T11.1 Chapter Outline Chapter 11 Project Analysis and Evaluation Chapter Organization 11.1Evaluating...

T11.1 Chapter Outline

Chapter 11Project Analysis and Evaluation

Chapter Organization

11.1 Evaluating NPV Estimates

11.2 Scenario and Other “What-if” Analyses

11.3 Break-Even Analysis

11.4 Operating Cash Flow, Sales Volume, and Break-Even

11.5 Operating Leverage

11.6 Additional Considerations in Capital Budgeting

11.7 Summary and Conclusions

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copyright © 2002 McGraw-Hill Ryerson, Ltd.

copyright © 2002 McGraw-Hill Ryerson, Ltd Slide 2

T11.2 Evaluating NPV Estimates I: The Basic Problem

The basic problem: How reliable is our NPV estimate? Projected vs. Actual cash flows

Estimated cash flows are based on a distribution of possible outcomes each period

Forecasting risk

The possibility of a bad decision due to errors in cash flow projections - the GIGO phenomenon

Sources of value

What conditions must exist to create the estimated NPV?

“What If” analysis

A. Scenario analysis

B. Sensitivity analysis


T11.3 Evaluating NPV Estimates II: Scenario and Other “What-If” Analyses

Scenario and Other “What-If” Analyses “Base case” estimation

Estimated NPV based on initial cash flow projections

Scenario analysis

Posit best- and worst-case scenarios and calculate NPVs

Sensitivity analysis

How does the estimated NPV change when one of the input variables changes?

Simulation analysis

Vary several input variables simultaneously, then construct a distribution of possible NPV estimates


T11.4 Fairways Driving Range Example

Fairways Driving Range expects rentals to be 20,000 buckets at $3 per bucket. Equipment costs $20,000 and will be depreciated using SL over 5 years and have a $0 salvage value. Variable costs are 10% of rentals and fixed costs are $40,000 per year. Assume no increase in working capital nor any additional capital outlays. The required return is 15% and the tax rate is 15%.

Revenues $60,000

Variable costs 6,000

Fixed costs 40,000

Depreciation 4,000

EBIT $10,000

Taxes (@15%) 1500

Net income $ 8,500


T11.4 Fairways Driving Range Example (concluded)

Estimated annual cash inflows:

$10,000 + 4,000 - 1,500 = $12,500

At 15%, the 5-year annuity factor is 3.352. Thus, the base-case NPV is:

NPV = $-20,000 + ($12,500 3.352) = $21,900.


T11.5 Fairways Driving Range Scenario Analysis

INPUTS FOR SCENARIO ANALYSIS

Base case: Rentals are 20,000 buckets, variable costs are 10% of revenues, fixed costs are $40,000, depreciation is $4,000 per year, and the tax rate is 15%.

Best case: Rentals are 25,000 buckets, variable costs are 8% of revenues, fixed costs are $40,000, depreciation is $4,000 per year, and the tax rate is 15%.

Worst case: Rentals are 18,000 buckets, variable costs are 12% of revenues, fixed costs are $40,000, depreciation is $4,000 per year, and the tax rate is 15%.


T11.5 Fairways Driving Range Scenario Analysis (concluded)

Net ProjectScenario Rentals Revenues Income Cash Flow NPV

Best Case 25,000 $75,000 $21,250 $25,250 $64,635

Base Case 20,000 60,000 8,500 12,500 21,900

Worst Case 18,000 54,000 2,992 6,992 3,437


T11.6 Fairways Driving Range Sensitivity Analysis

INPUTS FOR SENSITIVITY ANALYSIS

Base case: Rentals are 20,000 buckets, variable costs are 10% of revenues, fixed costs are $40,000, depreciation is $4,000 per year, and the tax rate is 15%.

Best case: Rentals are 25,000 buckets and revenues are $75,000. All other variables are unchanged.

Worst case: Rentals are 18,000 buckets and revenues are $54,000. All other variables are unchanged.


T11.6 Fairways Driving Range Sensitivity Analysis (concluded)

Net ProjectScenario Rentals Revenues income cash flow NPV

Best case 25,000 $75,000 $19,975 $23,975 $60,364

Base case 20,000 60,000 8,500 12,500 21,900

Worst case 18,000 54,000 3,910 7,910 6,514


T11.7 Fairways Driving Range: Rentals vs. NPV

Fairways Sensitivity Analysis - Rentals vs. NPV

Base case

NPV = $21,900

NPV

Worst case

NPV = $3,437

Rentals per Year

Best case

NPV = $60,035

0

-$60,00015,000

25,00020,000

$60,000

x

x

x


Break - Even Analysis

Where the crucial variable for a project and its success is sales volume - various forms of break-even analysis can be developed essentially addressing the question of ‘how bad can sales get before we start losing money’

an understanding of the fixed and variable costs associated with the project is important in developing the break-even analysis.

Variable Costs - ‘costs that change when the quantity of output changes.’

Variable cost VC = total quantity (Q) * cost per unit (v) Fixed Costs - ‘costs that do not change when the quantity of output changes

during a particular time period’

• fixed costs are not fixed forever - only for a prescribed period of time; in the long run all costs are variable

Total Costs TC for a given level of output is the sum of the Variable costs VC and fixed costs FC

TC = VC+FC or v*Q + FC Marginal or incremental cost is the change in costs that occurs when there

is a small change in output - what happens to our costs when we produce one more unit


Accounting Break-Even

Accounting break-even is the sales level that results in zero project net income

P = Selling Price per unit v = Variable cost per unit Q = total units sold FC = Fixed Costs D = Depreciation t = Tax rate VC = Variable cost in dollars

Accounting break-even;

Q =(FC+D)/(P-v)


Operating Cash Flow, Sales Volume and Break-Even

Given our focus on cash flow, the next evolution in break-even analysis is to look at the relationship between operating cash flow and sales volume

Cash break-even - the point where operating cash flow (OCF) is zero

OCF = (P-v) *Q - FC or Q = (FC + OCF)/(P-v) Cash break-even then is where OCF = 0

Q = (FC + 0)/(P-v)


Financial Break-Even

The point where the sales level results in a zero NPV the first step is determining OCF for the NPV to be zero a zero NPV occurs when the PV of the OCF equals the original

investment - if the cash flow is the same each year we can use the annuity formula to solve for OCF

• original investment or PV = OCF * annuity future value factor

• OCF = original investment/Annuity future value factor

the financial break-even is often greater than the accounting break-even or conversely when a project just breaks even in an accouning sense it will usually be losing money in a financial or economic sense


Total Cost = Variable cost + Fixed cost

Variable Fixed Total TotalRentals Revenue cost cost cost Depr. acct. cost

0 $0 $0 $40,000 $40,000 $4,000 $44,000

15,000 45,000 4,500 40,000 44,500 4,000 48,500

20,000 60,000 6,000 40,000 46,000 4,000 50,000

25,000 75,000 7,500 40,000 47,500 4,000 51,500

T11.8 Fairways Driving Range: Total Cost Calculations


T11.9 Fairways Driving Range: Break-Even AnalysisFairways Break-Even Analysis - Sales vs. Costs and Rentals

Accounting

break-even point

16,296 Buckets

Rentals per Year

$50,000

$20,00015,000

25,000

$80,000

Total revenues

Fixed costs + Dep

$44,000

Net

Income < 0

Net

Income > 0

20,000


T11.10 Fairways Driving Range: Accounting Break-Even Quantity

Fairways Accounting Break-Even Quantity (Q)

Q = (Fixed costs + Depreciation)/(Price per unit - Variable cost per unit)

= (FC + D)/(P - V)

= ($40,000 + 4,000)/($3.00 - .30)

= 16,296 buckets

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


T11.11 Chapter 11 Quick Quiz -- Part 1 of 2

Assume you have the following information about Vanover Manufacturing:

Price = $5 per unit; variable costs = $3 per unit

Fixed operating costs = $10,000

Initial cost is $20,000

5 year life; straight-line depreciation to 0, no salvage value

Assume no taxes

Required return = 20%


T11.11 Chapter 11 Quick Quiz -- Part 1 of 2 (concluded)

Break-Even Computations

A. Accounting Break-Even

Q = (FC + D)/(P - V) = ($_____ + $4,000)/($5 - 3) = ______ units

IRR = ______ ; NPV ______ ( = -$______ )

B. Cash Break-Even

Q = FC/(P - V) = $10,000/($5 - 3) = ______ units

IRR = ______ ; NPV = ______

B. Financial Break-Even

Q = (FC + $6,688)/(P - V)

= ($10,000 + 6,688)/($5 - 3) = 8,344 units

IRR = ______ ; NPV = ______


T11.11 Chapter 11 Quick Quiz -- Part 1 of 2 (concluded)

Break-Even Computations

A. Accounting Break-Even

Q = (FC + D)/(P - V) = ($10,000 + $4,000)/($5 - 3) = 7,000 units

IRR = 0 ; NPV = -$8,038

B. Cash Break-Even

Q = FC/(P - V) = $10,000/($5 - 3) = 5,000 units

IRR = -100% ; NPV = -$20,000

B. Financial Break-Even

Q = (FC + $6,688)/(P - V)

= ($10,000 + 6,688)/($5 - 3) = 8,344 units

IRR = 20% ; NPV = 0


T11.12 Summary of Break-Even Measures (Table 11.1)

I. The General Expression

Q = (FC + OCF)/(P - V)

where: FC = total fixed costsP = Price per unitv = variable cost per unit

II. The Accounting Break-Even Point

Q = (FC + D)/(P - V)

At the Accounting BEP, net income = 0, NPV is negative, and IRR of 0.

III. The Cash Break-Even Point

Q = FC/(P - V)

At the Cash BEP, operating cash flow = 0, NPV is negative, and IRR = -100%.

IV. The Financial Break-Even Point

Q = (FC + OCF*)/(P - V)

At the Financial BEP, NPV = 0 and IRR = required return.


Operating Leverage

Operating leverage is ‘ the degree to which a firm or project relies on fixed costs’ - what is the relationship between fixed and variable costs for the firm or project.

Low operating leverage means low fixed costs as a proportion of total costs

High operating leverage reflects high fixed costs - often high investmetn in plant and equipment OR in the ‘new economy high investment in research and development to develop software for example.

Once a break-even point is reached, firms or projects with high operating leverage generate higher cash flow/earnings or NPV for each additonal unit sold vs firms with low operating leverage - conversely lower sales volume can magnify cash flow/earnings or NPV in the other direction!

The higher the degree of operating leverage the greater the impact from forecasting risk


Operating Leverage continued

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

% change in OCF = DOL * % change in Q DOL = 1+ FC/OCF

The issue of sub-contracting out certain functions is often a question of operating leverage - sub-contracting has the effect of reducing the DOL as more costs become variable and fixed costs are reduced

Firms operating in the ‘new economy’ e.g. High tech firms can have a high DOL as much of the their investment in research and development is a fixed cost that does not vary with sales volumes - thus the higher degree of leverage to sales volumes

in today’s economic downturn, we are seeing dramatic reductions in reported earnings from prior periods - DOL at work!!


T11.13 Fairways Driving Range DOL

Since % in OCF = DOL % in Q, DOL is a “multiplier” which measures the effect of a change in quantity sold on OCF.

For Fairways, let Q = 20,000 buckets. Ignoring taxes,

OCF = $14,000 and fixed costs = $40,000, and

Fairway’s DOL = 1 + FC/OCF = 1 + $40,000/$14,000 = 3.857.

In other words, a 10% increase (decrease) in quantity sold will result in a 38.57% increase (decrease) in OCF.

Two points should be kept in mind:

Higher DOL suggests greater volatility (i.e., risk) in OCF;

Leverage is a two-edged sword - sales decreases will be magnified as much as increases.


T11.14 Managerial Options and Capital Budgeting

Managerial options and capital budgeting What is ignored in a static DCF analysis?

Management’s ability to modify the project as events occur.

Contingency planning

1. The option to expand

2. The option to abandon

3. The option to wait

Strategic options

1. “Toehold” investments

2. Research and development

Generally, the exclusion of managerial options from the analysis causes us to underestimate the “true” NPV of a project.


T11.15 Capital Rationing

Capital rationing Definition: The situation in which the firm has more good

projects than money.

Soft rationing - limits on capital investment funds set within the firm.

How could this occur in a firm run by rational managers?

Hard rationing - limits on capital investment funds set outside of the firm (i.e., in the capital markets).

How could this occur in capital markets populated by rational investors?


T11.16 Chapter 11 Quick Quiz -- Part 2 of 2

1. What is forecasting risk?

It is the possibility that errors in projected cash flows will lead to incorrect decisions.

2. What is scenario analysis? Why might this exercise be useful for decision-makers to perform, even if their estimates ultimately turn out to be incorrect?

It uses estimates of “Best- and Worst-case” outcomes to see what happens to NPV estimates if things turn out differently than expected. It forces decision-makers to think about the possibility of alternative outcomes.

3. Is it conceivable that the opposite of capital rationing could exist?

Yes - since capital rationing means more good projects than money, the opposite simply means more money than good projects.


T11.17 Solution to Problem 11.1

BetaBlockers, Inc. (BBI) manufactures biotech sunglasses. The variable materials cost is $0.68 per unit and the variable labor cost is $2.08 per unit.

What is the variable cost per unit?

VC = variable material cost + variable labor cost

= $0.68 + $2.08 = $2.76

Suppose BBI incurs fixed costs of $520,000 during a year when production is 250,000 units. What are total costs for the year?

TC = total variable costs + fixed costs

= ($2.76)( ______ ) + $ ______ = $ ______



BetaBlockers, Inc. (BBI) manufactures biotech sunglasses. The variable materials cost is $0.68 per unit and the variable labor cost is $2.08 per unit.

What is the variable cost per unit?

VC = variable material cost + variable labor cost

= $0.68 + $2.08 = $2.76

Suppose BBI incurs fixed costs of $520,000 during a year when production is 250,000 units. What are total costs for the year?

TC = total variable costs + fixed costs

= ($2.76)(250,000) + $520,000 = $1,210,000


T11.17 Solution to Problem 11.1 (concluded)

If the selling price is $6.00 per unit, does BBI break even on a cash basis? If depreciation is $150,000 per year, what is the accounting break-even point?

Qcash = $520,000/($ ______ – $ ______ )

= ______ units

Qacct = ($ ______ + $ ______)/($6.00 – $2.76)

= ______ units



If the selling price is $6.00 per unit, does BBI break even on a cash basis? If depreciation is $150,000 per year, what is the accounting break-even point?

Qcash = $520,000/($ 6.00 – $ 2.76 )

= 160,494 units

Qacct = ($520,000 + $150,000)/($6.00 - $2.76)

= 206,790 units



In each of the following cases, calculate the accounting break-even and the cash break-even points. Ignore any tax effects in calculating the cash break-even.

Unit price Unit VC Fixed costs Depreciation

$1,900 $1,750 $16 million $7 million

30 26 60,000 150,000

7 2 300 365



Solutions

(1) Qacct = ($16M + $___ )/($1,900 - $1,750) = ______ units

Qcash = $16M/($_____ - $ _____ ) = 106,667 units

(2) Qacct = ($60K + $150K)/($__ - $26) = 52,500 units

Qcash = $______ /($30 - $26) = ______ units

(3) Qacct = ($300 + $365)/($7 - $2) = ___ units

Qcash = $300/($7 - $2) = 60 units



Solutions

(1) Qacct = ($16M + $ 7m )/($1,900 - $1,750) = 153,334 units

Qcash = $16M/($1,900 - $ 1,750) = 106,667 units

(2) Qacct = ($60K + $150K)/($30 - $26) = 52,500 units

Qcash = $60,000/($30 - $26) = 15,000 units

(3) Qacct = ($300 + $365)/($7 - $2) = 133 units

Qcash = $300/($7 - $2) = 60 units



A proposed project has fixed costs of $20,000 per year. OCF at 7,000 units is $55,000. Ignoring taxes, what is the degree of operating leverage (DOL)?

If units sold rises from 7,000 to 7,300, what will be the increase in OCF? What is the new DOL?

DOL = 1 + ($20,000/$55,000) = 1.3637

% Q = (7,300 - 7,000)/7,000 = 4.29%

and

% OCF = DOL(% Q) = ______ (4.29) = ____ %

New OCF = ($55,000)(_______ ) = $_______

DOL at 7,300 units = 1 + ($20,000/$ _______ ) = _______



A proposed project has fixed costs of $20,000 per year. OCF at 7,000 units is $55,000. Ignoring taxes, what is the degree of operating leverage (DOL)?

If units sold rises from 7,000 to 7,300, what will be the increase in OCF? What is the new DOL?

DOL = 1 + ($20,000/$55,000) = 1.3637

% Q = (7,300 - 7,000)/7,000 = 4.29%

and

% OCF = DOL(% Q) = 1.3637 (4.29) = 5.85%

New OCF = ($55,000)(1.0585) = $58,218

DOL at 7,300 units = 1 + ($20,000/$58,218) = 1.3435

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