) Wettyway sailboat CO considering whether to launch its new Margo-class sailboat.

• The selling price will be $40,000 per boat.• Variable cost per boat is $20,000.• Annual Fixed costs is $500,000.• Total investment to launch the project is $3,500,000. It

would be depreciated straight line to zero over five years.

• Salvage value is zero.• There are no working capital consequences.• 20% required rate of return on new project is expected.• Wettyway forecasts about 85 boat sales in a year.• Ignore tax

• Operating cash flow = EBIT + depreciation – tax = (Sale –Variable costs – Fixed costs –Depreciation) +Depreciation - 0

• = 85*(40,000-20,000)-500,000 = 1,200,000 per year.

• NPV with 20% and 5 year =

• 1,200,000*(1-1/(1+0.2)^5)/0.2-3,500,000 =88,735

• Break-even: (FC + D) / (p - v) = (500,000 + 3,500,000/5) / (40,000-20,000) = 60.

• Thus this project looks good.

• At break even, • 1) operating cash flow under assumptions is only

depreciation. OCF = 60*(40,000-20,000)-500,000 -3,500,000/5 + 3,500,000/5 =700,000.

• NPV with 20% = -1,406,572.• 2) IRR = 0.• Ex) 3,500,000 = 700,000/(1+IRR) + 700,000/(1+IRR)^2+

….+700,000/(1+IRR)^5.• 3) Life of the project is a payback period.Thus if a project’ s performance is better than break even,

IRR would be positive and payback period is shorter than the life of the project.

• 7) Relationship between operating cash flows and break even point (quantity:q).

• OCF = (Sale – Variable costs – Fixed costs – Depreciation) + Depreciation – Tax (ignored) = (p-v) * q – FC

• q = (FC + OCF) / (p-v), What does it mean?

• Here (1) accounting break-even (q) means zero net income or EBIT. In that case, OCF is a depreciation.

• q= (500,000 + 3,500,000/5) / (40,000-20,000) = 60

• (2) Cash break-even (q) means the sales level that results in a zero OCF. q covers only Fixed costs. In that case OCF is 0.

• q= (500,000 + 0) / (40,000-20,000) = 25

• (3) Financial break-even (q) mean zero NPV. • In order to calculate financial break-even, at first

we have to calculate a periodic payment of an annuity (operating cash flows) that would make PV of the annuity equal to initial investment.

• 3,500,000 = payment * (1-1/(1.2^5))/0.2• Payment (operating cash flow) = 1,170,329• q= (500,000 + 1,170,329) / (40,000-20,000) =

83.5

• Thus financial break-even is much higher than accounting break-even.

8) Operating leverage.• Def: the degree to which a project or firm

is committed to fixed production costs.• The fixed costs can act like a lever in the

sense that small change in revenue can be magnified into a large percentage change in operating cash flow and NPV.

• The higher the degree of operating leverage, the greater the forecasting risk.

• Thus managers try to reduce the operating leverage through outsourcing the project.

Base Worst BestUnit Sales 6,000 5500 6500Price per Unit 80 75 85Variable costs per unit 60 60 60Fixed costs per year 50,000 50000 50000

Sales 480,000 412,500 552,500Total variable costs 360,000 330,000 390,000Fixed costs per year 50,000 50,000 50,000Depreciation 40,000 40,000 40,000EBIT 30,000 (7,500) 72,500Tax (34%) 10,200 0 24,650Net Income 19,800 (7,500) 47,850

Operating cash flow 59,800 32,500 87,850Project cost 200,000 200,000 200,000NPV $15,565.62 ($82,844.77) $116,679.59Change of NPV -632.23% 649.60%Change of OCF -45.65% 46.91%

Base Worst BestUnit Sales 6,000 5500 6500Price per Unit 80 75 85Variable costs per unit 60 60 60Fixed costs per year 10,000 10000 10000

Sales 480,000 412,500 552,500Total variable costs 360,000 330,000 390,000Fixed costs per year 10,000 10,000 10,000Depreciation 40,000 40,000 40,000EBIT 70,000 32,500 112,500Tax (34%) 23,800 0 38,250Net Income 46,200 32,500 74,250

Operating cash flow 86,200 72,500 114,250Project cost 200,000 200,000 200,000NPV $110,731.71 $61,346.27 $211,845.68Change of NPV -44.60% 91.31%Change of OCF -15.89% 32.54%

• How to measure the operating leverage, degree of operating leverage (DOL)?

• Percentage change in OCF = DOL × Percentage change in q. Here OCF = (Sale – Variable costs – Fixed costs – Depreciation) + Depreciation – Tax (ignored) = (p-v) * q – FC. Thus one unit change in q will increase (p-v) in OCF.

• Percentage change in OCF = DOL × Percentage change in q.

• (p-v) / OCF = DOL × 1 / q• DOL = (p-v) × q / OCF• Here, OCF +FC = (p-v) × q• Thus DOL = 1 + FC / OCF

• Ex) Wettyway sail boat case, at q =50.

• DOL = 1+500,000/[(40,000-20,000) × 50-500,000)] =2.

• It means that at q=50 level, 1% increase in quantity will increase 2% in OCF.

• Here operating degree of operating leverage (DOL) is influenced by fixed and variable costs. Depending on a choice of subcontracting projects, fixed and variable costs changes and then DOL will change too.

• 9) Capital Rationing: The situation that exists if a firm has positive NPV projects but can not find the necessary financing.

• Soft rationing: The situation that occurs when units in a business are allocated a certain amount of financing for capital budgeting.

• Hard rationing: The situation that occurs when a business can not raise financing for a project under any circumstances.