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Contemporary Financial Management
Chapter 11:
Capital Budgeting and Risk
© 2004 by Nelson, a division of Thomson Canada Limited
Introduction
 This chapter considers adjusting a project’s risk
level when it has more or less risk than the
firm’s average level of risk
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© 2004 by Nelson, a division of Thomson Canada Limited
Risk
 Project risk
 The risk that a project will perform below
expectations
 Some of the risk can be diversified away
 Systematic risk
 Depends on the risk of the project relative to
the market portfolio
 Systematic risk cannot be diversified away
 Capital Asset Pricing Model
 Used to estimate risk-adjusted discount rates
for capital budgeting
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© 2004 by Nelson, a division of Thomson Canada Limited
Adjusting for Total Project Risk
 Net Present Value (NPV) - Payback approach
 Simulation approach
 Sensitivity analysis
 Scenario analysis
 Risk-adjusted discount rate approach
 Certainty equivalent approach
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© 2004 by Nelson, a division of Thomson Canada Limited
NPV-Payback Approach
 A project must have a positive net present
value and a payback of less than a critical
number of years to be acceptable
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© 2004 by Nelson, a division of Thomson Canada Limited
Simulation Approach
 Estimate the probability distribution of each
element influencing a project’s cash flows.
 Calculate the NPV using randomly chosen
numerical values for the stochastic elements
 Repeat the process until a probability
distribution of the NPV can be estimated
 Possible stochastic elements:
 Number of units sold, market price, net
investment, unit production costs, unit selling
cost, project life, cost of capital
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© 2004 by Nelson, a division of Thomson Canada Limited
Sensitivity Analysis
 Involves systematically changing relevant
variables to identify which variables the NPV/IRR
seems most sensitive to
 Useful to make sensitivity curves to show the
impact of changes in a variable on the project’s
NPV
 Electronic spreadsheets and financial modeling
make sensitivity analysis easy to perform.
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© 2004 by Nelson, a division of Thomson Canada Limited
Scenario Analysis
 Estimate the expected NPV for each of:
 Optimistic
 Pessimistic
 Most likely
 Estimate the Probability of each scenario
 Compute the expected NPV
 Compute the standard deviation (SD) of the
NPV
 Considers the impact of simultaneous changes
in key variables on the desirability of an
investment project
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© 2004 by Nelson, a division of Thomson Canada Limited
Risk-Adjusted Discount Rate Approach
 An individual project is discounted at a discount
rate adjusted to the riskiness of the project
instead of discounting all projects at one rate
 ka* = rf + risk premium
 Calculate the NPV substituting ka* for k in the six
steps of capital budgeting
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© 2004 by Nelson, a division of Thomson Canada Limited
Certainty Equivalent Approach
 Involves converting expected risky Cash Flows
to their certainty equivalents and then
computing the NPV
 Risk-free rate (rf) is used as the discount rate
rather than the cost of capital (k)
 The certainty equivalent factor is the ratio of
the certainty equivalent Cash Flows to the
risky Cash Flows
certain return
t 
risky return
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© 2004 by Nelson, a division of Thomson Canada Limited
The Certainty-Equivalent NPV
n
NPV  Net Investment  0   
t 1
Net Cash Flowt t
1  rf 
t
 0 = Certainty equivalent factor for net investment at t=0
n = Expected economic life of the project
 t = Certainty equivalent factor for expected net cash flows
in each period, t
rf = risk free rate
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© 2004 by Nelson, a division of Thomson Canada Limited
Elements of Risk if Investing Abroad
 Captive funds – inability to repatriate
 Foreign government expropriates the assets
 Exchange rate risk
 Uncertain tax rates
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Calculating k: All Equity Case
 The project’s risk-adjusted discount rate is found
using the security market line (SML) equation:
k  rf   rm  rf 
*
e
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© 2004 by Nelson, a division of Thomson Canada Limited
The Equity and Debt Case
 Betas can be observed for firms in the same
investment class as the proposed investment
 These betas can be used to estimate riskadjusted discount rates
 A two-step process is used
 Calculate an unleveraged beta
 Calculate a new leveraged beta to reflect
appropriate debt capacity
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© 2004 by Nelson, a division of Thomson Canada Limited
Step 1: Calculate Unleveraged Beta
 Convert observed, leveraged beta (l) into an
unleveraged, or pure project beta (u)
u 
l
D
1  1  T   
E
T = Firm’s marginal tax rate
D = Market value of firm’s debt
E = Market value of firm’s equity
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© 2004 by Nelson, a division of Thomson Canada Limited
Step 2: Calculate New Leveraged Beta
 Calculate the new leveraged beta (l) for the
proposed capital structure of the new line of
business

 D 
l  u 1  1  T    
 E 

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© 2004 by Nelson, a division of Thomson Canada Limited
Step 2 (Continued)
 Calculate the required rate of return, ke, based
on the new leveraged beta, l:
k  rf  l rm  rf 
*
e
 Calculate the risk-adjusted required return,
ka*, on the new line of business:
E 
 D 
* 
k  k d 1  T  
 ke 


D  E
D  E
*
a
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© 2004 by Nelson, a division of Thomson Canada Limited
 
Major Points
 Adjust for project risk using any one of six
methods
 Net Present Value (NPV) -Payback approach
 Simulation approach
 Sensitivity analysis
 Scenario analysis
 Risk-adjusted discount rate approach
 Certainty equivalent approach
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© 2004 by Nelson, a division of Thomson Canada Limited