14 Chapter Risk Topics and Real Options in Capital Budgeting Slides Developed by: Terry Fegarty Seneca College

© 2006 by Nelson, a division of Thomson Canada Limited 2 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 and Simulation  Scenario/Sensitivity Analysis  Computer (Monte Carlo) Simulation  Decision Tree Analysis Real Options  Valuing Real Options  Designing for Real Options

© 2006 by Nelson, a division of Thomson Canada Limited 3 Chapter 14 – Outline (2) Incorporating Risk Into Capital Budgeting — The Theoretical Approach and Risk-Adjusted Rates of Return  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

© 2006 by Nelson, a division of Thomson Canada Limited 4 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

© 2006 by Nelson, a division of Thomson Canada Limited 5 Figure 14.1: The Probability Distribution of a Future Cash Flow as a Random Variable

© 2006 by Nelson, a division of Thomson Canada Limited 6 Figure 14.2: Risk in Estimated Cash Flows

© 2006 by Nelson, a division of Thomson Canada Limited 7 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

© 2006 by Nelson, a division of Thomson Canada Limited 8 Figure 14.3: Project NPVs Reflecting Risky Cash Flows

© 2006 by Nelson, a division of Thomson Canada Limited 9 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

© 2006 by Nelson, a division of Thomson Canada Limited 10 Scenario/Sensitivity Analysis Involves selecting a worse, most likely and best case for each cash flow  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

© 2006 by Nelson, a division of Thomson Canada Limited 11 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$450$400$700 Most likely Best case 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] + $700[0.7722] = –$ Most likely: NPV = $ (the project’s traditional NPV) Best case: NPV = $ Example

© 2006 by Nelson, a division of Thomson Canada Limited 12 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)

© 2006 by Nelson, a division of Thomson Canada Limited 13 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

© 2006 by Nelson, a division of Thomson Canada Limited 14 Figure 14.4: Results of Monte Carlo Simulation for NPV

© 2006 by Nelson, a division of Thomson Canada Limited 15 Computer (Monte Carlo) Simulation Sample output from Crystal Ball simulation.

© 2006 by Nelson, a division of Thomson Canada Limited 16 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

© 2006 by Nelson, a division of Thomson Canada Limited 17 Figure 14.5: A Simple Decision Tree

© 2006 by Nelson, a division of Thomson Canada Limited 18 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. Example 14.2 : Decision Tree Analysis Example

© 2006 by Nelson, a division of Thomson Canada Limited 19 Example 14.2: Decision Tree Analysis A:First, draw a decision tree diagram for the project. Then calculate the NPV along each path. Example $1.5M ($5M) $3M P =.6 P =.4 NPV $2.461M $-1.270M Then calculate the weighted NPV for the tree. $1.077M Expected NPV = $-.508M40%$-1.270MPoor $1.585M60%$2.641MGood ProductProbabilityNPVDemand The decision tree points out that a big loss is quite possible, although the expected NPV is positive.

© 2006 by Nelson, a division of Thomson Canada Limited 20 Figure 14.6 : A More Complex Decision Tree

© 2006 by Nelson, a division of Thomson Canada Limited 21 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

© 2006 by Nelson, a division of Thomson Canada Limited 22 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

© 2006 by Nelson, a division of Thomson Canada Limited 23 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

© 2006 by Nelson, a division of Thomson Canada Limited 24 Incorporating Risk Into Capital Budgeting Cost of capital (k) plays key role in both NPV and IRR  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

© 2006 by Nelson, a division of Thomson Canada Limited 25 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

© 2006 by Nelson, a division of Thomson Canada Limited 26 Incorporating Risk Into Capital Budgeting Choosing the Risk-Adjusted Rate for Various Projects  Arbitrary process, subjective  Replacement projects—replacing something the firm has already been doing Firm's cost of capital is nearly always appropriate for this type of project  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 projects—usually involve much more risk than current projects Portfolio theory and the CAPM may be useful

© 2006 by Nelson, a division of Thomson Canada Limited 27 Estimating Risk-Adjusted Rates Using the Capital Asset Pricing Model (CAPM) Portfolio theory and the CAPM can sometimes be used to generate risk- adjusted rates 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

© 2006 by Nelson, a division of Thomson Canada Limited 28 Estimating Risk-Adjusted Rates Using the Capital Asset Pricing Model (CAPM) Diversifiable and Non-Diversifiable Risk for Projects  Projects have two levels of diversifiable risk Some risk is diversified away within the firm's portfolio of projects Some risk is diversified away by the shareholders' investment portfolios  Remaining risk is the market (systematic) risk of the project

© 2006 by Nelson, a division of Thomson Canada Limited 29 Figure 14.7 : Components of Project Risk

© 2006 by Nelson, a division of Thomson Canada Limited 30 Estimating the Risk-Adjusted Rate Through Beta Security Market Line (SML) can be used to determine a risk-adjusted rate for new venture project  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)

© 2006 by Nelson, a division of Thomson Canada Limited 31 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? Example

© 2006 by Nelson, a division of Thomson Canada Limited 32 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. Example

© 2006 by Nelson, a division of Thomson Canada Limited 33 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 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. Example Since the NPV is barely positive, the project is marginal at best.

© 2006 by Nelson, a division of Thomson Canada Limited 34 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

© 2006 by Nelson, a division of Thomson Canada Limited 35 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

© 2006 by Nelson, a division of Thomson Canada Limited 36 Projects in Divisions—The Accounting Beta Method If pure play division is found within a corporation, may be able to estimate the beta of that division using the accounting beta method  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

© 2006 by Nelson, a division of Thomson Canada Limited 37 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