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
Vigdis Boasson MGF301, School of Management, SUNY at Buffalo
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
Vigdis Boasson MGF301, School of Management, SUNY at Buffalo
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
Vigdis Boasson MGF301, School of Management, SUNY at Buffalo
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.
Vigdis Boasson MGF301, School of Management, SUNY at Buffalo
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%.
Vigdis Boasson MGF301, School of Management, SUNY at Buffalo
11.5 Fairways Driving Range Best Case Scenario
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%.
Revenues (25k x $3): $75,000
Variable Costs (.08 x 75k): 6,000
Fixed Costs: 45,000
Depreciation (20k /5yrs): 4,000
EBIT: 20,000
Taxes (@15%) 3,000
Net Income $ 17,000
OCF = EBIT + Dep. - Taxes = 20,000 + 4,000 - 3,000 = 21,000
Vigdis Boasson MGF301, School of Management, SUNY at Buffalo
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
Variable Costs (.12 x 45k): 5,400
Fixed Costs: 45,000
Depreciation (20k /5yrs): 4,000
EBIT: -9,400
Taxes (@15%) 0
Net Income $ -9,400
OCF = EBIT + Dep. - Taxes = -9,400 + 4,000 - 0 = -5,400
Vigdis Boasson MGF301, School of Management, SUNY at Buffalo
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.
Vigdis Boasson MGF301, School of Management, SUNY at Buffalo
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.
Vigdis Boasson MGF301, School of Management, SUNY at Buffalo
11.6 Fairways Driving Range : Best Case Sensitivity Analysis
Best Case: Rentals are 25,000 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 (25k x $3): $75,000
Variable Costs (.10 x 75k): 7,500
Fixed Costs: 45,000
Depreciation (20k /5yrs): 4,000
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.
Vigdis Boasson MGF301, School of Management, SUNY at Buffalo
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): $45,000
Variable Costs (.10 x 45k): 4,500
Fixed Costs: 45,000
Depreciation (20k /5yrs): 4,000
EBIT: -8,500
Taxes (@15%) 1,275
Net Income -$ 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.
Vigdis Boasson MGF301, School of Management, SUNY at Buffalo
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.
Vigdis Boasson MGF301, School of Management, SUNY at Buffalo
11.7 Fairways Driving Range: Rentals vs. NPV
Fairways Sensitivity Analysis - Rentals vs. NPV
Base case
NPV = $7,655
NPV
Worst case
NPV = -$30,811
Rentals per Year
Best case
NPV = $46,121
0
-$60,00015,000
25,00020,000
$60,000
x
x
x
Vigdis Boasson MGF301, School of Management, SUNY at Buffalo
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
Vigdis Boasson MGF301, School of Management, SUNY at Buffalo
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
Vigdis Boasson MGF301, School of Management, SUNY at Buffalo
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
Vigdis Boasson MGF301, School of Management, SUNY at Buffalo
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%
Vigdis Boasson MGF301, School of Management, SUNY at Buffalo
11.11 Chapter 11 Example
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
Vigdis Boasson MGF301, School of Management, SUNY at Buffalo
11.11 Chapter 11 Example
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
Vigdis Boasson MGF301, School of Management, SUNY at Buffalo
11.11 Chapter 11 Example
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.
Vigdis Boasson MGF301, School of Management, SUNY at Buffalo
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.)
Vigdis Boasson MGF301, School of Management, SUNY at Buffalo
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.
Vigdis Boasson MGF301, School of Management, SUNY at Buffalo
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.
Vigdis Boasson MGF301, School of Management, SUNY at Buffalo
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).
Vigdis Boasson MGF301, School of Management, SUNY at Buffalo
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
Vigdis Boasson MGF301, School of Management, SUNY at Buffalo
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
Vigdis Boasson MGF301, School of Management, SUNY at Buffalo
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