Transcript Chapter 1: Risk Topics and Real Options in Capital Budgeting
14
Risk Topics and Real Options in Capital Budgeting
Slides Developed by: Terry Fegarty Seneca College
Chapter 14 – Outline (1)
• • • Risk in Capital Budgeting — General Considerations Cash Flows as Random Variables The Importance of Risk in Capital Budgeting Incorporating Risk in Capital Budgeting Scenario/Sensitivity Analysis Computer (Monte Carlo) Simulation Decision Tree Analysis — Scenario / Sensitivity Analysis and Simulation Real Options Valuing Real Options Designing for Real Options 2 © 2006 by Nelson, a division of Thomson Canada Limited
Chapter 14 – Outline (2)
• Incorporating Risk Into Capital Budgeting of Return — The Theoretical Approach and Risk-Adjusted Rates Estimating Risk-Adjusted Rates Using the Capital Asset Pricing Model (CAPM) Estimating the Risk-Adjusted Rate Through Beta Problems with the Theoretical Approach Projects in Divisions—The Accounting Beta Method A Final Comment on Risk in Capital Budgeting 3 © 2006 by Nelson, a division of Thomson Canada Limited
Cash Flows as Random Variables
• Risk is chance that a random variable will take on a value significantly different from the
expected value (mean)
In capital budgeting estimate of each future period's cash flow is random variable NPV and IRR of project are random variables with expected values and variances that reflect risk • Thus, actual value is likely to be different than mean • Amount that actual value is likely to differ from expected value related to variance or
standard deviation
4 © 2006 by Nelson, a division of Thomson Canada Limited
Figure 14.1: The Probability Distribution of a Future Cash Flow as a Random Variable © 2006 by Nelson, a division of Thomson Canada Limited 5
Figure 14.2:
Flows Risk in Estimated Cash
© 2006 by Nelson, a division of Thomson Canada Limited 6
The Importance of Risk in Capital Budgeting
• • • Thus far we've viewed cash flows as
point estimates
We could be making wrong decision by using point estimates for NPV and IRR The
riskiness
of project's cash flows must be considered when deciding upon a project 7 © 2006 by Nelson, a division of Thomson Canada Limited
Figure 14.3:
Project NPVs Reflecting Risky Cash Flows
© 2006 by Nelson, a division of Thomson Canada Limited 8
The Importance of Risk in Capital Budgeting
• • Risk Aversion All other things being equal, we prefer
less risky
capital projects to those with more risk Changing the Nature of the Company A company is a
portfolio of projects
Thus, if a firm undertakes new projects while ignoring risk, it could change its fundamental risk characteristics • A company adopting riskier projects than it used to will become a riskier company • Will lead to a higher
beta
• Can generally lead to a
share price reduction
9 © 2006 by Nelson, a division of Thomson Canada Limited
Scenario/Sensitivity Analysis
• Involves selecting a
worse, most likely best case
for each cash flow and Most likely is cash flow estimate we've worked with before • Recalculate the project's NPV (or IRR) under
each
scenario Gives subjective feel for variability of NPV to changes in assumptions • Referred to as
sensitivity analysis
10 © 2006 by Nelson, a division of Thomson Canada Limited
Example 14.1:
Scenario/Sensitivity Analysis
Q: Project A has an initial outflow of $1,400 and three variable cash inflows:
C 1 C 2 C 3
Worst case Most likely Best case $450 $400 $700 550 650 450 500 800 900 Analyze project A’s NPV. Assume the cost of capital is 9%.
A:
Worst case: NPV = –$1,400 + $450[PVF9,1] + $400[PVF9,2] +$700[PVF9,3] = –$1,400 + $450[0.9174] + $400[0.8417] + $700[0.7722] = –$109.95
Most likely: NPV = $101.10 (the project’s traditional NPV) Best case: NPV = $312.14
© 2006 by Nelson, a division of Thomson Canada Limited 11
Computer (Monte Carlo) Simulation
• • • • Involves making assumptions about shape of probability distribution for
each
future cash flow in project Computer model draws a set of random observations for each cash flow and calculates NPV of project Repeats process to generate many (1000s?) possible values for NPV (IRR) Computer then simulates project by constructing probability distribution of the project's NPV (IRR) 12 © 2006 by Nelson, a division of Thomson Canada Limited
Computer (Monte Carlo) Simulation
• Benefits Provides most likely values for NPV (IRR) • Expected profitability Provides approximate shapes of probability distribution for NPV (IRR) • Risk assessment • Drawbacks Probability distributions have to be estimated subjectively Project cash flows tend to be positively correlated— hard to estimate the extent of that correlation Interpretation of results is
subjective
13 © 2006 by Nelson, a division of Thomson Canada Limited
Figure 14.4:
Results of Monte Carlo Simulation for NPV
© 2006 by Nelson, a division of Thomson Canada Limited 14
Computer (Monte Carlo) Simulation
3,000 Trials
.026
Forecast: NPV Frequency Chart 13 O utlie rs
78 .020
.013
.007
.000
-20,000, 000.00
0.00
20, 000,000. 00 40, 000,000. 00 Certainty i s 81. 83% from 0.00 t o +I nf init y Dol lars 0 60, 000,000. 00
Sample output from Crystal Ball simulation .
58. 5 39 19. 5 © 2006 by Nelson, a division of Thomson Canada Limited 15
Decision Tree Analysis
• •
Decision tree
— time line which branches into alternate paths whenever an event can turn out more than one way Place at which branches separate is called a
node
Any number of branches can emanate from a node but the probabilities must sum to 1.0 (or 100%)
Path
— following the tree along a branch Evaluating project involves calculating NPVs along all possible paths and assigning probability to each NPV From that, probability distribution for NPV is developed 16 © 2006 by Nelson, a division of Thomson Canada Limited
Figure 14.5:
A Simple Decision Tree
© 2006 by Nelson, a division of Thomson Canada Limited 17
Example 14.2
:
Decision Tree Analysis
Q:
The Wing Foot Shoe Company is considering a three-year project to market a running shoe based on new technology. A market study indicates a 60% probability that demand will be good and a 40% chance that it will be poor . It will cost $5M to bring the new shoe to market. Cash flow estimates indicate inflows of $3M per year for three years at full manufacturing capacity if demand is good, but just $1.5M per year if it’s poor. Wing Foot’s cost of capital is 10%. Analyze the project and develop a rough probability distribution for NPV.
18 © 2006 by Nelson, a division of Thomson Canada Limited
Example 14.2:
Decision Tree Analysis
A
: First, draw a decision tree diagram for the project. Then calculate the NPV along each path.
0
P = .6
1 $3M 2 $3M 3 $3M
NPV $2.461M
($5M)
P = .4
$1.5M
$1.5M
$1.5M
$-1.270M
Then calculate the weighted NPV for the tree.
Demand Good Poor NPV $2.641M
$-1.270M
Probability 60% 40% Expected NPV = Product $1.585M
$-.508M
$1.077M
The decision tree points out that a big loss is quite possible, although the expected NPV is positive.
19 © 2006 by Nelson, a division of Thomson Canada Limited
Figure 14.6
:
A More Complex Decision Tree
© 2006 by Nelson, a division of Thomson Canada Limited 20
Real Options
• •
Option
— ability or right to take certain course of action
Real options
— options that exist in a real physical, business sense Ex; a revolving credit agreement for a commitment fee • Firm has right but not obligation to borrow 21 © 2006 by Nelson, a division of Thomson Canada Limited
Valuing Real Options
• • Real options frequently occur in capital budgeting Generally
increase project's expected NPV
• Increase is estimate of option's value Real options are generally worth more than their impact on expected NPV because they generally
reduce risk
However, difficult to quantify reduction in risk 22 © 2006 by Nelson, a division of Thomson Canada Limited
Designing for Real Options
• • • •
Abandonment options
can increase expected NPV and lower risk But contractual obligations can make abandonment tough
Expansion options
Frequently require little or no early commitment and should be planned in whenever possible
Investment timing options
Allow a firm to delay an investment until it's sure about other relevant issues Ex; a land option contract
Flexibility options
Allow company ability to respond more easily to changes in business conditions 23 © 2006 by Nelson, a division of Thomson Canada Limited
Incorporating Risk Into Capital Budgeting
•
Cost of capital
NPV and IRR (
k
) plays key role in both For NPV, k used as discount rate • A higher k leads to a lower NPV, reducing the chance of project acceptance For IRR, IRR is compared to k • A higher k leads to a lower chance of project acceptance 24 © 2006 by Nelson, a division of Thomson Canada Limited
Incorporating Risk Into Capital Budgeting
• Riskier Projects Should Be Less Acceptable Idea is to make risky projects less acceptable than others with similar expected cash flows Using a
higher
,
risk-adjusted rate
for risky projects lowers their chance of acceptance • The Starting Point for Risk-Adjusted Rates The cost of capital is used to analyze projects if their risk is comparable to the firm’s overall risk Higher rates are used for riskier projects 25 © 2006 by Nelson, a division of Thomson Canada Limited
Incorporating Risk Into Capital Budgeting
• Choosing the Risk-Adjusted Rate for Various Projects Arbitrary process, subjective
Replacement
firm has already been doing • Firm's cost of capital is nearly always appropriate for this type of project projects—replacing something the
Expansion
• projects—more risky than the current level, but not much more Rule of thumb is to add 1-3% points to the cost of capital
New venture
risk than current projects • projects—usually involve much more
Portfolio theory
and the
CAPM
may be useful 26 © 2006 by Nelson, a division of Thomson Canada Limited
Estimating Risk-Adjusted Rates Using the Capital Asset Pricing Model (CAPM)
• •
Portfolio theory
adjusted rates and the
CAPM
can sometimes be used to generate risk The Project as a Diversification If firm is viewed as a collection of projects, new venture diversifies the company New venture also diversifies investment portfolios of the firm's
shareholders
27 © 2006 by Nelson, a division of Thomson Canada Limited
Estimating Risk-Adjusted Rates Using the Capital Asset Pricing Model (CAPM)
• Diversifiable and Non-Diversifiable Risk for Projects Projects have two levels of
diversifiable
• Some risk is diversified away within the firm's portfolio of projects risk • Some risk is diversified away by the shareholders' investment portfolios Remaining risk is the risk of the project
market
(systematic) 28 © 2006 by Nelson, a division of Thomson Canada Limited
Figure 14.7
:
Components of Project Risk
© 2006 by Nelson, a division of Thomson Canada Limited 29
Estimating the Risk-Adjusted Rate Through Beta
• •
Security Market Line (SML)
determine a risk-adjusted rate for new venture project can be used to SML: k x = k RF + (k M - k RF ) X Where X is beta, used as a measure of new venture project’s market risk If project is viewed as a business in a particular field, use a beta common to that field Method most appropriate when independent, publicly traded firm can be found that is in the same business as the new venture
(pure play
firm) 30 © 2006 by Nelson, a division of Thomson Canada Limited
Example 14.6
:
Estimating the Risk Adjusted Rate Through Beta
Q:
Orion Inc. is considering producing a sophisticated tactical radio for sale to the Canadian Forces, but is concerned because the military market is known to be quite risky. The military radio market is dominated by Milrad Inc., which holds a 60% market share. Antex Radio Corp. Is another established competitor with a 20% share. Both Milrad and Antex make only military radios. Milrad's beta is 1.4 and Antex's is 2.0 Orion's beta is 1.1. The return on an average publicly traded stock (
k
M ) is about 10%. The yield on short-term Treasury bills (
k
RF ) is currently 5%. Orion's cost of capital is 8%.
The military ratio project is expected to require an initial outlay of $10 million. Subsequent cash inflows are expected to be $3 million per year over a five-year contract.
Should Orion undertake the project?
31 © 2006 by Nelson, a division of Thomson Canada Limited
Estimating the Risk-Adjusted Rate Through Beta—Example
A:
The military radio business division would clearly be more risky than Orion's current business projects given the high betas of Milrad and Antex vs. Orion. Milrad and Antex are both pure play firms, but since Milrad is the market leader it probably has less risk than Antex. We need to use a beta from a company that will be in a similar position as our own firm; thus, we will use Antex's beta of 2.0 to evaluate the military radio project.
First, calculate the risk-adjusted beta for the project: K = 5% + (10% - 5%)2.0 = 15.0% Note that this rate is considerably higher than Orion's current 8% cost of capital.
© 2006 by Nelson, a division of Thomson Canada Limited 32
Estimating the Risk-Adjusted Rate Through Beta—Example
A:
Next calculate the proposed project's NPV using the 15% risk adjusted rate: NPV = -$10.0M + $3M[PVFA15,5] = -$10M + $3M[3.3522] = $0.1M
Since the NPV is barely positive, the project is marginal at best.
NOTE: If the project had been evaluated at Orion's 8% cost of capital, it would have lead to an NPV of $2.0M
However, adjusting for risk has shown the project to be only marginal.
33 © 2006 by Nelson, a division of Thomson Canada Limited
Problems with the Theoretical Approach
• • Pure play firm must be solely in the business of the new venture Finding pure play firm is difficult Betas of conglomerates are influenced by other divisions (in other industries) Thus, we have to estimate betas by using firms in similar (but not exactly) the same businesses • Reduces credibility of technique 34 © 2006 by Nelson, a division of Thomson Canada Limited
Problems with the Theoretical Approach
• Another problem—market risk may not be only risk that is important Major business-specific risks may be present (not diversified away) If total risk is much higher than market risk, it would lead to an even higher risk-adjusted rate 35 © 2006 by Nelson, a division of Thomson Canada Limited
Projects in Divisions—The Accounting Beta Method
• If pure play division is found method
within
a corporation, may be able to estimate the beta of that division using the accounting beta Develop beta for division from its accounting records (rather than share price data) • Regress historical divisional return on equity against return on a major market index (TSX/S&P Composite Index) • Slope of the regression line represents the division's beta 36 © 2006 by Nelson, a division of Thomson Canada Limited
A Final Comment on Risk in Capital Budgeting
• Virtually every firm uses capital budgeting techniques but only a few overtly try to incorporate risk • Business managers do recognize risk but they do it judgmentally 37 © 2006 by Nelson, a division of Thomson Canada Limited