P i
i l
f M
i l
Principles of Managerial
Fi
Finance
9th Edition
9th Edition
Chapter 10
Chapter 10
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
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
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.
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
Behavioral Approaches for Dealing with Risk
Sensitivity
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
Behavioral Approaches for Dealing with Risk
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
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
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
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
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
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
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
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
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-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%
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
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
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
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.
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.
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
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
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
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
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
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.
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.
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.
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
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
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,
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
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
