9-1 Copyright 2007 McGraw-Hill Australia Pty Ltd PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan

9-1Copyright 2007 McGraw-Hill Australia Pty Ltd PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan

Chapter Nine

Project Analysis and Evaluation


9.1 Evaluating NPV Estimates

9.2 Scenario and Other ‘What If’ Analysis

9.3 Break-even Analysis

9.4 Operating Cash Flow, Sales Volume and Break-even

9.5 Operating Leverage

9.6 Additional Considerations in Capital Budgeting

Summary and Conclusions

Chapter Organisation


Chapter Objectives• Understand and apply scenario analysis, sensitivity

analysis and simulation analysis to capital project evaluation.

• Apply break-even analysis, distinguishing between accounting break-even, cash break-even and financial break-even.

• Measure the degree of operating leverage of a firm.• Discuss the various managerial options in capital

budgeting.• Outline capital rationing and the difference between

soft and hard rationing.


Evaluating NPV EstimatesThe basic problem: How reliable is our NPV estimate?

• Projected cash flows are based on a distribution of possible outcomes each period, resulting in an ‘average’ cash flow.

• Forecasting risk: the possibility of an incorrect decision due to errors in cash flow projections (GIGO system).

• What sources of value create the estimated NPV?


Scenario and Other ‘What If’ Analysis• Getting started

– Estimate NPV based on initial cash flow projections.

• Scenario analysis– The determination of what happens to NPV estimates when we

ask ‘what if’ questions.

• Sensitivity analysis– Investigation of what happens to NPV when only one variable is

changed.

• Simulation analysis– A combination of scenario and sensitivity analysis used to

construct a distribution of possible NPV estimates.


Example—Fairways Driving Range

Fairways Driving Range expects annual rentals to be 20,000 buckets at $3 per bucket. Equipment costs $20,000 and is depreciated using the straight-line method over five years to a zero salvage value. Variable costs are 10 per cent of rentals income and fixed costs are $40,000 per year. Assume no increase in working capital and no additional capital outlays. The required rate of return is 15 per cent and the tax rate is 30 per cent.


Fairways Example—Net Profit


Fairways Example—Getting Started• Estimated annual cash flow:

$10 000 + $4000 – $3000 = $11 000

• At 15%, the 5-year annuity factor is 3.3522.

• The base case NPV is then:

NPV = – $20 000 + ($11 000 × 3.3522)

= $16 874


Fairways Example—Scenario Analysis

Inputs for scenario analysis:

• Base case: Rentals are 20,000 buckets p.a., variable costs

are 10 per cent of rental income, fixed costs are $40,000,

depreciation is $4,000 p.a.

• Best case: Rentals are 25,000 buckets p.a., variable costs are 8 per cent of rental income, fixed costs are $40,000, depreciation is $4,000 p.a.

• Worst case: Rentals are 18,000 buckets p.a., variable costs are 12 per cent of rental income, fixed costs are $40,000, depreciation is $4,000 p.a.


Fairways Example—Scenario Analysis


Fairways Example—Sensitivity Analysis

Inputs for sensitivity analysis:

• Base case: Rentals are 20,000 buckets p.a., variable costs are 10 per cent of rental income, fixed costs are $40,000, depreciation is $4,000 p.a.

• Best case: Rentals are 25,000 buckets p.a. All other variables are the same as the base case.

• Worst case: Rentals are 18,000 buckets p.a. All other variables are the same as the base case.




Base case

NPV = $16 874

NPV

Worst case

NPV = $4 202

Rentals per Year

Best case

NPV = $48 552

0

–$60 00015 000

25 00020 000

$60 000

x

x

x



Simulation Analysis• An extended version of scenario analysis that uses

probability distributions and considers the interrelationships between variables.

• Usually performed with computer programs.• Program selects values for each variable and

calculates NPV. This process is repeated many times.

• End result: Probability distribution of NPV based on a sample of 1,000 or more values.

• Use is becoming more common, particularly for large-scale projects.


Simulation Analysis – Sample Output

• Output shows that there is a less than 50% chance that the NPV will be positive.


Break-even Analysis• Useful for analysing the relationship between sales

volume and profitability.

• Break-even point is the sales volume at which the present value of the project’s cash inflows and outflows are equal NPV = 0.

• Important distinction between variable costs and fixed costs.

• Accounting break-even is the sales volume that results in a zero net profit.


Fixed, Variable and Total Costs• Variable costs:

– Variable costs change when the quantity of output changes– Total variable costs = quantity × cost per unit

• Fixed costs:– Fixed costs are constant, regardless of output, over some

time period

• Total costs:– Total Costs = fixed + variable = FC + vQ


Example―Fixed, Variable and Total Costs• Your firm pays $8,000 per month in fixed costs. You

also pay $3 per unit to produce your product. What is the total cost if you produce 1,000 units? What about 5,000? 10,000?

Total cost if you produce 1,000 units = 8,000 + 3(1,000) = $11,000




Output Level and Total Costs


Average versus Marginal Cost• Average Cost

– TC/number of units– Decreases as number of units increases.

• Marginal Cost

– The cost to produce one more unit– Same as variable cost per unit


Example―Average versus Marginal Cost• Example:

What is the average cost and marginal cost under each situation in the previous example?

Produce 1,000 units: Average = $11,000/1,000 = $11

Produce 5,000 units: Average = $23,000/5000 = $4.60

Produce 10,000 units: Average = $38,000/10,000 = $3.80

Marginal cost of producing one more unit is $3.


Accounting Break-even PointGeneral expression

Q = (FC + D)/(P – v)

where:

Q = total units sold

FC = total fixed costs

D = depreciation

P = price per unit

v = variable cost per unit

Note: At accounting break-even, net income = 0, NPV is

negative and IRR =0.


Using Accounting Break-even• Accounting break-even is often used as an early-

stage screening number.

• If a project cannot break even on an accounting basis, then it is not going to be a worthwhile project.

• Accounting break-even gives managers an indication of how a project will impact accounting profit.


Fairways Example—Accounting Break-even Analysis

ndep' cost fixed cost variable costs accounting Total

cost fixed cost variablecost Total



buckets 296 16

$0.30$3.00

$4000000 $40

unitper cost Variableunitper Price

onDepreciatiFCcosts Fixed

v P

D Q

Solve algebraically for break-even quantity (Q):

If sales do not reach 16,296 buckets, Fairways will incur losses in both the accounting sense and the financial sense.


Accounting

break-even point

16 296 buckets

Rentals per Year

$50 000

$20 00015 000

25 000

$80 000

Total revenues

Fixed costs

+ Dep’n =

$44 000Net

Income < 0

Net

Income > 0

20 000

Total accounting

costs



Other Break-even Measures• Cash break-even

– Q = FC/(p – v)– At cash break-even, OCF = 0, NPV is negative and IRR =

–100%.

• Financial break-even– Q = (FC + OCF)/(P – v)– At financial break-even, NPV = 0 and IRR = required

return.


Fairways Example—Break-even Measures

0 NPV 15% IRR

units 024 17 $0.30 $3.00

$5966 000 $40 even -break Financial

000 $20 NPV 100% IRR

units 815 14 $0.30 $3.00

000 $40 even -breakCash

591 $6 NPV 0 IRR

units 296 16 $0.30 $3.00

$4000 000 $40 even -break Accounting


Operating Leverage• The degree to which a firm or project is committed

to its fixed costs.

• The degree of operating leverage (DOL) is the percentage change in operating cash flow relative to the percentage change in quantity sold.

OCF

FC1DOL

in %DOLOCFin %

Q


Operating Leverage (continued)• The higher the degree of operating leverage, the

greater the danger from forecasting risk.

• The lower the degree of operating leverage, the lower the break-even point.

• DOL depends on the current sales level.


Fairways Example—DOL• Let Q = 20 000 buckets and, ignoring taxes, OCF = $14 000 and

FC = $40 000.

• A 10 per cent increase (decrease) in quantity sold will result in a 38.57 per cent increase (decrease) in OCF.

• Note: Higher DOL equals greater volatility (risk) in OCF and leverage is a two-edged sword—sales decreases will be magnified as much as increases.

3.857 000 $14

000 $40 1 DOL


Managerial Options• A static DCF analysis ignores management’s ability

to modify the project as events occur.

• Managerial options are opportunities that managers can exploit if certain things happen in the future.

• There are a great number of these options. For example, a product’s pricing, manufacturing and advertising can all be changed after the product is launched.


Contingency Planning• Contingency planning takes into account the

managerial options that are implicit in a project.

• The broad classes of options are:– The option to expand– The option to abandon– The option to wait– Strategic options (e.g. ‘toe hold’ investments, and research

and development).


Capital Rationing• A situation that exists if a firm has positive NPV

projects but cannot find the necessary financing.

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

• Hard rationing occurs when the firm is unable to raise the financing for a project under any circumstances.


Summary and Conclusions• Errors in projected future cash flows lead to

misleading NPVs. This is forecasting risk.• Scenario and sensitivity analysis help identify

variables critical to a project.• Break-even analysis in its various forms is useful for

identifying critical sales levels.• Operating leverage is a key determinant of break-

even levels.• Projects usually have future managerial options

associated with them.• Capital rationing occurs when profitable projects

cannot be funded.

Documents

9-1 Copyright 2007 McGraw-Hill Australia Pty Ltd PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan