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Note 3

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http://faculty.fuqua.duke.edu/~charvey/Research/Published_Papers/P67_The_theory_and.pdf

http://faculty.fuqua.duke.edu/~charvey/Research/Published_Papers/P67_The_theory_and.pdfhttp://faculty.fuqua.duke.edu/~charvey/Research/Published_Papers/P67_The_theory_and.pdf

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Book Rate of Return

Average income divided by average book value

over project life

Also called accounting rate of return

Components reflect tax and accounting figures,

not market values or cash flows

assetsbook

incomebookreturnofrateBook

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Payback Period

Number of years before cumulative cash flow

equals initial outlay

Payback Rule

Only accept projects that pay back within desired

time frame

Ignores later year cash flows and present value offuture cash flows

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Example

Find disadvantage of only taking projects with

payback period of two years or less

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Example

Tool A costs $4,000. Investment will generate

$2,000 and $4,000 in cash flows for two years.

What is IRR?

0

)IRR1(

000,4

)IRR1(

000,2000,4NPV

21

%08.28IRR

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Pitfall 1: Lending or Borrowing?

NPV of project increases as discount rate

increases for some cash flows

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Pitfall 2: Multiple Rates of Return

Certain cash flows generate NPV = 0 at two

different discount rates

Following cash flow generates NPV = $A253 million atIRR% of 3.5% and 19.54%

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Pitfall 2: Multiple Rates of Return

Project can have 0 IRR and positive NPV

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Pitfall 3: Mutually Exclusive Projects

IRR sometimes ignores magnitude of project

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Pitfall 4: More than One Opportunity Cost of Capital

Term Structure Assumption

Assume discount rates stable during term ofproject

Implies all funds reinvested at IRR

False assumption

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While the internal rate of return (IRR) assumes thecash flows from a project are reinvested at the IRR,

the modified IRR assumes that positive cash flows

are reinvested at the firm's cost of capital, and theinitial outlays are financed at the firm's financing

cost.

Therefore, MIRR more accurately reflects the costand profitability of a project.

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For example, say a two-year project with an initialoutlay of $195 and a cost of capital of 12%, will return$121 in the first year and $131 in the second year. Tofind the IRR of the project so that the net presentvalue (NPV) = 0:

NPV = 0 = -195 + 121/(1+ IRR) + 131/(1 + IRR)2

NPV = 0 when IRR = 18.66%

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To calculate the MIRR of the project, we have to assume that the positivecash flows will be reinvested at the 12% cost of capital. So the futurevalue of the positive cash flows is computed as:

$121(1.12) + $131 = $266.52 = Future Value of positive cash flows at t = 2

Now you divide the future value of the cash flows by the present value ofthe initial outlay, which was $195, and find the geometric return for 2periods.

MIRR=sqrt($266.52/195) -1 = 16.91%

You can see here that the 16.91% MIRR is materially lower than the IRRof 18.66%. In this case, the IRR gives a too optimistic picture of thepotential of the project, while the MIRR gives a more realistic evaluation

of the project.

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investment

NPVindexityProfitabil

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Example

Select best projects for $300,000

Project NPV Investment PI

A 230,000 200,000 1.15

B 141,250 125,000 1.13

C 194,250 175,000 1.11D 162,000 150,000 1.08

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Project NPV Investment PI

A 230,000 200,000 1.15

B 141,250 125,000 1.13

C 194,250 175,000 1.11

D 162,000 150,000 1.08

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Example, continued

Select projects with highest weighted average PI WAPI (BD) = 1.01

WAPI (A) = 0.77

WAPI (BC) = 1.12

Project NPV Investment PI

A 230,000 200,000 1.15

B 141,250 125,000 1.13

C 194,250 175,000 1.11

D 162,000 150,000 1.08

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Capital Rationing

Limit set on amount of funds available for

investment

Soft Rationing

Imposed by management

Hard Rationing

Imposed by unavailability of funds in capitalmarket

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Rule 1: Only Cash Flow Is Relevant

Capital Expenses

Record capital expenditures when they occur

To determine cash flow from income, add back

depreciation and subtract capital expenditure

Working Capital

Difference between companys short-termassets and liabilities

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Rule 2: Estimate Cash Flows on an IncrementalBasis

Include taxes, salvage value, incidental

effects, and opportunity costs Do not confuse average with incremental

payoffs

Forecast sales today, recognize after-salescash flow to come later

Forget sunk costs

Beware of allocated overhead costs

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Rule 3: Treat Inflation Consistently

Use nominal interest rates to discount

nominal cash flows

Use real interest rates to discount real cashflows

Same results from real and nominal figures

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Inflation

Example

Project produces real cash flows of -$100 in year zero andthen $35, $50, and $30 in three following years. Nominaldiscount rate is 15% and inflation rate is 10%. What isNPV?

045.110.1

15.11rateinflation+1

ratediscountnominal+1

=ratediscountReal

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Inflation

ExampleReal figures

50.5$

26.29=30345.79=502

33.49=351

1001000PV@4.50%FlowCashYear

3

2

1.045

30

1.045

50

1.045

35

=

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Separate Investment and Financing Decisions

Regardless of financing, treat cash outflows

required for project as coming from investors

Regardless of financing, treat cash inflows as

going to investors

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NPV Using Nominal Cash Flows

$3,520,000or,520,3

20.1

444,3

20.1

110,6

20.1

136,10

20.1

685,10

20.1

205,6

20.1

381,2

20.1

630,1600,12NPV

76

5432

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Problem 1: Investment Timing Decision

Some projects are more valuable if undertaken in

the future

Examine start dates (t) for investment and

calculate net future value for each date

Discount net values back to present

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Problem 2: Choice between Long- and Short-Term Equipment

Example

Given the following cash flows from operating two

machines and a 6% cost of capital, which machine hasthe higher value using the equivalent annual annuitymethod?

Year

Machine 0 1 2 3 PV@6% E.A.A.A +15 +5 +5 +5 28.37 10.61

B +10 +6 +6 21.00 11.45

E =

1(1+)

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Equivalent Annual Cash Flow, Inflation, andTechnological Change

Inflation increases nominal costs of operatingequipment, but real costs remain unchanged

Real cash flows are not always constant

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Equivalent Annual Cash Flow and Taxes

Lifetime costs should be calculated after tax

Operating costs are tax-deductible Capital investment generates depreciation tax

shields

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Problem 3: When to Replace an Old Machine

Example

A machine is expected to produce a net inflow of $4,000this year and $4,000 next year before breaking. You canreplace it now with a machine that costs $15,000 and willproduce an inflow of $8,000 per year for three years.Should you replace now or wait a year?

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Problem 3: When to Replace an Old Machine

Example, continued

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Problem 4: Cost of Excess Capacity

Example

A computer system costs $500,000 to buy andoperate at a discount rate of 6% and lasts fiveyears

Equivalent annual cost of $118,700

Undertaking project in year 4 has a present value of118,700/(1.06)4, or about $94,000

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Types of Analysis

Sensitivity Analyzes effects of changes in sales, costs, etc., on project

Scenario Project analysis given particular combination of assumptions

Simulation Estimates probabilities of different outcomes

Break Even Level of sales (or other variable) at which project breaks even

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Example

Given expected cash-flow forecasts for Otobai

Companys Motor Scooter project, determine theNPV of project given changes in cash- flow

components using 10% cost of capital. Assume

constant variables, except the one you are

changing.

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Example, continued

315-FlowCashNet

3.0flowcashOperating

1.5after taxProfit

1.550%@Taxes

3.0profitPretax

1.5onDepreciati

3costsFixed

30costsVariable

37.5Sales

15-Investment

10-1Years0Year

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Example, continued

bil2bil3bil4costFixed

275,000300,000360,000costUnit var380,000375,000350,000priceUnit

.16.1.04shareMarket

mil1.1mil1.0mil.9sizeMarket

OptimisticExpectedcPessimistiVariable

Outcomes

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Example, continued

NPV calculationsOptimistic scenario

3.3815-FlowCashNet

3.38flowcashOperating

1.88after taxProfit

1.8850%@Taxes

3.75profitPretax

1.5onDepreciati

3costsFixed

33costsVariable

41.25Sales15-Investment

10-1Years0Year

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Modeling Process

Step 1: Model Project

Step 2: Specify Probabilities

Step 3: Simulate Cash Flows

Step 4: Calculate Present Value

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Decision Trees

Diagram of sequential decisions and possible

outcomes

Help companies analyze options by showingvarious choices and outcomes

Option to avoid a loss or produce extra profit has

value Ability to create option has value that can be

bought or sold

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Real Options

Option to expand

Option to abandon

Timing option

Flexible production facilities

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$700 (.80)

$ 0 (.20)$ 300 (.80)

$ 0 (.20)$ 100 (.80)

$ 0 (.20)

InvestYes / No

NPV= ?

- $18

- $130

- $130

- $130

.25

.50

.25

$ 0

.44

.56

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$700 (.80)

$ 0 (.20)$ 300 (.80)

$ 0 (.20)

$ 100 (.80)

$ 0 (.20)

560

240

80

InvestYes / No

NPV= ?

- $18

- $130

- $130

- $130

.25

.50

.25

$ 0

.44

.56

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$700 (.80)

$ 0 (.20)

$ 300 (.80)

$ 0 (.20)

$ 100 (.80)

$ 0 (.20)

560

240

80

InvestYes /

NoNPV= ?

-$18

- $130

- $130

- $130

.25

.50

.25

$ 0

.44

.56

56020.080.700

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$700 (.80)

$ 0 (.20)$ 300 (.80)

$ 0 (.20)$ 100 (.80)

$ 0 (.20)

560

240

80

InvestYes / No

NPV= ?

- $18

- $130

- $130

- $130

.25

.50

.25

$ 0

.44

.56

295

096.1

560130(upside)NPV

3

NPV = $295

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$700 (.80)

$ 0 (.20)$ 300 (.80)

$ 0 (.20)

$ 100 (.80)

$ 0 (.20)

560

240

80

InvestYes / No

NPV= ?

- $18

- $130

- $130

- $130

.25

.50

.25

$ 0

.44

.56

NPV = $295

NPV = $52

NPV = - $69(do not invest, so NPV = 0)

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$700 (.80)

$ 0 (.20)$ 300 (.80)

$ 0 (.20)

$ 100 (.80)

$ 0 (.20)

560

240

80

InvestYes / No

NPV= ?

- $18

- $130

- $130

- $130

.25

.50

.25

$ 0

.44

.56

NPV = $295

NPV = $52

NPV = - $69(do not invest, so NPV =

0)

83$

096.1)25.295()5.52()25.0(NPV 2

NPV = $83

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$700 (.80)

$ 0 (.20)$ 300 (.80)

$ 0 (.20)

$ 100 (.80)

$ 0 (.20)

560

240

80

InvestYes / No

NPV= $19

- $18

- $130

- $130

- $130

.25

.50

.25

$ 0

.44

.56

NPV = $295

NPV = $52

NPV = - $69(do not invest, so NPV = 0)

NPV = $83

19$

)056(.)8344(.18NPV

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$700 (.80)

$ 0 (.20)

$ 300 (.80)

$ 0 (.20)

$ 100 (.80)

$ 0 (.20)

560

240

80

InvestYes / No

NPV= $19

- $18

- $130

- $130

- $130

.25

.50

.25

$ 0

.44

.56

NPV = $295

NPV = $52

NPV = - $69(do not invest, so NPV = 0)

NPV = $83

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Boyne mountain resort

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Chapter 5

9, 12, 14 15

Chapter 6 19, 21,26