Corporate Finance - Chap 2

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Chapter 2

Risk Analysis, RealOptions, and CapitalBudgeting


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Key Concepts and Skills

Understand forecasting risk and sources of

value

Understand and be able to conduct scenario

and sensitivity analysis

Understand the various forms of break-even

analysis

Understand decision tree

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Chapter Outline

Evaluating NPV Estimates

Scenario and Other What-If Analyses

Break-Even Analysis

Operating Cash Flow, Sales Volume, and

Break-Even

Decision tree

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Evaluating NPV Estimates

NPV estimates are just that estimates

A positive NPV is a good start now we need

to take a closer look

Forecasting risk how sensitive is our NPV to

changes in the cash flow estimates; the more

sensitive, the greater the forecasting risk

Sources of value why does this project createvalue?

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Scenario Analysis

What happens to the NPV under different cash flow

scenarios?

At the very least, look at:

Best case high revenues, low costs

Worst case low revenues, high costs

Measure of the range of possible outcomes

Best case and worst case are not necessarily

probable, but they can still be possible

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New Project Example

Consider the project discussed in the text

The initial cost is $200,000, and the project has a 5-

year life. There is no salvage. Depreciation is straight-

line, the required return is 12%, and the tax rate is34%.

The base case NPV is 15,567

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Summary of Scenario Analysis

Scenario Net Income Cash Flow NPV IRR

Base case 19,800 59,800 15,567 15.1%

Worst Case -15,510 24,490 -111,719 -14.4%

Best Case 59,730 99,730 159,504 40.9%

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Sensitivity Analysis

What happens to NPV when we change onevariable at a time

This is a subset of scenario analysis where weare looking at the effect of specific variables

on NPV The greater the volatility in NPV in relation to

a specific variable, the larger the forecastingrisk associated with that variable, and the

more attention we want to pay to itsestimation

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Summary of Sensitivity Analysis for New

Project

Scenario Unit Sales Cash Flow NPV IRR

Base case 6,000 59,800 15,567 15.1%

Worst case 5,500 53,200 -8,226 10.3%

Best case 6,500 66,400 39,357 19.7%

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Simulation Analysis

Simulation is really just an expanded sensitivity and scenarioanalysis

Monte Carlo simulation can estimate thousands of possibleoutcomes based on conditional probability distributions andconstraints for each of the variables

The output is a probability distribution for NPV with anestimate of the probability of obtaining a positive net presentvalue

The simulation only works as well as the information that isentered, and very bad decisions can be made if care is nottaken to analyze the interaction between variables

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Making a Decision

Beware Paralysis of Analysis At some point you have to make a decision

If the majority of your scenarios have positiveNPVs, then you can feel reasonably comfortable

about accepting the project If you have a crucial variable that leads to a

negative NPV with a small change in theestimates, then you may want to forego the

project

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Break-Even Analysis

Common tool for analyzing the relationship

between sales volume and profitability

There are three common break-even measures

Accounting break-even sales volume at which NI =0

Cash break-even sales volume at which OCF = 0

Financial break-even sales volume at which NPV =

0

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Example: Costs There are two types of costs that are important in

breakeven analysis: variable and fixed

Total variable costs = quantity * cost per unit

Fixed costs are constant, regardless of output, over some

time period

Total costs = fixed + variable = FC + vQ

Example:

Your firm pays $3,000 per month in fixed costs. You also

pay $15 per unit to produce your product.

What is your total cost if you produce 1,000 units?

What if you produce 5,000 units?

Produce 1000 units: TC = 3000 + 15*1000 = 18,000

Produce 5000 units: TC = 3000 + 15*5000 = 78,000

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Average vs. Marginal Cost

Average Cost TC / # of units

Will decrease as # of units increases

Marginal Cost

The cost to produce one more unit Same as variable cost per unit

Example: What is the average cost and marginal cost under

each situation in the previous example

Produce 1,000 units: Average = 18,000 / 1000 = $18

Produce 5,000 units: Average = 78,000 / 5000 = $15.60

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Accounting Break-Even

The quantity that leads to a zero net income

NI = (Sales VC FC D)(1 T) = 0

QP vQ FC D = 0

Q(P v) = FC + D

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

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Using Accounting Break-Even

Accounting break-even is often used as an

early stage screening number

If a project cannot break-even on an

accounting basis, then it is not going to be a

worthwhile project

Accounting break-even gives managers an

indication of how a project will impact

accounting profit

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Accounting Break-Even and Cash Flow

We are more interested in cash flow than we are in

accounting numbers

As long as a firm has non-cash deductions, there will be

a positive cash flow If a firm just breaks even on an accounting basis, cash

flow = depreciation

If a firm just breaks even on an accounting basis, NPV

will generally be < 0

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Example

Consider the following project A new product requires an initial investment of $5

million and will be depreciated to an expectedsalvage of zero over 5 years

The price of the new product is expected to be$25,000, and the variable cost per unit is $15,000

The fixed cost is $1 million

What is the accounting break-even point each year?

Depreciation = 5,000,000 / 5 = 1,000,000

Q = (1,000,000 + 1,000,000)/(25,000 15,000) =200 units

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Sales Volume and Operating Cash Flow

What is the operating cash flow at the accounting break-even point (ignoring taxes)? OCF = (S VC FC - D) + D

OCF = (200*25,000 200*15,000 1,000,000 -1,000,000) +1,000,000 = 1,000,000

What is the cash break-even quantity? OCF = [(P-v)Q FC D] + D = (P-v)Q FC

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

Q = (0 + 1,000,000) / (25,000 15,000) = 100 units(Cash break-even occurs where operating cash flow = 0).

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Three Types of Break-Even Analysis Accounting Break-even

Where NI = 0

Q = (FC + D)/(P v) Cash Break-even

Where OCF = 0

Q = (FC + OCF)/(P v) (ignoring taxes)

Financial Break-even

Where NPV = 0 Cash BE < Accounting BE < Financial BE

With taxes included. The equations change as follows:OCF = [(P v)Q FCD](1 T) + DUse a tax rate = 40% and rework the Wettways example from the

book:Need 1170 in OCF to break-even on a financial basisOCF = [(40 20)(Q) 500 700](1 - .4) + 700 = 1170; Q =

99.2

You end up with a new quantity of 100 units. The firm must sell anadditional 16 units to offset the effects of taxes.

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Example: Break-Even Analysis

Consider the previous example Assume a required return of 18%

Accounting break-even = 200

Cash break-even = 100

What is the financial break-even point? Similar process to that of finding the bid price

What OCF (or payment) makes NPV = 0? N = 5; PV = 5,000,000; I/Y = 18; CPT PMT = 1,598,889 =

OCF

Q = (1,000,000 + 1,598,889) / (25,000 15,000) = 260units

The question now becomes: Can we sell atleast 260 units per year?

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Real Options

One of the fundamental insights of modernfinance theory is that options have value.

The phrase We are out of options is surely a

sign of trouble. Because corporations make decisions in a

dynamic environment, they have options that

should be considered in project valuation.

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Real Options (cont)

The Option to Expand Has value if demand turns out to be higher

than expected

The Option to Abandon Has value if demand turns out to be lower

than expected

The Option to Delay

Has value if the underlying variables are

changing with a favorable trend

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Discounted CF and Options

We can calculate the market value of a project as thesum of the NPV of the project without options and the

value of the managerial options implicit in the project.

M = NPV+ Opt

A good example would be comparing the desirability ofa specialized machine versus a more versatile machine.

If they both cost about the same and last the same

amount of time, the more versatile machine is more

valuable because it comes with options.

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The Option to Abandon: Example

Suppose we are drilling an oil well. The drillingrig costs $300 today, and in one year the well is

either a success or a failure.

The outcomes are equally likely. The discount

rate is 10%.

The PVof the successful payoff at time one is

$575.

The PVof the unsuccessful payoff at time oneis $0.

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Traditional NPV analysis would indicate

rejection of the project.

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=Expected

Payoff

Prob.Success

Successful

Payoff+

Prob.Failure

FailurePayoff

ExpectedPayoff

= (0.50$575) + (0.50$0) = $287.50

NPV= = $38.641.10

$287.50$300 +


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However, traditional NPV analysis overlooks the option to abandon.

The firm has two decisions to make: drill or not, abandon or stay.

Do notdrill

Drill

0$NPV

Failure

Success: PV= $575

Sell the rig;salvage value =

$250

Sit on rig; stare atempty hole: PV=

$0.


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When we include the value of the option toabandon, the drilling project should proceed:

=Expected

Payoff

Prob.Success

SuccessfulPayoff +

Prob.Failure

FailurePayoff

ExpectedPayoff

= (0.50$575) + (0.50$250) = $412.50

NPV = = $75.001.10

$412.50$300 +


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Recall that we can calculate the market valueof a project as the sum of the NPV of theproject without options and the value of the

managerial options implicit in the project.

M= NPV+ Opt$75.00 = $38.64 + Opt

$75.00 + $38.64 = Opt

Opt= $113.64

Valuing the Option to Abandon


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The Option to Delay: Example

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Year Cost PV NPVt NPV0

0 20,000$ 25,000$ 5,000$ 5,000$

1 18,000$ 25,000$ 7,000$ 6,364$

2 17,100$ 25,000$ 7,900$ 6,529$3 16,929$ 25,000$ 8,071$ 6,064$

4 16,760$ 25,000$ 8,240$ 5,628$

2

)10.1(

900,7$529,6$

Consider the above project, which can be undertaken in any of the next 4

years. The discount rate is 10 percent. The present value of the benefits atthe time the project is launched remains constant at $25,000, but since

costs are declining, the NPV at the time of launch steadily rises.

The best time to launch the project is in year 2this schedule yields the

highest NPV when judged today.


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Decision Trees

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Allow us to graphically represent thealternatives available to us in each periodand the likely consequences of our actions

This graphical representation helps toidentify the best course of action.


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Example of a Decision Tree

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Squares represent decisions to be made.

Do notstudy

Studyfinance

Circles represent receiptof information, e.g., atest score.

The lines leading away fromthe squares represent thealternatives.

C

A

B

F

D


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Decision Tree for Stewart

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Do nottest

Test

Failure

Success

Do notinvest

Invest

Invest

The firm has two decisions to make:

To test or not to test.

To invest or not to invest.

0$NPV

NPV= $3.4 b

NPV= $0

NPV= $91.46 m


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Decision Tree for Stewart

If you dont invest, the NPV = 0, even if you

test first, because the cost of testing becomes

a sunk cost.

If you are so unwise as to invest in the face ofa failed test, you incur lots of additional costs,

but not much in the way of revenue, so you

have a negative NPV as of date 1.

Referring back to previous slide (Decision to

Test) may help to clarify the application of

decision trees.


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Comprehensive Problem

A project requires an initial investment of $1,000,000 and is

depreciated straight-line to zero salvage over its 10-year life.

The project produces items that sell for $1,000 each, with

variable costs of $700 per unit. Fixed costs are $350,000 per

year. What is the accounting break-even quantity, operating cash

flow at accounting break-even at that output level?

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Quick Quiz

What are sensitivity analysis, scenario analysis, break-even

analysis, and simulation?

Why are these analyses important, and how should they be

used?

How do real options affect the value of capital projects?

What information does a decision tree provide?

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Corporate Finance - Chap 2

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