Chapter 7

Project Cash Flows and Risk

Cash Flow Estimation

Most important and most difficult step in the analysis of a capital project

Financial staff’s role includes:Coordinating other departments’ effortsEnsuring that everyone uses the same set

of economic assumptionsMaking sure that no biases are inherent in

forecasts

Relevant Cash Flows

Cash Flow Versus Accounting Income

Incremental Cash Flows

Cash Flow Versus Accounting Income

2010 Situation Accounting Profits Cash Flows

Sales $50,000 $50,000

Costs except depreciation (25,000) (25,000)

Depreciation (15,000) --

Net operating income or cash flow$10,000 $25,000

Taxes based on operating income (30%)(3,000) (3,000)

Net income or net cash flow $7,000 $22,000

Net cash flow = Net income plus depreciation = $7,000 + $15,000 = $22,000

Cash Flow Versus Accounting Income

2011 Situation Accounting Profits Cash Flows

Sales $50,000 $50,000

Costs except depreciation (25,000) (25,000)

Depreciation (5,000) --

Net operating income or cash flow$20,000 $25,000

Taxes based on operating income (30%)(6,000) (6,000)

Net income or net cash flow $14,000 $19,000

Net cash flow = Net income plus depreciation = $14,000 + $5,000 = $19,000

Incremental Cash Flows

An Incremental Cash FlowAn Incremental Cash Flow is the change in a firm’s net cash flow attributable to an investment project.

Problems in Determining Incremental Cash Flows Sunk Cost:Sunk Cost: A cash outlay that already has

been incurred and cannot be recovered

Opportunity Cost:Opportunity Cost: The return on the best alternative use of an asset

Externalities:Externalities: The effect of accepting a project on the cash flows in other parts of the firm

Shipping and Installation CostsShipping and Installation Costs

InflationInflation

Identifying Incremental Cash Flows

Initial Investment Outlay:Initial Investment Outlay: the incremental cash flows associated with a project that will occur only at the start of a project’s life

Incremental Operating Cash Flow:Incremental Operating Cash Flow: the changes in day-to-day cash flows that result from the purchase of a capital project and continue until the firm disposes of the asset

Terminal Cash Flow:Terminal Cash Flow: the net cash flows that occur only at the end of a project’s life

Incremental Operating Cash Flow

Incrementaloperatingcash flowt

= NOIt x (1 - T) + Deprt

= (St - OCt - Deprt) x (1 - T) + Deprt

= (St - OCt) x (1 - T) + T(Deprt)

= Cash revenuest- Cash expensest- Taxest

Capital Budgeting Project Capital Budgeting Project EvaluationEvaluation

Expansion Project:Expansion Project: A project that is intended to increase sales; provides growth to the firm

Replacement Analysis:Replacement Analysis: An analysis involving the decision of whether to replace an existing, still productive asset with a new asset

Expansion Project Analysis of the Cash

Flows

2010 $5,000 = ($30,000 - $18,000 - $5,000) (1 – 0.40) + $2,000(0.40)

2011 $5,480 = ($30,000 - $18,000 - $5,000) (1 – 0.40) + $3,200(0.40)

2012 $4,960 = ($30,000 - $18,000 - $5,000) (1 – 0.40) + $1,900(0.40)

2013 $4,680 = ($30,000 - $18,000 - $5,000) (1 – 0.40) + $1,200(0.40)

Year

Incremental Operating Cash Flow Computation

k = 15%

5,000 4,9605,480(14,000)4,3844,1433,2616,038

$3,790

10,560

0 1 2 3 4

NPV =

2011 20132012 20142010

Net cashflows

IRR = 26.3% Payback period = 2.7 years

Expansion Project Cash Flow Time Line

IRR = 14.0% Payback period = 3.6 years

Replacement Project Cash Flow Time Line

k = 15%

3,484 2,6204,060(11,400)3,0303,0701,7231,2782,038

$(261)

2,236

0 1 2 3 4

NPV =

2011 20132012 20142010

Net cashflows

52015

4,100

Introduction to Project Risk Analysis

Stand-Alone Risk:Stand-Alone Risk: the risk an asset would have if it were a firm’s only riskMeasured by the variability of the asset’s

expected returns Corporate (Within-Firm) Risk:Corporate (Within-Firm) Risk: risk not

considering the effects of stockholder’s diversificationMeasured by a project’s effect on the firm’s

earnings variability Beta (Market) Risk:Beta (Market) Risk: part of a project’s risk that

cannot be eliminated by diversificationMeasured by the project’s beta coefficient

Techniques for MeasuringStand-Alone Risk

Sensitivity Analysis:Sensitivity Analysis: Key variables are changed and the resulting changes in the NPV and the IRR are observed.

Scenario Analysis:Scenario Analysis: “Bad” and “good” sets of financial circumstances are compared with the most likely situation.

Monte Carlo Simulation:Monte Carlo Simulation: Probable future events are simulated on a computer.

Sensitivity Analysis Graph

NPV (000s)

-60

-40

-20

0

20

40

60

80

-30 -20 -10 0 10 20 30

Base

Unit sales

SV

k

% changefrom base

Assume we know all variables except unit sales, which could range from 75,000 to 125,000 (or 75 to 125). Here are the scenario NPVs:

Scenario Probability NPV (000)

Worst 0.25 -$27.8

Base 0.50 15.0

Best 0.25 57.8

E(NPV) = $15.0(NPV) =$30.3

Scenario Analysis

Standard Deviation:Standard Deviation:

σNPV = $30.3

Coefficient of Variation:Coefficient of Variation:

.0 2$15

$30.3NPVENPV

σ

NPVCV

Scenario Analysis

Advantages / Disadvantages of

Simulation Analysis

Reflects probability of each input Shows range of NPVs, expected

NPV, σNPV, and CVNPV

Difficult to specify probability distributions and correlation

If inputs are bad, output will be bad: GIGO = Garbage In, Garbage Out!

AdvantagesAdvantages

DisadvantagesDisadvantages

Beta Beta (or Market) Risk and Risk and Required Rate of Return for a Required Rate of Return for a ProjectProject

Security Market Line equation:Security Market Line equation:kS = kRF + (kM - kRF)βs

Erie Steel is all equity financed, so cost of equity is also its averaged required rate of return, or cost of capital.

Erie’s β = 1.1; kRF = 8%; and kM = 12%kS = 8% + (12% - 8%)1.1 = 12.4%

= Erie’s cost of equity

Investors should be willing to give Erie money to invest in average-risk projects.

Required Rate of Return for a Project

kproj = the risk-adjusted required rate of return for an individual project

kproj = kRF + (kM - kRF)proj

Measuring Beta Risk for a Project

Pure Play Method:Pure Play Method: 1. Identify companies whose only

business is the project in question.2. Determine the beta for each

company.3. Average the betas to find an

approximation of proposed project’s beta.

How Project Risk Is Considered in Capital Budgeting Decisions

Most firms use: Risk-Adjusted Discount RateRisk-Adjusted Discount Rate

Discount rate that applies to particularly risky stream of income

It is equal to the risk-free rate of interest plus a risk premium.

Capital Rationing

A situation in which a constraint is placed on the total size of the firm’s capital investment.