1

Valuation Methods & Capital Budgeting

• Payback/Discounted Payback

• IRR

• MIRR

• Benefit Cost Ratio (BCR)

• NPV (DCF)– FCF: Free cash flow– FTE: Flow to equity– APV: Adjusted present value

2

Payback Rule

• Payback period: The amount of time it takes to recover the original cost.

• Payback rule: If the calculated payback period is less than or equal to some pre-specified payback period, then accept the project. Otherwise reject it.

3

The Payback Rule

Time

$200 $420 $855

$-600

0 1 3 42

$645

Payback period=2+((600-420)/225)=2.8 yearsAccept because payback < 3 years

4

Advantages and Disadvantages of the Payback Rule

• Advantages– Easy– Biased toward liquidity– Quick evaluation– Adjusts long term cash flow uncertainty (by ignoring them)

• Disadvantages– Ignores TVM– Ignores cash flow beyond payback period– Biased against long term projects

• Popular among many large companies– Commonly used when the:

• capital investment is small• merits of the project are obvious so more formal analysis is unnecessary

5

The Discounted Payback Rule

Time

$-600

0 1 3 42

The project never pays back so reject.What is the NPV?

67.166

)2.01(200

193.550

)2.01(210

444.319

)2.01(220

265.449

)2.01(225

3

Accumulated discounted cash flows

6

Discounted Payback Rule?

• Things to Consider– Involves discounting– How do you choose r? – How do you choose the cut-off period?

• Advantages– If project ever pays back then NPV>0– Biased toward liquidity– Easy

• Disadvantages– May reject NPV>0 projects– Cut-off period is arbitrary– Biased against long term projects

• Bottom Line: Why not just use NPV?

7

Benefit-Cost Ratio (BCR)

OutflowsCashofValueesent

InflowsCashofValueesentBCR

Pr

Pr

Rato of discounted inflows to outflows.

Rule: Accept project if BCR greater than 1.

Use caution if using to compare mutually exclusive projects. Similar BCRs can have radically different NPV’s.

8

Internal Rate of Return (IRR) RuleIRR is that r that makes the NPV=0

T

0=tt

t

r)+(1

CF = NPV

9

IRR Rule

• Accept the project if the IRR is greater than the required rate of return. Otherwise, reject the project.

• Comparison of NPV and IRR– If cash flows are conventional and project is

independent, then NPV and IRR lead to same accept and reject decisions.

10

IRR Rule and UnconventionalCash Flows

• Unconventional cash flows: A negative cash flow after a positive one.

• Strip Mining Project

• Year Cash Flows

• 0 -60

• 1 155

• 2 -100

11

Problems with the IRR RuleUnconventional cash flows lead to multiple IRR’s

25% and 33.33%

-1.74

-0.31

-0.28

0

0

0.06

-2-1.8-1.6-1.4-1.2

-1

-0.8-0.6-0.4-0.2

00.2

0 10 20 30 40 50

12

Mutually Exclusive• Taking one project means another is not taken

• The highest IRR may not have the highest NPV

• To evaluate we need to find the crossover rate– Take the differences between the two projects cash

flows and compute the IRR for those incremental flows

13

Mutually Exclusive Cash Flows

Period Proj. A Proj. B Incremental(A - B)

0 -500 -400 -100

1 325 325 0

2 325 200 125

IRR 19.43 22.17 11.8

14

NPV Profiles of Mutually Exclusive Projects

Crossover Rate = 11.8

IRRA=19.43

IRRB=22.17

($50.00)

($30.00)

($10.00)

$10.00

$30.00$50.00

$70.00

$90.00

$110.00

$130.00

$150.00

0 5 10 15 20 25

Project A Project B

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Reinvestment Rate Assumption

• During the life of a project, what are the investment assumptions of the intermediate cash flows?

• Implicitly the PV oriented methods assume that the cash flows can be reinvested at r.

• Is this reasonable?– NPV– IRR

16

Modified IRR (MIRR)• Solves the

reinvestment rate problem

• Example: A project’s cash flows are -400, 325 and 200. Appropriate r is 12%

• Accept the project because 18.74%>12%

• Note: The IRR on this project is 22.16%

400)12.1(

400)(

0)1(

)(

0

0

outflowsPV

Cifr

CoutflowsPV t

T

tt

t

564)12.01(200)12.01(325)(inf

0)1()(inf

2212

0

lowsFV

CifrClowsFV t

T

t

tTt

1874.01400

564

1)1(2/1

/1

MIRR

PV

FVMIRR

MIRR

FVPV

T

T

17

Summary of IRR/MIRR• Advantages: Easy to understand

– Conventional Cash Flows and Independent Projects:• Same Decisions as NPV Rule

– Required Rate of Return Benchmark• Often same discount rate in NPV

– MIRR has more realistic reinvestment rate (use instead of IRR if possible)

• Disadvantages: – Unconventional cash flows may result multiple answers– If projects are mutually exclusive may lead to incorrect decisions– Not always easy to calculate– Difficult to interpret (particularly if the project has multiple r’s)– IRR may have unrealistic reinvestment rate

• Very Popular: People like to talk in terms of returns– Survey of 100 largest Fortune 500 Ind.

• 99% use IRR Rule• 85% use NPV Rule

18

NPV(DCF) Valuation Methods• FCF: All relevant cash flows excluding financing costs

discounted by the “whole firm” r (typically estimated with WACC(adjusted for taxes))

• FTE: FCF minus payments to other finance sources (typically debt holders) discounted by re

• APV: All relevant cash flow components separately discounted by the appropriate r’s

• Note: – re (e=equity) is the same as rS (S=stock)

– rd (d=debt) is the same as rB (B=bond)

19

Compare Methods• FCF

– Very strict assumptions of constant proportion capital structure (from WACC)

– Can adjust r if risk or capital structure is different from existing firm– Tax debt shield must be cD (for WACC(adjusted))

• FTE– Probability of payments to other finance sources, i.e. debt holders

• Option to default usually not considered so FTE value is usually low

– Difficult to extrapolate entire firm value

• APV– Flexible and works well for changing capital structure– Usually will need an estimate of unlevered r

• Potential for estimation error depending on NPV of financing

20

•Incremental cash flows: Only the incremental portion of any flow is relevant

•Otherwise known as the Stand-Alone Principle•Project = "Mini-firm"•Allows us to evaluate the investment project separately from other activities of the firm•Allows us to make optimal decisions with a relatively simple process

Relevant Cash Flows

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Relevant Cash Flows?•Sunk Costs—No•Opportunity Costs—Yes•Side Effects (Erosion)—Yes•Net Working Capital—Yes•Value of cash flow volatility change—Yes•Financing Costs—No (there are some methods where this is relevant)•Allocated Overhead Costs―No

All Cash Flows should be after-tax cash flows

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How do we make reasonable cash flow estimates?

•Estimate them from scratch•Pro forma financial statements

•Probably the best current estimate of future flows. •Make sure you adjust the financial statements for the difference between accounting flows and finance flows.

•Finance flows are based on the principle of opportunity costs and the timing of the flows is based on when the money is actually paid/received•Accounting flows (as presented in financial statements) are based on historical costs and the timing of the flows is usually based on accrual (not cash) accounting

•Use statements to get the basic project cash flow•Need an after tax terminal value

•Assume the project goes on forever and use a perpetuity•Assume the project ends and the balance sheet is zeroed out (everything is sold and settled)

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Two Approaches•Item by item Discounting: Separately forecast relevant flows then discount them

•Very flexible: Can use different discount rates for each flow

•Whole Project Discounting: determine project’s relevant cash flows, sum them in each year then discount the yearly sum•FCF=OCF + Net Capital Spending - Changes in NWC

•Operating Cash Flows (OCF): EBIT+Depreciation+Other Non-Cash Expenses-Taxes•Net Capital Spending

•Project specific assets, initial costs•After tax salvage value (if project ends)

•Changes in NWC•NWC=CA-CL•Changes in NWC = NWC(t)-NWC(t-1)•Recover all NWC at the end of the project (if project ends)

24

Alternate Ways to Compute OCF• GOAL: Make sure that all relevant cash inflows

and outflows are included (Holden shows several of these methods)

• Bottom Up: OCF=Net Income + Non-cash deductions– CAUTION: This method only works if there are no

financing costs already taken out of net income!

• Top Down: OCF=Sales - Costs - Taxes– Subtract all deductions except non-cash items

• Tax Shield: OCF=(Sales-Costs) x (1-tc) + (non-cash deductions x tc)

25

Scenario Analysis

• WHAT IF?

• Estimate NPV with various assumptions– Statistical distribution– Best case, worst cast, most likely case

• Sensitivity analysis: Change in NPV due to one or a few items

26

Capital Rationing• NPV>0 then accept, is based on unlimited capital

• NPV is still the best criteria but we need to ration

• Profitability Index is NPV per investment dollar

• Order the projects by PI– Choose projects until PI<0 or you run out of money

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You have $500,000 to spend

• Project B, $200,000

• Project D, $250,000

• Project C, $50,000 (partial investment)

• What if you can’t do partial investments?

Project Investment NPV PI

A 500,000 80,000 16%

B 200,000 45,000 22.5%

C 300,000 55,000 18.3%

D 250,000 50,000 20%

28

Evaluating projects with different economic lives

• Assumptions– Different lives– The project can go on forever

• Equivalent Annual Cash (EAC) flows

trr

EACPV

)1(

11

29

EAC Example

• Assume you need to choose between two production processes– Original process:

NPV=4,402,679, 8 year life

– Alternative: NPV=3,200,000, 4 year life

• Which process is better?

272,886

)12.01(

11

12.0679,402,4

8

EAC

EAC

r)+(1

1 - 1

r

EAC = PV t

550,053,1

12.012.0000,200,3 4

EAC

)+(1

1 - 1

EAC =

30

Biases

• Systematic deviation from the actual value

31

Cognitive Bias

• When conscious beliefs do not reflect the information– Easy to recall/available information is used– Adjustment and anchoring– Representative

32

Motivational Bias

• Statements do not reflect beliefs– Dishonesty– Greed– Asymmetric Reward– Brown-nosing– Fear

33

Managing Bias

• Recognize it!

• Keep going back to the economics

• Sensitivity analysis

• Information management

• Check and recheck assumptions