Risk & refinements in capital budgeting

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P i

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f M

i l

Principles of Managerial

Fi

Finance

9th Edition

9th Edition

Chapter 10

Chapter 10

Ri k & R fi

t

Risk & Refinements

in Capital Budgeting

in Capital Budgeting


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Learning Objectives

• Understand the importance of explicitly recognizing risk in the analysis of capital budgeting projects.y p g g p j

• Discuss breakeven cash flow, sensitivity and scenario analysis, and simulation as behavioral approaches for dealing with risk, and the unique risks facing

dealing with risk, and the unique risks facing multinational companies.

• Describe the two basic risk-adjustment techniques in terms of NPV and the procedures for applying the

terms of NPV and the procedures for applying the certainty equivalent (CE) approach.


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Learning Objectives

• Review the use of risk-adjusted discount rates

(RADRs) portfolio effects and the practical aspects of (RADRs), portfolio effects, and the practical aspects of RADRs relative to CEs.

• Recognize the problem caused by unequal-lived

t ll l i j t d th f li d

mutually exclusive projects and the use of annualized net present values (ANPVs) to resolve it.

• Explain the objective of capital rationing and the two basic approaches to project selection under it.


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Behavioral Approaches for Dealing with Risk

• In the context of the capital budgeting projects

discussed in this chapter risk results almost entirely discussed in this chapter, risk results almost entirely from the uncertainty about future cash inflows

because the initial cash outflow is generally known because the initial cash outflow is generally known. • These risks result from a variety of factors including

uncertainty about future revenues, expenditures and taxes.

• Therefore, to asses the risk of a potential project, the analyst needs to evaluate the riskiness of the cash y inflows.


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Behavioral Approaches for Dealing with Risk

Sensitivity Analysis

Treadwell Tire has a 10% cost of capital and is

considering investing in one of two mutually exclusive considering investing in one of two mutually exclusive

projects A or B. Each project has a $10,000 initial cost d f l lif f 15

and a useful life of 15 years.

As financial manager, you have provided pessimistic, most-likely, and optimistic estimates of the equal annual

cash inflows for each project as shown in the following p j g table.


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Behavioral Approaches for Dealing with Risk

Sensitivity

Analysis


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Behavioral Approaches for Dealing with Risk

Simulation

• Simulation is a statistically-based behavioral approach that applies predetermined probability distributions

and random numbers to estimate risky outcomes.

Fi 10 1 t fl h t f th i l ti f

• Figure 10.1 presents a flowchart of the simulation of the NPV of a project.

• The use of computers has made the use of simulation economically feasible and the resulting output

economically feasible, and the resulting output provides an excellent basis for decision-making.


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Behavioral Approaches for Dealing with Risk


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Behavioral Approaches for Dealing with Risk

International Risk Consideration

E h t i k i th i k th t t d

• Exchange rate risk is the risk that an unexpected change in the exchange rate will reduce NPV of a project’s cash flows.

• In the short term, much of this risk can be hedged by using financial instruments such as foreign currency futures and options.p

• Long-term exchange rate risk can best be minimized by financing the project in whole or in part in the local by financing the project in whole or in part in the local currency.


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Behavioral Approaches for Dealing with Risk

International Risk Considerations

• Political risk is much harder to protect against once a project is implemented.

p j p

• A foreign government can block repatriation of profits and even seize the firm’s assets.

• Accounting for these risks can be accomplished by • Accounting for these risks can be accomplished by

adjusting the rate used to discount cash flows -- or better -- by adjusting the project’s cash flows.


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Behavioral Approaches for Dealing with Risk

International Risk Considerations

Si t d l f b d t d MNC

• Since a great deal of cross-border trade among MNCs takes place between subsidiaries, it is also important to determine the net incremental impact of a project’s

h fl ll

cash flows overall.

• As a result, it is important to approach international , p pp capital projects from a strategic viewpoint rather than

f i l fi i l i


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Risk-Adjustment Techniques

Certainty Equivalents

Bennett Company is currently evaluating two projects, A and B.

The firm’s cost of capital is 10% and the initial investment and operating cash flows are shown investment and operating cash flows are shown


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Risk-Adjustment Techniques

B tt C

Certainty Equivalents

Bennett Company

Project's A and B (10% cost of Captial)

Year Project A Project B

0 $ (42,000) $ (45,000)

( p )

1 14,000 28,000 2 14,000 12,000 3 14,000, 10,000, 4 14,000 10,000 5 10,00014,000


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Risk-Adjustment Techniques

Certainty Equivalents

Assume that it is determined that Project A is actually more risky than B.

To adjust for this risk, you decide to apply certainty equivalents (CEs) to the cash flows certainty equivalents (CEs) to the cash flows, where CEs represent the percentage of the cash

fl th t ld b ti fi d t i f flows that you would be satisfied to receive for

certain rather than the original (possible) cash flows.


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Risk-Adjustment Techniques

Certainty Equivalents

Bennett Company Bennett Company

Certainty Equivalents Applied to Project A (Risk-free rate = 6%)

Certain Present Year Project A CE Cash flow s PVIF Value

0 $ (42 000) 1 00 $ (42 000) 1 0000 $ (42 000) 0 $ (42,000) 1.00 $ (42,000) 1.0000 $ (42,000) 1 14,000 12,6000.90 $ 0.9434 11,887 2 14,000 12,6000.90 $ 0.8900 11,214

$

3 14,000 0.80 $ 11,200 0.8396 9,404 4 14,000 9,8000.70 $ 0.7921 7,763 5 14,000 8,4000.60 $ 0.7473 6,277


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Risk-Adjustment Techniques

Certainty Equivalents

Bennett Company Bennett Company

Certainty Equivalents Applied to Project B (Risk-free rate = 6%)

Certain Present Year Project B CE Cash flow s PVIF Value

0 $ (45,000) 1.00 $ (45,000) 1.0000 $ (45,000) 1 28,000 28,0001.00 $ 0.9434 26,415 2 12,000 10,8000.90 $ 0.8900 9,612 3 10,000 9,0000.90 $ 0.8396 7,557 4 10,000 8,0000.80 $ 0.7921 6,337 5 10,000 0.70 $ 7,000 0.7473 5,231 5 10,000 0.70 $ 7,000 0.7473 5,231


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Risk-Adjustment Techniques

Risk-Adjusted Discount Rates

Bennett Company also wishes to apply the Risk-Adjusted Discount Rate (RADR) approach to j ( ) pp determine whether to implement Project A or B.

To do so, Bennett has developed the following Risk Index to assist them in their endeavor.


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Risk-Adjustment Techniques

Required

Risk-Adjusted Discount Rates

Risk Return Index (RADR)

0.0 6%

0.2 7%

0.4 8%

0 6 9%

0.6 9%

0.8 10%

1.0 11%

1 2 12%

1.2 12%

1.4 13%

1.6 14%

1.8 15%


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Risk-Adjustment Techniques

Risk-Adjusted Discount Rates

Project B has been assigned a Risk Index Value of 1.0 (average risk) with a RADR of 11%, and Project A has been assigned a Risk Index Value of 1.6 (above average risk) with a RADR of 14%.

These rates are then applied as the discount rates to the two projects to determine NPV as p j


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Risk-Adjustment Techniques

Risk-Adjusted Discount Rates

Risk Adjusted Discount Rate Applied to Project A Bennett Company

(RADR = 14%)

Present Year Project A PVIF Value

0 $ (42,000) 1.0000 $ (42,000) 0 $ (42,000) 1.0000 $ (42,000) 1 14,000 0.8772 12,281 2 14,000 0.7695 10,773

3 14 000 0 6750 9 450

3 14,000 0.6750 9,450 4 14,000 0.5921 8,289 5 14,000 0.5194 7,271


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Risk-Adjustment Techniques

Risk-Adjusted Discount Rates

Bennett Company Bennett Company

Risk Adjusted Discount Rate Applied to Project B (RADR = 11%)

Present Year Project B PVIF Value

0 $ (45,000) 1.0000 $ (45,000) 1 28,000 0.9009 25,225 2 12,000, 0.8116 9,739, 3 10,000 0.7312 7,312 4 10,000 0.6587 6,587

5 10 000 0 5935 5 935

5 10,000 0.5935 5,935


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Risk-Adjustment Techniques

Portfolio Effects

• As noted in Chapter 6, individual investors must hold p , diversified portfolios because they are not rewarded for assuming diversifiable risk.

• Because business firms can be viewed as portfolios of assets, it would seem that it is also important that they , p y too hold diversified portfolios.

• Surprisingly, however, empirical evidence suggestsSurprisingly, however, empirical evidence suggests that firm value is not affected by diversification.

• In other words diversification is not normally rewardedIn other words, diversification is not normally rewarded and therefore is generally not necessary.


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Risk-Adjustment Techniques

Portfolio Effects

• It turns out that firms are not rewarded forIt turns out that firms are not rewarded for diversification because investors can do so themselves

themselves.

• An investor can diversify more readily, easily, and costlessly simply by holding portfolios of stocks.


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Risk-Adjustment Techniques

CE Versus RADR in Practice

• In general CEs are the theoretically preferredIn general, CEs are the theoretically preferred

approach for project risk adjustment because they separately adjust for risk and time.

• The first eliminate risk from the cash flows and then discount the certain cash flows at a risk-free rate.

• RADRs on the other hand, have a major theoretical problem: they combine the risk and time adjustments in a single discount rate adjustment.


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Risk-Adjustment Techniques

CE Versus RADR in Practice

• Because of the mathematics of discounting, the RADR approach implicitly assumes that risk is an increasing function of time.

function of time.

• However, because of the complexity in developing

CE RADR ft d i ti

CEs, RADRs are more often used in practice.

• More specifically, firms often establish a number of risk classes, with an RADR assigned to each.

• Projects are then placed in the appropriate risk class • Projects are then placed in the appropriate risk class


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Capital Budgeting Refinements

Comparing Projects With Unequal Lives

• If projects are independent, comparing projects with unequal lives is not critical.

B t h l li d j t t ll

• But when unequal-lived projects are mutually exclusive, the impact of differing lives must be

considered because they do not provide service over comparable time periods

comparable time periods.

• This is particularly important when continuing service is needed from the projects under consideration.


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Capital Budgeting Refinements

Comparing Projects With Unequal Lives

The AT Company, a regional cable-TV firm, is evaluating p y, g , g two projects, X and Y. The projects’ cash flows and resulting NPVs at a cost of capital of 10% is given below.

Project X Project Y Year

0 $ (70 000) $ (85 000)

Cash Flow s

0 $ (70,000) $ (85,000) 1 $ 28,000 $ 35,000 2 $ 33,000 $ 30,000 3 $ 38 000 $ 25 000 3 $ 38,000 $ 25,000 4 $ - $ 20,000 5 $ - $ 15,000 6 $ - $ 10,000


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Capital Budgeting Refinements

Comparing Projects With Unequal Lives

The AT Company, a regional cable-TV firm, is evaluating p y, g , g two projects, X and Y. The projects’ cash flows and resulting NPVs at a cost of capital of 10% is given below.

Ignoring the difference in their useful lives, both projects are acceptable (have positive NPVs). Furthermore, if the

projects were mutually exclusive project Y would be projects were mutually exclusive, project Y would be

preferred over project X. However, it is important to recognize that at the end of its 3 year life, project Y must

be replaced, or renewed.

Although a number of approaches are available for dealing with unequal lives, we will present the most


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Capital Budgeting Refinements

Comparing Projects With Unequal Lives

Annualized NPV (ANPV)

The ANPV approach converts the NPV of unequal-lived projects into an equivalent (in NPV terms) annual amount

( )

projects into an equivalent (in NPV terms) annual amount that can be used to select the best project.

1 Calc late the NPV of each project o er its li e sing the 1. Calculate the NPV of each project over its live using the

appropriate cost of capital.

2 Divide the NPV of each positive NPV project by the 2. Divide the NPV of each positive NPV project by the

PVIFA at the given cost of capital and the project’s live to get the ANPV for each project.


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Capital Budgeting Refinements

Comparing Projects With Unequal Lives

Annualized NPV (ANPV)

1. Calculate the NPV for projects X and Y at 10%.

( )

NPVX = $11,277; NPVY = $19,013.

2. Calculate the ANPV for Projects X and Y.

ANPVX = $11,277/PVIFA10%,3 years = $4,534 ANPVYY = $19,013/PVIFA10%,6 years = $4,366

3. Choose the project with the higher ANPV.

Pick project X Pick project X.


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Capital Rationing

’ f f

• Firm’s often operate under conditions of capital

rationing -- they have more acceptable independent

j t th th f d

projects than they can fund.

• In theory, capital rationing should not exist -- firms should accept all projects that have positive NPVs. • However, research has found that management

internally imposes capital expenditure constraints to avoid what it deems to be “excessive” levels of new financing, particularly debt.

• Thus, the objective of capital rationing is to select the group of projects within the firm’s budget that provides the highest overall NPV


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Capital Rationing

Example

Gould Company Investment Proposals

Project Initial Investm ent IRR PV of Inflow s NPV A $ 80,000 12% $ 100,000 $ 20,000

B 70,000, 20% 112,000, 42,000,

C 10,000 16% 145,000 135,000

D 40,000 8% 36,000 (4,000)

E 60 000 15% 79 000 19 000

E 60,000 15% 79,000 19,000


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Capital Rationing

IRR Approach

Gould Proposals

P j t IRR I iti l I t t

Gould Proposals

(Ranked by IRR)

Project IRR Initial Investm ent B 20% $ 70,000

C 16% 10,000

E 15% 60,000

A 12% 80,000

F 11% 110,000


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Capital Rationing

IRR Approach

Assume the firm’s

Gould Proposals

(Cum ulative Investm ent) cost of capital

is 10% and has a maximum of

Initial Cum ulative Project IRR Investm ent Investm ent

(Cum ulative Investm ent) a maximum of

$250,000 available for investment.

R ki th B 20% $70,000 $ 70,000

C 16% 100,000 170,000

E 15% 60,000 230,000

Ranking the

projects according

to IRR, the E 15% 60,000 230,000 A 12% 80,000 310,000

F 11% 110,000 420,000

optimal set of projects for

Gould is B C D 8% 40,000 460,000 Gould is B, C,


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Capital Rationing

NPV Approach

Gould Company Investment Proposals

(Ranked by NPV)

If we ration capital using the

NPV approach

PV of Initial

( y )

NPV approach and maintain the rankings provided

Project IRR Inflow s Investment NPV B 20% $ 112,000 $ 70,000 $ 42,000 C 16% 145 000 100 000 45 000

g p

by IRR, the total PV of inflows and

NPV ld b C 16% 145,000 100,000 45,000 E 15% 60,00079,000 19,000 T t l $ 336 000 $ 230 000 $ 106 000

NPV would be $336,000 and

$106,000 Totals $ 336,000 $ 230,000 $ 106,000 $106,000


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Capital Rationing

NPV Approach

Gould Company Investment Proposals

(Ranked by NPV)

However, if we rank them such

that NPV is

PV of Initial (Ranked by NPV)

that NPV is maximized, then

we can use our

Project IRR Inflow s Investment NPV B 20% $ 112,000 $ 70,000 $ 42,000

C 16% 145 000 100 000 45 000

entire budget and raise the PV of

i fl d NPV t C 16% 145,000 100,000 45,000

A 12% 80,000100,000 20,000

Totals $ 357 000 $ 250 000 $ 107 000

inflows and NPV to $357,000 and

$107,000 Totals $ 357,000 $ 250,000 $ 107,000 $107,000


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Capital Rationing

f

f

• Firm’s often operate under conditions of capital

rationing -- they have more acceptable independent

j

t th

th

f

d

projects than they can fund.

• In theory, capital rationing should not exist -- firms

should accept all projects that have positive NPVs.

• However, research has found that management

internally imposes capital expenditure constraints to

avoid what it deems to be “excessive” levels of new

financing, particularly debt.

• Thus, the objective of capital rationing is to select the

group of projects within the firm’s budget that provides

the highest overall NPV


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Capital Rationing

Example

Gould Company Investment Proposals

Project Initial Investm ent IRR PV of Inflow s NPV A $ 80,000 12% $ 100,000 $ 20,000

B 70,000, 20% 112,000, 42,000,

C 10,000 16% 145,000 135,000

D 40,000 8% 36,000 (4,000)

E 60 000 15% 79 000 19 000

E 60,000 15% 79,000 19,000


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Capital Rationing

IRR Approach

Gould Proposals

P

j

t

IRR

I iti l I

t

t

Gould Proposals

(Ranked by IRR)

Project

IRR

Initial Investm ent

B

20%

$

70,000

C

16%

10,000

E

15%

60,000

A

12%

80,000

F

11%

110,000


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Capital Rationing

IRR Approach

Assume the firm’s

Gould Proposals (Cum ulative Investm ent) cost of capital

is 10% and has a maximum of

Initial Cum ulative Project IRR Investm ent Investm ent

(Cum ulative Investm ent) a maximum of

$250,000 available for investment.

R ki th B 20% $70,000 $ 70,000

C 16% 100,000 170,000

E 15% 60,000 230,000

Ranking the

projects according

to IRR, the E 15% 60,000 230,000 A 12% 80,000 310,000

F 11% 110,000 420,000

optimal set of projects for

Gould is B C D 8% 40,000 460,000 Gould is B, C,


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Capital Rationing

NPV Approach

Gould Company Investment Proposals

(Ranked by NPV)

If we ration capital using the

NPV approach

PV of Initial

( y )

NPV approach and maintain the rankings provided

Project IRR Inflow s Investment NPV B 20% $ 112,000 $ 70,000 $ 42,000

C 16% 145 000 100 000 45 000 g p

by IRR, the total PV of inflows and

NPV ld b C 16% 145,000 100,000 45,000

E 15% 60,00079,000 19,000

T t l $ 336 000 $ 230 000 $ 106 000 NPV would be

$336,000 and

$106,000 Totals $ 336,000 $ 230,000 $ 106,000 $106,000


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Capital Rationing

NPV Approach

Gould Company Investment Proposals

(Ranked by NPV)

However, if we rank them such

that NPV is

PV of Initial (Ranked by NPV)

that NPV is maximized, then

we can use our

Project IRR Inflow s Investment NPV B 20% $ 112,000 $ 70,000 $ 42,000

C 16% 145 000 100 000 45 000

entire budget and raise the PV of

i fl d NPV t C 16% 145,000 100,000 45,000

A 12% 80,000100,000 20,000

Totals $ 357 000 $ 250 000 $ 107 000

inflows and NPV to $357,000 and

$107,000 Totals $ 357,000 $ 250,000 $ 107,000 $107,000