1

CHAPTER 13

Capital Budgeting: Estimating Cash Flows and

Analyzing Risk

2

Chapter Topics Estimating cash flows:

Issues in Project Analysis Depreciation & Tax Effects on Salvage Value Inflation

Risk Analysis: Sensitivity Analysis Scenario Analysis Simulation Analysis

Decision Trees Real Options

3

Relevant Cash Flows:Incremental Cash Flow for a Project

Project’s incremental cash flow is:

Corporate cash flow with the projectMinus

Corporate cash flow without the project.

4

Free Cash Flow

ΔNOWCesExpenditur Capital

Amort& Deprec T)EBIT(1FCF

Capital Expenditures = FA + Deprec

ΔNOWC = Current Operating Assets

– Current Operating Liabilities

Current Operating Assets excludes Marketable Securities

Current Operating Liabilities excludes Notes Payable

5

Free Cash Flow

CF SalvageCF NOWC

CF Operating CF outlay InvestmentFCF

Capital Operating in Investment- OCF FCF

ΔNOWCesExpenditur Capital

Amort& Deprec T)EBIT(1FCF

“Investment outlay CF = CF0

“Operating CF” = Net Income + Non-cash items (deprec) each year

“NOWC CF” = Net working capital requirements each year

“Salvage CF” = After-tax salvage value of assets and NOWC recovery

6

Issues in Project Analysis Purchase of Fixed Assets …………… Y Non-cash charges …………………….. Y Changes in Net Working Capital……Y Interest/Dividends …………..……….. N “Sunk” Costs …………………………….. N Opportunity Costs …………………….. Y Externalities/Cannibalism …………… Y Tax Effects ………………………..…….. Y

7

Depreciation Basics

• Straight Line Salvage Value

• MACRS 0•Recovery Period = Class Life•1/2 Year Convention

8

TABLE 13.1

MACRS Depreciation Classes

9TABLE 13.2

MACRS Depreciation

10

Annual Depreciation Expense (000s)

Year1234

% 0.330.450.150.07

Depr$ 79.2 108.0 36.0 16.8

x Basis = $240

Book Depr Value 79.2 160.8 187.2 52.8 223.2 16.8 240.0 0

SCC (Minicase): Equipment cost $200

Shipping 10Installation 30

11

Tax Effect on Salvage

• Net Cash flow from sale = Sale proceeds

- taxes paid

• Tax basis = difference between sales price and book value, where:

Book value = Original basis - Accumulated

depreciation

12

Tax Effect on Salvage

Net Salvage Cash Flow = SP - (SP-BV)(T)

Where:SP = Selling PriceBV = Book ValueT = Corporate tax rate

13

BV (EOY 3) = $17

IF: Selling price = $20 TCF = $20 - (20-17)(.4) = $18.8

IF: Selling price = $10 TCF = $10 - (10-17)(.4) = $12.8

Example: If Asset Sold After 3 Years

14

Adjusting for Inflation

Nominal r > real r The cost of capital, r, includes a

premium for inflation Nominal CF > real CF

Nominal cash flows incorporate inflation

If you discount real CF with the higher nominal r, then your NPV estimate is biased downward.

15

INFLATIONReal vs. Nominal Cash flows

tt

n

0t WACC1

CFNPV

Nominal

Real

16

INFLATIONReal vs. Nominal Cash flows 2 Ways to adjust

Adjust WACC Cash Flows = Real Adjust WACC to remove inflation

Adjust Cash Flows for Inflation Use Nominal WACC

17

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A B C

Regency Integrated Chips Chapter 13

Part I: Background Data: (000)Inputs

Building Cost (=Depreciable base) 12,000$

Building MACRS class 39 yearEquipment Cost (= Depreciable base) 8,000$ Equipment MACRS class 5 yearNet Operating WC/Sales 10%First year sales (in units) 20,000 Growth rate in units sold 0%

Sales price per unit 3.00$ Variable cost per unit 2.10$ Fixed costs 8,000.00$ Market value of Building in Year 4 7,500.00$ Market Value of Equipment in Year 4 2,000.00$ Tax rate 40%WACC 12%Inflation: growth in sales price 2%Inflation: growth in VC per unit 2%Inflation: growth in fixed costs 1%

18

RIC – Depreciation & Salvage Value

2324252627282930313233343536373839404142

A B C D E F GPart 2: Depreciation Calculations:

Building 12,000$ 1 2 3 4MACRS % (Bldg-39 yr)) 1.3% 2.6% 2.6% 2.6%

Recovery Allowance 156$ 312$ 312$ 312$ Accumulated Depreciation 156$ 468$ 780$ 1,092$

Book Value 11,844$ 11,532$ 11,220$ 10,908$ Equipment 8,000$

MACRS % (Eqpt-5 yr) 20.0% 32.0% 19.0% 12.0%Recovery Allowance 1,600$ 2,560$ 1,520$ 960$

Accumulated Depreciation 1,600$ 4,160$ 5,680$ 6,640$ Book Value 6,400$ 3,840$ 2,320$ 1,360$

Part 3: Salvage Values in Year 4Building Equipment

Market (salvage) Value (Year 4) 7,500$ 2,000$ Book Value (Year 4) 10,908 1,360Capital Gain/Loss (3,408) 640Taxes (1,363) 256Net SV (SV-Taxes) 8,863 1,744

Total Net Salvage Value 10,607

Year

19

RIC – Sales, Costs and NWC

4546474849505152

A B C D E F GYEAR Number 0 1 2 3 4

Part 4: Projected Net Cash ($000)Units Sold 20,000 20,000 20,000 20,000 Sales Price/Unit 3.00$ 3.06 3.12 3.18Fixed Cost 8,000$ 8,080$ 8,161$ 8,242$ Variable Cost per unit 2.10$ 2.14$ 2.18$ 2.23$ Sales 60,000$ 61,200$ 62,424$ 63,672$ NWC Required 6,000$ 6,120$ 6,242$ 6,367$ -$

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B CFirst year sales (in units) 20,000 Growth rate in units sold 0%

Sales price per unit 3.00$ Variable cost per unit 2.10$ Fixed costs 8,000.00$ Inflation: growth in sales price 2%Inflation: growth in VC per unit 2%Inflation: growth in fixed costs 1%

20

RIC – Cash Flow Estimation

454654555657585960616263646566676869707172

A B C D E F GYEAR Number 0 1 2 3 4

Part 4: Projected Net Cash ($000)Initial Investment

Building (12,000)$ Equipment (8,000)Net Working Capital (see below)Total Investment (20,000)Sales 60,000$ 61,200$ 62,424$ 63,672$ Variable Costs 42,000 42,840 43,697 44,571Fixed Costs 8,000 8,080 8,161 8,242Depreciation (Bldg) 156 312 312 312Depreciation (Eqpt)) 1,600 2,560 1,520 960

EBT 8,244 7,408 8,734 9,587Taxes 3,298 2,963 3,494 3,835Net Operating Income 4,946 4,445 5,241 5,752Add back Depreciation 1,756 2,872 1,832 1,272CASH FLOW from Operations 6,702 7,317 7,073 7,024Investment in NWC (6,000) (120) (122) (125) 0Recovery of NWC 6,367Salvage Value 10,607TOTAL PROJECTED CF (26,000)$ 6,582$ 7,194$ 6,948$ 23,999$

21

RIC: Cash Flow Analysis

45467273747576777879808182

838485868788

A B C D E F GYEAR Number 0 1 2 3 4

Part 4: Projected Net Cash ($000)TOTAL PROJECTED CF (26,000)$ 6,582$ 7,194$ 6,948$ 23,999$

Discounted Cash Flows (26,000)$ 5,877$ 5,735$ 4,945$ 15,252$

0 1 2 3 4Cumulative Cash Flows for Payback (26,000)$ (19,418)$ (12,223)$ (5,275)$ 18,723$

FALSE FALSE FALSE FALSE 3.22

Cumulative Discounted Cash Flows (26,000)$ (20,123)$ (14,388)$ (9,442)$ 5,809$ FALSE FALSE FALSE FALSE 3.62

NPV 5,809$ IRR 20.12%

MIRR 17.79%PB 3.22

DPB 3.62PI 1.22

22

Excel Functions

838485868788

C D H INPV 5,809$ =NPV(C18,D72:G72)+C72IRR 20.12% =IRR(C72:G72)

MIRR 17.79% =MIRR(C72:G72,C18,C18)PB 3.22 =MAX(C78:G78)

DPB 3.62 =MAX(C81:G81)PI 1.22 =(D83-C72)/-C72

23

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838485868788

A B C D E F G H I

Regency Integrated Chips Chapter 13

Part I: Background Data: (000) SOURCES ("L" = Line)Inputs

Building Cost (=Depreciable base) 12,000$ RESULTS Data from textbook

Building MACRS class 39 year NPV 5,809$ Equipment Cost (= Depreciable base) 8,000$ IRR 20.12%Equipment MACRS class 5 year MIRR 17.79% Results recapped from belowNet Operating WC/Sales 10% PB 3.22First year sales (in units) 20,000 DPB 3.62Growth rate in units sold 0% PI 1.22

Sales price per unit 3.00$ Variable cost per unit 2.10$ Fixed costs 8,000.00$ Market value of Building in Year 4 7,500.00$ Market Value of Equipment in Year 4 2,000.00$ Tax rate 40%WACC 12%Inflation: growth in sales price 2%Inflation: growth in VC per unit 2%Inflation: growth in fixed costs 1%

Part 2: Depreciation Calculations:Building 12,000$ 1 2 3 4

MACRS % (Bldg-39 yr)) 1.3% 2.6% 2.6% 2.6% Footnote: Page 461Recovery Allowance 156$ 312$ 312$ 312$ C24 * MACRS recovery % (L25)

Accumulated Depreciation 156$ 468$ 780$ 1,092$ Book Value 11,844$ 11,532$ 11,220$ 10,908$ C24-Accumulated Depreciation (L27)

Equipment 8,000$ MACRS % (Eqpt-5 yr) 20.0% 32.0% 19.0% 12.0% Table on page 461Recovery Allowance 1,600$ 2,560$ 1,520$ 960$ C29 * MACRS recovery % (L30)

Accumulated Depreciation 1,600$ 4,160$ 5,680$ 6,640$ Book Value 6,400$ 3,840$ 2,320$ 1,360$ C29-Accumulated Depreciation (L32)

Part 3: Salvage Values in Year 4Building Equipment

Market (salvage) Value (Year 4) 7,500$ 2,000$ C15; C16Book Value (Year 4) 10,908 1,360 G28; G33Capital Gain/Loss (3,408) 640 Market value - Book value (L37-L38)Taxes (1,363) 256 Gain/loss * tax rate (L39*$C17)Net SV (SV-Taxes) 8,863 1,744 Market value - taxes (L37-L40)

Total Net Salvage Value 10,607 Sum of building + equipment D41+E41

YEAR Number 0 1 2 3 4Part 4: Projected Net Cash ($000)

Units Sold 20,000 20,000 20,000 20,000 C10Sales Price/Unit 3.00$ 3.06 3.12 3.18 C12 adjusted for inflation (C19)Fixed Cost 8,000$ 8,080$ 8,161$ 8,242$ C14 adjusted for inflation (C21)Variable Cost per unit 2.10$ 2.14$ 2.18$ 2.23$ C13 adjusted for inflation (C20)Sales 60,000$ 61,200$ 62,424$ 63,672$ L47 * L48NWC Required 6,000$ 6,120$ 6,242$ 6,367$ -$ 10% (C9) of next year's sales (L51)

Initial InvestmentBuilding (12,000)$ C5Equipment (8,000) C7Net Working Capital (see below)Total Investment (20,000)Sales 60,000$ 61,200$ 62,424$ 63,672$ L51 = L47 * L48Variable Costs 42,000 42,840 43,697 44,571 L50 * L47Fixed Costs 8,000 8,080 8,161 8,242 L49Depreciation (Bldg) 156 312 312 312 L26Depreciation (Eqpt)) 1,600 2,560 1,520 960 L31

EBT 8,244 7,408 8,734 9,587 L59-L60-L61-L62-L63Taxes 3,298 2,963 3,494 3,835 L64 * tax rate (C17)Net Operating Income 4,946 4,445 5,241 5,752 L64-L65Add back Depreciation 1,756 2,872 1,832 1,272 L62+L63CASH FLOW from Operations 6,702 7,317 7,073 7,024 L66+L67Investment in NWC (6,000) (120) (122) (125) 0 =IF(D52=0,0,C52-D52)Recovery of NWC 6,367 =-SUM(C69:G69)Salvage Value 10,607 E42TOTAL PROJECTED CF (26,000)$ 6,582$ 7,194$ 6,948$ 23,999$ E59+E70+E71+E72+E73

Discounted Cash Flows (26,000)$ 5,877$ 5,735$ 4,945$ 15,252$ L72 discounted at WACC (C18)

0 1 2 3 4 L45Cumulative Cash Flows for Payback (26,000)$ (19,418)$ (12,223)$ (5,275)$ 18,723$

FALSE FALSE FALSE FALSE 3.22 =IF(C77>0,B76+ABS(B77)/C72)

Cumulative Discounted Cash Flows (26,000)$ (20,123)$ (14,388)$ (9,442)$ 5,809$ FALSE FALSE FALSE FALSE 3.62 =IF(C80>0,B76+ABS(B80)/C74)

NPV 5,809$ =NPV(C18,D72:G72)+C72IRR 20.12% =IRR(C72:G72)

MIRR 17.79% =MIRR(C72:G72,C18,C18)PB 3.22 =MAX(C78:G78)

DPB 3.62 =MAX(C81:G81)PI 1.22 =(D83-C72)/-C72

Year

RIC

Background Data

Salvage Value

Basic Calculations

Cash Flow Estimation

Cash Flow Analysis

Key

24

“Risk” in Capital Budgeting

Uncertainty about a project’s future profitability

Measured by σNPV, σIRR, beta Will taking on the project increase

the firm’s and stockholders’ risk?

25

Three types of relevant risk

Stand-alone risk Corporate risk Market (or beta) risk

26

Stand-Alone Risk

The project’s risk if it were the firm’s only asset and there were no shareholders.

Ignores both firm and shareholder diversification.

Measured by the σ or CV of NPV, IRR, or MIRR.

27

0 E(NPV)

Flatter distribution,larger , largerstand-alone risk.

NPV

Probability Density

28

Corporate Risk

Reflects the project’s effect on corporate earnings stability.

Considers firm’s other assets (diversification within firm).

Depends on project’s σ, and its correlation, ρ, with returns on firm’s other assets.

Measured by the project’s corporate beta.

29

Profitability

0 Years

Project X

Total Firm

Rest of Firm

Project X is negatively correlated to firm’s other assets → big

diversification benefits

If r = 1.0, no diversification benefits. If r < 1.0, some diversification benefits

30

Market Risk

Reflects the project’s effect on a well-diversified stock portfolio.

Takes account of stockholders’ other assets.

Depends on project’s σ and correlation with the stock market.

Measured by the project’s market beta.

31

Conclusions on Risk Stand-alone risk is easiest to

measure, more intuitive. Core projects are highly correlated

with other assets, so stand-alone risk generally reflects corporate risk.

If the project is highly correlated with the economy, stand-alone risk also reflects market risk.

32

Sensitivity Analysis

Shows how changes in an input variable affect NPV or IRR

Each variable is fixed except one Change one variable to measure the

effect on NPV or IRR Answers “what if” questions

33

RIC: Sensitivity Analysis

203204205206207208209210211212

B C D E F G HDeviation

from Sales Variable Growth Year 1 NonvariableBase Case Price Cost/Unit Rate Units Sold Cost WACC

-30% ($27,223) $29,404 ($4,923) ($3,628) $10,243 $9,030-15% ($10,707) $17,607 ($115) $1,091 $8,026 $7,3620% $5,809 $5,809 $5,809 $5,809 $5,809 $5,809

15% $22,326 ($5,988) $12,987 $10,528 $3,593 $4,36330% $38,842 ($17,785) $21,556 $15,247 $1,376 $3,014

Range $66,064 $47,189 $26,479 $18,875 $8,867 $6,016

NPV at Different Deviations from Base

34

RIC: Sensitivity Graph

($30,000)

($20,000)

($10,000)

$0

$10,000

$20,000

$30,000

$40,000

-30% -15% 0% 15% 30%

Deviation from Base-Case Value (%)

NPV ($)Sales price

Variable cost

Growth rate

Units sold

Nonvariable cost

WACC

35

Results of Sensitivity Analysis

Steeper sensitivity lines = greater risk Small changes → large declines in NPV

Unit sales line is steeper than salvage value or r, so for this project, should worry most about accuracy of sales forecast

36

RIC: Sensitivity Analysis148149150151152153154155156157158159160161162163164165166167168169170171172173174175

A B C D E F G% Deviation % Deviation

from NPV from Units NPVBase Case WACC 5,809 Base Case Sold $5,809

-30% 8.4% $9,030 -30% 14,000 -$3,628-15% 10.2% $7,362 -15% 17,000 $1,091

0% 12.0% $5,809 Base Case 0% 20,000 $5,80915% 13.8% $4,363 15% 23,000 $10,52830% 15.6% $3,014 30% 26,000 $15,247

% Deviation % Deviationfrom Variable NPV from Growth NPV

Base Case Cost $5,809 Base Case Rate % $5,809-30% $1.47 $29,404 -30% -30% -$4,923-15% $1.79 $17,607 -15% -15% -$115

0% $2.10 $5,809 Base Case 0% 0% $5,80915% $2.42 -$5,988 15% 15% $12,98730% $2.73 -$17,785 30% 30% $21,556

% Deviation % Deviationfrom Sales NPV from Nonvariable NPV

Base Case Price $5,809 Base Case Costs $5,809-30% $2.10 -$27,223 -30% $5,600 $10,243-15% $2.55 -$10,707 -15% $6,800 $8,026

0% $3.00 $5,809 Base Case 0% $8,000 $5,80915% $3.45 $22,326 15% $9,200 $3,59330% $3.90 $38,842 30% $10,400 $1,376

GROWTH RATE, UNITSVARIABLE COSTS

1st YEAR UNIT SALESWACC

SALES PRICE NONVARIABLE COSTS

Sensitivity Ratio %NPV = (New NPV - Base NPV)/Base NPV %VAR = (New VAR - Base VAR)/Base VAR

VAR

NPVSR

%

%

• If SR>0 Direct relationship• If SR<0 Inverse relationship

14-37

38

RIC: Sensitivity Ratios

Sensitivity Analysis: Sensitivity Ratios

Deviationfrom Sales Variable Growth Year 1 Nonvariable

Base Case Price Cost/Unit Rate Units Sold Cost WACC(0.30) (27,222.63) 29,403.84 (4,922.76) (3,628.27) 10,243.07 9,030.42(0.15) (10,706.58) 17,606.66 (114.64) 1,090.61 8,026.28 7,361.84

0% $5,809 $5,809 $5,809 $5,809 $5,809 $5,80915% $22,326 ($5,988) $12,987 $10,528 $3,593 $4,3630.30 38,841.59 (17,784.89) 21,556.34 15,247.22 1,375.88 3,014.07

%ΔNPV 284% -203% 124% 81% -38% -25%%ΔVAR 15% 15% 15% 15% 15% 15%

SR 18.95 (13.54) 8.24 5.42 (2.54) (1.66)

NPV at Different Deviations from Base

39

RIC: Sensitivity Ratios & Graph

Sales Variable Growth Year 1 NonvariablePrice Cost/Unit Rate Units Sold Cost WACC

%ΔNPV 284% -203% 124% 81% -38% -25%%ΔVAR 15% 15% 15% 15% 15% 15%

SR 18.95 (13.54) 8.24 5.42 (2.54) (1.66)

NPV at Different Deviations from Base

($30,000)

($20,000)

($10,000)

$0

$10,000

$20,000

$30,000

$40,000

-30% -15% 0% 15% 30%

Deviation from Base-Case Value (%)

NPV ($)Sales price

Variable cost

Growth rate

Units sold

Nonvariable cost

WACC

40

Sensitivity Analysis:Weaknesses

Does not reflect diversification Says nothing about the likelihood

of change in a variable i.e. a steep sales line is not a problem

if sales won’t fall Ignores relationships among

variables

41

Sensitivity Analysis:Strengths

Provides indication of stand-alone risk

Identifies dangerous variables Gives some breakeven information

42

Scenario Analysis

Examines several possible situations, usually: Worst case Base case or most likely case, and Best case

Provides a range of possible outcomes

43

RIC: Scenario Analysis

Table 13-4. Scenario Analysis (Dollars in Thousands) SquaredDeviation

Sales Unit Variable Growth TimesProbability Price Sales Costs Rate NPV Probability

25% $3.90 26,000 $1.47 30% $146,180 3,366,596,00150% $3.00 20,000 $2.10 0% $5,809 295,883,22025% $2.10 14,000 $2.73 -30% ($37,257) 1,135,428,840

4797908060

Expected NPV = sum, prob times NPV $30,135Standard Deviation = Sq Root of variance $69,267Coefficient of Variation = Std Dev / E(NPV) 2.30

Scenario

Best CaseBase Case

Worst Case

44

RIC: Scenario Analysis

a. Probability GraphProbability

50%

25%

(37,257) 0 30,135 146,180NPV ($)

Most Likely Mean of distribution5,809

45

Problems with Scenario Analysis

Only considers a few possible out-comes

Assumes that inputs are perfectly correlated All “bad” values occur together and

all “good” values occur together Focuses on stand-alone risk

46

Monte Carlo Simulation Analysis

A computerized version of scenario analysis which uses continuous probability distributions

Computer selects values for each variable based on given probability distributions

47

Monte Carlo Simulation Analysis

NPV and IRR are calculated Process is repeated many times

(1,000 or more) End result: Probability distribution

of NPV and IRR based on sample of simulated values

Generally shown graphically

48

Histogram of Results

0%

2%

4%

6%

8%

10%

12%

($60

,000

)

($30

,000

) $0

$30,

000

$60,

000

$90,

000

$120

,000

$150

,000

$180

,000

$210

,000

$240

,000

$270

,000

$300

,000

$330

,000

$360

,000

NPV

Pro

ba

bil

ity

of

NP

V

49

Advantages of Simulation Analysis

Reflects the probability distributions of each input

Shows range of NPVs, the expected NPV, σNPV, and CVNPV

Gives an intuitive graph of the risk situation

50

Disadvantages of Simulation Analysis

Difficult to specify probability distributions and correlations

If inputs are bad, output will be bad:“Garbage in, garbage out”

51

Disadvantages of Sensitivity, Scenario and Simulation Analysis

Sensitivity, scenario, and simulation analyses do not provide a decision rule They do not indicate whether a project’s

expected return is sufficient to compensate for its risk

Sensitivity, scenario, and simulation analyses all ignore diversification They measure only stand-alone risk, which

may not be the most relevant risk in capital budgeting

52

Subjective risk factors

Numerical analysis may not capture all of the risk factors inherent in the project For example, if the project has the

potential for bringing on harmful lawsuits, then it might be riskier than a standard analysis would indicate

53

Decision Trees

A technique for reducing risk Analyze multi-stage projects “Decision Nodes”

Points where managers can take action based on new information

Assign probabilities to each leg

54

United Robotics

Stage 1: (t=0) Invest $500,000 in market potential study

Stage 2: (t=1) If study results positive, invest $1 million in prototype

Stage 3: (t=2) Build plant at cost of $10 million

Stage 4: (t=3) Product acceptance?

55

United Robotics Decision Tree

Figure 13-5

56

416417418419420421422423424425426427428429430431

432433

A B C D E F G H ICost of capital = 11.5%

Joint=0 t=1 t=2 t=3 t=4 t=5 Probability NPV Prob.xNPV

$18,000 $18,000 $18,000 0.144 $25,635 $3,691

($10,000) $8,000 $8,000 $8,000 0.192 $6,149 $1,181

($1,000) ($2,000) Stop 0.144 ($10,883) ($1,567)

($500) Stop 0.320 ($1,397) ($447)

Stop 0.200 ($500) ($100)

1.000 Expected NPV= $2,758

= $10,584

0.8

0.2

0.6

0.4

0.40.3

0.3

United Robotics Decision Tree

57

Real Options

Real options exist when managers can influence the size and risk of a project’s cash flows by taking different actions during the project’s life in response to changing market conditions Alert managers always look for real options

in projects Smarter managers try to create real options

58

Types of Real Options Investment timing options Growth options

Expansion of existing product line New products New geographic markets

Abandonment options Contraction Temporary suspension

Flexibility options