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Principles of Managerial Finance
9th Edition
Chapter 10
Risk & Refinements
in 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.
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.
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.
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.
Behavioral Approaches for Dealing with Risk
Sensitivity
Analysis
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.
Simulation
Behavioral Approaches for Dealing with Risk
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.
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.
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
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.
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 $10,924
Bennett CompanyProject's A and B
(10% cost of Captial)
Risk-Adjustment TechniquesCertainty Equivalents
Risk-Adjustment TechniquesCertainty Equivalents
Assume that it is determined that Project A is
actually more risky than B.
To adjust for this risk, you decide to apply
certainty equivalents (CEs) to the cash flows,
where CEs represent the percentage of the cash
flows that you would be satisfied to receive for
certain rather than the original (possible) cash
flows.
Risk-Adjustment TechniquesCertainty Equivalents
Certain Present
Year Project A CE Cash flows PVIF Value
0 (42,000)$ 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%)
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
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.
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
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.
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%)
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
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.
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.
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.
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.
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.
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.
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.
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)
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 = $4,366
3. Choose the project with the higher ANPV.
Pick project X.
Annualized NPV (ANPV)
Capital Rationing• Firm’s often operate under conditions of capital
rationing -- they have more acceptable independent projects than they can fund.
• In theory, capital rationing should not exist -- firms should accept all projects that have positive NPVs.
• However, research has found that management internally imposes capital expenditure constraints to avoid what it deems to be “excessive” levels of new financing, particularly debt.
• Thus, the objective of capital rationing is to select the group of projects within the firm’s budget that provides the highest overall NPV
Capital RationingExample
Project Initial Investment IRR PV of Inflows NPV
A 80,000$ 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%
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)
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
$250,000 availablefor investment.
Ranking the projects according
to IRR, the optimal set of projects for
Gould is B, C,and E.
Capital RationingIRR Approach
PV of Initial
Project IRR Inflows Investment NPV
B 20% 112,000$ 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
$106,000respectively.
Capital RationingNPV Approach
PV of Initial
Project IRR Inflows Investment NPV
B 20% 112,000$ 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)
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