Top Banner
Principles of Managerial Finance 9th Edition Chapter 10 Risk & Refinements in Capital Budgeting
36

Risk and Refinements of Capital Budgeting

Mar 05, 2015

Download

Documents

Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Page 1: Risk and Refinements of Capital Budgeting

Principles of Managerial Finance

9th Edition

Chapter 10

Risk & Refinements

in Capital Budgeting

Page 2: Risk and Refinements of Capital Budgeting

Learning Objectives• Understand the importance of explicitly recognizing

risk in the analysis of capital budgeting projects.

• Discuss breakeven cash flow, sensitivity and scenario

analysis, and simulation as behavioral approaches for

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

certainty equivalent (CE) approach.

Page 3: Risk and Refinements of Capital Budgeting

Learning Objectives

• Review the use of risk-adjusted discount rates

(RADRs), portfolio effects, and the practical aspects of

RADRs relative to CEs.

• Recognize the problem caused by unequal-lived

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.

Page 4: Risk and Refinements of Capital Budgeting

Behavioral Approaches for Dealing with Risk

• In the context of the capital budgeting projects

discussed in this chapter, risk results almost entirely

from the uncertainty about future cash inflows

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

inflows.

Page 5: Risk and Refinements of Capital Budgeting

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

projects A or B. Each project has a $10,000 initial cost

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

table.

Page 6: Risk and Refinements of Capital Budgeting

Behavioral Approaches for Dealing with Risk

Sensitivity

Analysis

Page 7: Risk and Refinements of Capital Budgeting

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.

• 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

provides an excellent basis for decision-making.

Page 8: Risk and Refinements of Capital Budgeting

Simulation

Behavioral Approaches for Dealing with Risk

Page 9: Risk and Refinements of Capital Budgeting

International Risk Consideration

Behavioral Approaches for Dealing with Risk

• 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.

• Long-term exchange rate risk can best be minimized

by financing the project in whole or in part in the local

currency.

Page 10: Risk and Refinements of Capital Budgeting

Behavioral Approaches for Dealing with Risk

International Risk Considerations

• Political risk is much harder to protect against once a

project is implemented.

• A foreign government can block repatriation of profits

and even seize the firm’s assets.

• 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.

Page 11: Risk and Refinements of Capital Budgeting

Behavioral Approaches for Dealing with Risk

International Risk Considerations

• 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

cash flows overall.

• As a result, it is important to approach international

capital projects from a strategic viewpoint rather than

from a strictly financial perspective.如:搶市場灘頭堡,確保原料來源,即使是個 NPV似乎 <0的跨國 project

Page 12: Risk and Refinements of Capital Budgeting

Risk-Adjustment TechniquesCertainty 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

on the following slide.

Page 13: Risk and Refinements of Capital Budgeting

Year Project A Project B

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

1 14,000 28,000

2 14,000 12,000

3 14,000 10,000

4 14,000 10,000

5 14,000 10,000

NPV $11,071 $10,924

Bennett CompanyProject's A and B

(10% cost of Captial)

Risk-Adjustment TechniquesCertainty Equivalents

Page 14: Risk and Refinements of Capital Budgeting

Risk-Adjustment TechniquesCertainty 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,

where CEs represent the percentage of the cash

flows that you would be satisfied to receive for

certain rather than the original (possible) cash

flows.

Page 15: Risk and Refinements of Capital Budgeting

Risk-Adjustment TechniquesCertainty Equivalents

Certain Present

Year Project A CE Cash flows PVIF Value

0 (42,000)$ 1.00 (42,000)$ 1.0000 (42,000)$

1 14,000 0.90 12,600$ 0.9434 11,887

2 14,000 0.90 12,600$ 0.8900 11,214

3 14,000 0.80 11,200$ 0.8396 9,404

4 14,000 0.70 9,800$ 0.7921 7,763

5 14,000 0.60 8,400$ 0.7473 6,277

Net Present Value 4,544$

Bennett CompanyCertainty Equivalents Applied to Project A

(Risk-free rate = 6%)

Page 16: Risk and Refinements of Capital Budgeting

Risk-Adjustment TechniquesCertainty Equivalents

Certain Present

Year Project B CE Cash flows PVIF Value

0 (45,000)$ 1.00 (45,000)$ 1.0000 (45,000)$

1 28,000 1.00 28,000$ 0.9434 26,415

2 12,000 0.90 10,800$ 0.8900 9,612

3 10,000 0.90 9,000$ 0.8396 7,557

4 10,000 0.80 8,000$ 0.7921 6,337

5 10,000 0.70 7,000$ 0.7473 5,231

Net Present Value 10,151$

Bennett CompanyCertainty Equivalents Applied to Project B

(Risk-free rate = 6%)

和 project A相比較

Page 17: Risk and Refinements of Capital Budgeting

Risk-Adjustment TechniquesRisk-Adjusted Discount Rates

Bennett Company also wishes to apply the Risk-

Adjusted Discount Rate (RADR) approach to

determine whether to implement Project A or B.

To do so, Bennett has developed the following

Risk Index to assist them in their endeavor.

Page 18: Risk and Refinements of Capital Budgeting

Required

Risk Return

Index (RADR)

0.0 6%

0.2 7%

0.4 8%

0.6 9%

0.8 10%

1.0 11%

1.2 12%

1.4 13%

1.6 14%

1.8 15%

2.0 16%

Risk-Adjustment TechniquesRisk-Adjusted Discount Rates

Page 19: Risk and Refinements of Capital Budgeting

Risk-Adjustment TechniquesRisk-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

shown on the following slide.

Page 20: Risk and Refinements of Capital Budgeting

Risk-Adjustment TechniquesRisk-Adjusted Discount Rates

Risk Adjusted Discount Rate Applied to Project A

Present

Year Project A PVIF Value

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

4 14,000 0.5921 8,289

5 14,000 0.5194 7,271

Net Present Value 6,063$

Bennett Company

(RADR = 14%)

Page 21: Risk and Refinements of Capital Budgeting

Risk-Adjustment TechniquesRisk-Adjusted Discount Rates

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

Net Present Value 9,798$

Bennett CompanyRisk Adjusted Discount Rate Applied to Project B

(RADR = 11%)

“理論上”也可用CAPM來尋找project 的RADR :

])([)( fmifi rrErrE

β

SMLIRR

IRR rf

若 project 的 IRR落在 SML上方,則accept the project,因為其NPV>0若 project 的 IRR落在 SML下方,則reject the project,因為其 NPV<0

Page 22: Risk and Refinements of Capital Budgeting

Risk-Adjustment TechniquesPortfolio Effects

• As noted in Chapter 6, individual investors must hold 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 too hold diversified portfolios.

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

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

Page 23: Risk and Refinements of Capital Budgeting

Risk-Adjustment TechniquesPortfolio Effects

• It turns out that firms are not rewarded for

diversification because investors can do so

themselves.

• An investor can diversify more readily, easily, and

costlessly simply by holding portfolios of stocks.

Page 24: Risk and Refinements of Capital Budgeting

Risk-Adjustment TechniquesCE Versus RADR in Practice

• In general, CEs are the theoretically preferred

approach for project risk adjustment because they

separately adjust for risk and time.

• CEs 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.

Page 25: Risk and Refinements of Capital Budgeting

Risk-Adjustment TechniquesCE Versus RADR in Practice

• Because of the mathematics of discounting, the RADR

approach implicitly assumes that risk is an increasing

function of time.

• However, because of the complexity in developing

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

and the corresponding RADR is then applied.

Page 26: Risk and Refinements of Capital Budgeting

Capital Budgeting RefinementsComparing Projects With Unequal Lives

• If projects are independent, comparing projects with

unequal lives is not critical.

• 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.

• This is particularly important when continuing service

is needed from the projects under consideration.

Page 27: Risk and Refinements of Capital Budgeting

Capital Budgeting RefinementsComparing Projects With Unequal Lives

Project X Project Y

Year

0 (70,000)$ (85,000)$

1 28,000$ 35,000$

2 33,000$ 30,000$

3 38,000$ 25,000$

4 -$ 20,000$

5 -$ 15,000$

6 -$ 10,000$

NPV $11,277 $19,013

Cash Flows

The AT Company, a regional cable-TV firm, is evaluating two projects, X and Y. The projects’ cash flows and

resulting NPVs at a cost of capital of 10% is given below.

Page 28: Risk and Refinements of Capital Budgeting

Capital Budgeting RefinementsComparing Projects With Unequal Lives

The AT Company, a regional cable-TV firm, is evaluating 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 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 efficient technique -- the annualized NPV approach.

Page 29: Risk and Refinements of Capital Budgeting

Capital Budgeting RefinementsComparing Projects With Unequal Lives

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

that can be used to select the best project.

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

3. Select the project with the highest ANPV.

Annualized NPV (ANPV)

Page 30: Risk and Refinements of Capital Budgeting

Capital Budgeting RefinementsComparing Projects With Unequal Lives

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

ANPVY = $19,013/PVIFA10%,6 years = $4,366

3. Choose the project with the higher ANPV.

Pick project X.

Annualized NPV (ANPV)

Page 31: Risk and Refinements of Capital Budgeting

Capital Rationing• Firm’s often operate under conditions of capital

rationing -- they have more acceptable independent 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

Page 32: Risk and Refinements of Capital Budgeting

Capital RationingExample

Project Initial Investment IRR PV of Inflows NPV

A 80,000$ 12% 100,000$ 20,000$

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

C 100,000 16% 145,000 45,000

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

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

F 110,000 11% 126,500 16,500

Gould Company Investment Proposals

k=10%

Page 33: Risk and Refinements of Capital Budgeting

若 capital constraint為 $250,000,則選B 、 C 、 E 。

IRR Approach

Capital Rationing

Project IRR Initial Investment

B 20% 70,000$

C 16% 100,000

E 15% 60,000

A 12% 80,000

F 11% 110,000

D 8% 40,000

Gould Proposals(Ranked by IRR)

Page 34: Risk and Refinements of Capital Budgeting

Capital RationingIRR Approach

Initial Cumulative

Project IRR Investment Investment

B 20% 70,000$ 70,000$

C 16% 100,000 170,000

E 15% 60,000 230,000

A 12% 80,000 310,000

F 11% 110,000 420,000

D 8% 40,000 460,000

Gould Proposals(Cumulative Investment)

Assume the firm’s cost of capital is 10% and has a maximum of

$250,000 availablefor investment.

Ranking the projects according

to IRR, the optimal set of projects for

Gould is B, C,and E.

Page 35: Risk and Refinements of Capital Budgeting

Capital RationingIRR Approach

PV of Initial

Project IRR Inflows Investment NPV

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

C 16% 145,000 100,000 45,000

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

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

Gould Company Investment Proposals(Ranked by IRR)

If we rationcapital using the

IRR approachand maintain the

rankings providedby IRR, the total

PV of inflows andNPV would be$336,000 and

$106,000respectively.

Page 36: Risk and Refinements of Capital Budgeting

Capital RationingNPV Approach

PV of Initial

Project IRR Inflows Investment NPV

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

C 16% 145,000 100,000 45,000

A 12% 100,000 80,000 20,000

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

Gould Company Investment Proposals(Ranked by NPV)

However, if werank them such

that NPV is maximized, thenwe can use our

entire budget andraise the PV of

inflows and NPV to$357,000 and

$107,000respectively. 注意: B 、 C 、 E 、 A 、 F 的 IRR皆大於 k=10%

若選 C 、 B 、 A而非前面的 B 、 C 、 E,則可剛好用盡所有的資金 $250,000,且可提升NPV至 $107,000

(1)

(3)

(2)