Chapter 11 Project Analysis and Evaluation 11.1Evaluating NPV Estimates 11.2Scenario and Other...

Chapter 11

Project Analysis and Evaluation

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

Vigdis Boasson Mgf301, School of Management, SUNY at Buffalo

Vigdis Boasson MGF301, School of Management, SUNY at Buffalo

11.2 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

11.3 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

11.4 Fairways Driving Range Example

Fairways Driving Range expects rentals to be 20,000 buckets at $3 per bucket. Equipment costs are $20,000 depreciated using SL over 5 years and have a $0 salvage value. Variable costs are 10% of rentals and fixed costs are $45,000 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 (20k x $3): $60,000

Variable Costs (.10 x 60k): 6,000

Fixed Costs: 45,000

Depreciation (20k /5yrs): 4,000

EBIT: 5,000

Taxes (@15%) 750

Net Income $ 4,250

11.4 Fairways Driving Range Example (concluded)

Estimated annual cash inflows:

$5,000 + 4,000 - 750 = $8,250

r= 15%, t=5. The base-case NPV is:

NPV = -I + C x {1 - [1/(1 + r)t]}/rNPV = $-20,000 + ($8,250 {1 - [1/(1.15)5]}/.15) = $7,654.

11.5 Fairways Driving Range Scenario Analysis

INPUTS FOR SCENARIO ANALYSIS

Scenario analysis: putting lower and upper bounds on cash flows. Poor revenues with high costs, high revenues with low costs.

Base Case: Rentals are 20,000 buckets, variable costs are 10% of revenues, fixed costs are $45,000, 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 $45,000, depreciation is $4,000 per year, and the tax rate is 15%.

Worst Case: Rentals are 15,000 buckets, variable costs 12% of revenues, fixed costs are $45,000, depreciation is $4,000 per year, and the tax rate is 15%.

11.5 Fairways Driving Range Best Case Scenario

Revenues (25k x $3): $75,000

Fixed Costs: 45,000

EBIT: 20,000

Taxes (@15%) 3,000

Net Income $ 17,000

OCF = EBIT + Dep. - Taxes = 20,000 + 4,000 - 3,000 = 21,000

11.5 Fairways Driving Range:Worst Case Scenario

Worst Case: Rentals are 15,000 buckets, variable costs 12% of revenues, fixed costs are $45,000, depreciation is $4,000 per year, and the tax rate is 15%.

Revenues (15k x $3): $45,000

Fixed Costs: 45,000

EBIT: -9,400

Taxes (@15%) 0

Net Income $ -9,400

OCF = EBIT + Dep. - Taxes = -9,400 + 4,000 - 0 = -5,400

11.5 Fairways Driving Range Scenario Analysis (concluded)

Scenario Rentals(units) Revenues Net Income Cash Flow

Best Case 25,000 $75,000 $17,000 $21,000

Base Case 20,000 60,000 4,250 8,250

Worst Case 15,000 45,000 -9,400 -5,400

Note that the worst case results in a tax credit. This assumes that the owners had other income against which the loss is offset.

11.6 Fairways Driving Range Sensitivity Analysis

INPUTS FOR SENSITIVITY ANALYSIS

Sensitivity analysis: hold all projections constant except one, alter that one, and see how sensitive cash flow is to that one when it changes - the point is to get a fix on where forecasting risk may be especially severe.

Base Case: Rentals are 20,000 buckets, variable costs are 10% of revenues, fixed costs are $45,000, 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 15,000 buckets and revenues are $45,000. All other variables are unchanged.

11.6 Fairways Driving Range : Best Case Sensitivity Analysis

Revenues (25k x $3): $75,000

Fixed Costs: 45,000

EBIT: 18,500

Taxes (@15%) 2,775

Net Income $ 15,725

OCF = EBIT + Dep. - Taxes = 18,500 + 4,000 - 2,775 = 19,725

NPV = $-20,000 + ($19,725 {1 - [1/(1.15)5]}/.15) = $46,121.

11.6 Fairways Driving Range :Worst Case Sensitivity Analysis

Worst Case: Rentals are 15,000 buckets, variable costs are 10% of revenues, fixed costs are $45,000, depreciation is $4,000 per year, and the tax rate is 15%.

Revenues (15k x $3): $45,000

Fixed Costs: 45,000

EBIT: -8,500

Taxes (@15%) 1,275

Net Income -$ 7,225

OCF = EBIT + Dep. - Taxes = -8,500 + 4,000 + 1,275 = -3,225

*Assume a tax credit is created in the worst case.

NPV = $-20,000 + (-3,225 {1 - [1/(1.15)5]}/.15) = -$30,811.

11.6 Fairways Driving Range Sensitivity Analysis (concluded)

Scenario Rentals Revenues Net Income Cash Flow NPV

Best Case 25,000 $75,000 $15,725 $19,725 $46,121

Base Case 20,000 60,000 4,250 8,250 $7,655

Worst Case 15,000 45,000 -7,225 -3,225 -$30,811

Note that the worst case results in a tax credit. This assumes that the owners had other income against which the loss is offset.

11.7 Fairways Driving Range: Rentals vs. NPV

Fairways Sensitivity Analysis - Rentals vs. NPV

Base case

NPV = $7,655

Worst case

NPV = -$30,811

Rentals per Year

Best case

NPV = $46,121

-$60,00015,000

25,00020,000

$60,000

11.8 Fairways Driving Range: Total Cost Calculations

TC = VC + FC

TC = (Q x v ) + FC

Rentals Variable Cost Fixed Cost Total Cost

0 $0 $45,000 $45,000

15,000 4,500 45,000 49,500

20,000 6,000 45,000 51,000

25,000 7,500 45,000 52,500

11.9 Fairways Driving Range: Break-Even Analysis

Fairways Break-Even Analysis - Sales vs. Costs and Rentals

Break-Even Point

18,148 Buckets

Sales and Costs

Rentals per Year

$50,000

$20,00015,000

25,00020,000

$80,000

Total Revenues

Fixed Costs + Dep

$49,000

Net Income > 0

Net Income < 0

11.10 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)

= ($45,000 + 4,000)/($3.00 - .30)

= 18,148 buckets

11.11 Chapter 11 Example

Assume you have the following information:

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%

Break-Even Computations

A. Accounting Break-Even

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

EBIT = 5 x 7,000 - 3 x 7,000 - 10,000 - 4,000) = 0

OCF = 0 + 4,000 - 0 = 4,000

r = 20% t = 5 years Initial cost = $20,000

IRR = 0 ; NPV = -$8,038

Break-Even Computations

B. Cash Break-Even

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

EBIT = 5 x 5,000 - 3 x 5,000 - 10,000 - 4,000) = -4,000

OCF = -4,000 + 4,000 - 0 = 0

r = 20% t = 5 years Initial cost = $20,000

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

C. Financial Break-Even

Q = (FC + OCF)/(P - v), where OCF is the level of OCF that results in a zero NPV. A project that breaks even on a financial basis has a discounted payback equal to its life, a zero NPV, and IRR just equal to the required return.

NPV = -I + C x {1 - [1/(1 + r)t]}/r

C x {1 - [1/(1 + r)t]}/r = NPV + I

NPV = 0, r = 20%, t = 5 years, Initial cost = $20,000

C x {1 - [1/(1.205]}/.20 = 0 + 20,000

C x 2.9906 = 20,000

C = 20,000 / 2.9906 = 6,688

Q = (FC + OCF)/(P - v)=($10,000 + 6,688)/($5 - 3) = 8,344 units

IRR = 20% ; NPV = 0, Payback=5 years.

11.12 Summary of Break-Even Measures (Table 11.1)

I. The General Expression

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

where: FC = total fixed costs, P =Price per unit, v =variable cost per unit.

II. The Accounting Break-Even Point

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

At the Accounting BEP, Net income = 0.

III. The Cash Break-Even Point

Q = FC/(P - v)

At the Cash BEP, OCF = 0.

IV. The Financial Break-Even Point

Q = (FC + OCF*)/(P - v) At the Financial BEP, NPV = 0. (OCF* is the OCF at which NPV = 0.)

11.13 Fairways Driving Range: Degree of Leverage (DOL)

DOL is a “multiplier” which measures the effect of a change in quantity sold on OCF.

% in OCF = DOL % in Q

DOL = 1 + FC/OCF

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

OCF = $9,000 and fixed costs = $45,000.

Fairway’s DOL = 1 + FC/OCF = 1 + $45,000/$9,000 = 6.0.

In other words, a 10% increase (decrease) in quantity sold will result in a (6 x 10%) = 60% increase (decrease) in OCF.

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.

11.14 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

Possible future investments that may result from an investment under consideration.

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

11.15 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.

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

11.17 Solution to Problem 11.1

BetaBlockers, Inc. (BBI) manufactures sunglasses. The variable material cost is $0.63 per unit and the variable labor cost is $2.02 per unit.

a. What is the variable cost per unit?

VC = variable material cost + variable labor cost

= $0.63 + $2.02 = $2.65

b. Suppose BBI incurs fixed costs of $415,000 during a year when production is 250,000 units. What are total costs for the year?

TC = total variable costs + fixed costs

= ($2.65)(250,000) + $ 415,000 = $ 1,077,500

11.17 Solution to Problem 11.1 (concluded)

c. If the selling price is $5.50 per unit, does BBI break even on a cash basis? If depreciation is $150,000, what is the accounting break-even point?

Q cash = (FC ) / (P - v) = $415,000/($5.5 - $ 2.65)

= 145,614 units

Q account = (FC + Dep) / (P - v) = ($415,000 + $ 150,000)/($5.50 -

$2.65)

= 198,246 units

11.18 Solution to Problem 11.13

A proposed project has fixed costs of $25,000 per year. OCF at 4,000 units is $60,000.

1. Ignoring taxes, what is the degree of operating leverage (DOL)?

DOL = 1 + FC/OCF = 1 + ($25,000/$60,000) = 1.4167

2. If quantity sold rises from 7,000 to 7,300, what will the increase in OCF be?

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

% OCF = DOL(% Q) =1.4167 x 4.29% = 6.07%

New OCF = ($60,000)(1.0607) = $63,642

3. What is the new DOL?

DOL at 7,300 units = 1 + ($25,000/$63,642) = 1.3928

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