Chapter 12 Risk Topics and Real Options in Capital Budgeting and Cash Flow Estimation Cash Flows as Random Variables “Risk” in every day usage: the probability that something bad will happen “Risk” in financial theory: Associated with random variables and their probability distributions Cash Flows as Random Variables Risk – the chance that a random variable will take on a value significantly different from the expected value – In capital budgeting the future period's cash flow estimate is a random variable Figure 12-1 The Probability Distribution of a Future Cash Flow as a Random Variable Cash Flows as Random Variables The NPV and IRR are random variables with their own probability distributions – Actual value may be different than the mean – The amount the actual value is different from expected is related to the variance or standard deviation Figure 12-2 Risk in Estimated Cash Flows The Importance of Risk in Capital Budgeting Until now we have viewed cash flows as point estimates – a single number rather than a range of possibilities Actual cash flows are estimates, a wrong decision could be made using point estimates for NPV and IRR The riskiness of a project's cash flows must be considered Figure 12-3 Project NPVs Reflecting Risky Cash Flows The Importance of Risk in Capital Budgeting Risk Aversion Changing the Nature of a Company – A company is a portfolio of projects – Ignoring risk when undertaking new projects can change the firm’s overall risk characteristics Scenario/Sensitivity Analysis Select a worst, most likely, and best case for each cash flow Recalculate the project's NPV (or IRR) under several scenarios – Gives an intuitive sense of the variability of NPV – Also called sensitivity analysis 10 Valuing Real Options The Risk Effect is Tricky – – – – Not all real options have a risk effect To lower risk an option has to reduce a potential loss not make a success better A case by case analysis is necessary An Approach Through Rate of Return – If lower risk is associated with a lower rate of return in NPV calculations, the result is higher NPV 28 Designing Real Options into Projects Abandonment option – Usually increase NPV and lower risk – Contract obligations can make abandonment tough Expansion options – Often require little or no early commitment – Should be planned in whenever possible Investment timing options – Permit delaying investment until more certain about surrounding Flexibility options – Preserve ability to respond to changing business conditions 29 issues Incorporating Risk Into Capital Budgeting – – For NPV k is used as the discount rate – – For IRR Compare IRR to k A higher k leads to lower NPV A higher k leads to a lower chance that reducing the chance of project IRR>k reducing probability of project acceptance acceptance The cost of capital (k) plays a key role in both NPV and IRR 30 Incorporating Risk Into Capital Budgeting Riskier Projects Should Be Less Acceptable – Using a higher, risk-adjusted rates for risky projects lowers their chance of acceptance The Starting Point for Risk-Adjusted Rates is the firm’s current risk level reflected in its cost of capital 31 Incorporating Risk Into Capital Budgeting Relating Interest Rates to Risk – Interest rates are comprised of a base rate plus a risk premium – Investors demand a higher interest rates – risk premiums  higher if they are to bear more risk In capital budgeting the company is the investor 32 Incorporating Risk Into Capital Budgeting Choosing the Risk-Adjusted Rate for Various Projects – An arbitrary, subjective process Three categories of increasing risk – Replacements – low risk, use cost of capital – Expansion projects - slightly more risky than the current level – New ventures – generally involve a lot more risk 33 Estimating Risk-Adjusted Rates Using CAPM The project as a diversification – If viewed as a collection of projects, a new venture diversifies the firm – A new venture also diversifies the stockholders’ investment portfolios 34 Estimating the Risk-Adjusted Rate Through Beta The Security Market Line (SML) can be used to determine a risk-adjusted rate for a new venture SML: kx = kRF + (kM - kRF) bX – bX = beta = the measure of a company's systematic risk If a project is viewed as a business in a particular field, use a beta common to that field to estimate a risk-adjusted rate for project analysis 35 Estimating Risk-Adjusted Rates Using CAPM The project as a diversification Diversifiable and non-diversifiable risk for projects – Projects have two levels of diversifiable risk Some risk diversified away within the firm's portfolio of projects Some risk diversified away by the shareholders' investment portfolios The remaining risk is systematic risk 36 Figure 12-7 Components of Project Risk 37 Concept Connection Example 12-6 Risk-Adjusted Rates - SML Orion Inc makes radio communications equipment beta = 1.1 cost of capital = 8% Considering a venture into risky military radios Military radio market is dominated by Milrad Inc - 60% market share, beta = 1.4 Antex Radio Corp - 20% market share, beta = 2.0 Both make only military radios kM = 10% , kRF = 5% C0 = $10M, Ci= $3M n = years Should Orion undertake the project? 38 Concept Connection Example 12-6 Risk-Adjusted Rates - SML Calculate the risk-adjusted rate for the project: k = 5% + (10% - 5%)2.0 = 15.0% Then calculate the 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 NPV at Orion’s own 8% cost of capital is $2.0M clearly indicating acceptance Adjusted for risk, however, the project is marginal This is a crucial insight! 39 Problems with the Theoretical Approach It is often difficult to find a pure play firm from which to obtain an appropriate beta – If a pure play division is found within a corporation, estimate the beta of that division using the accounting beta method Systematic risk may not be only important risk – If total risk is important, an even higher risk-adjusted rate would be appropriate 40 Certainty Equivalents (CE) For every cash flow management develops a lower risk free (certain) figure that is as attractive as the forecast risky figure – Then calculate a risk adjusted NPV or IRR with those cash flows Alternatively choose a CE factor (0< 1) for each cash flow and multiply – CE factors generally decline as they proceed further into the future A Final Comment on Risk in Capital Budgeting Virtually every firm of any size uses capital budgeting techniques – But few explicitly include risk Business managers recognize risk but they it through subjective judgments 42 [...]... project with this additional possibility is on the next slide 20 Concept Connection Example 12- 3 More Complex Decision Trees The NPV for the new upper path is 21 Concept Connection Example 12- 3 More Complex Decision Trees 22 Concept Connection Example 12- 3 More Complex Decision Trees 23 Concept Connection Example 12- 3 More Complex Decision Trees The project’s probability distribution expected return are... Drawbacks – Probability distributions are difficult to estimate – Cash flows tend to be correlated – Interpretation of results is subjective 14 Figure 12- 4 Results of Monte Carlo Simulation for NPV 15 Figure 12- 5 A Simple Decision Tree 16 Concept Connection Example 12- 2 Decision Tree Analysis The Wing Foot Shoe Company is considering a new running shoe A market study indicates a 60% probability that demand... Connection Example 12- 2 Decision Tree Analysis A decision tree diagram and NPVs along each path are: NPV 0 1 P = 6 2 3 $2.461M $3M $3M $3M $1.5M $1.5M $1.5M ($5M) P = 4 $-1.270M The expected NPV is: The decision tree explicitly calls out the fact that a big loss is quite possible, although the expected NPV is positive 18 Figure 12- 6 A More Complex Decision Tree 19 Concept Connection Example 12- 3 More Complex...Concept Connection Example 12- 1 Scenario Analysis 11 Concept Connection Example 12- 1 Scenario Analysis 12 Decision Tree Analysis Decision Tree: A graphic representation of a project in which certain events have multiple outcomes Decision Tree Analysis – Develops a probability... probability distribution expected return are as follows 24 Real Options An option is the right or ability to take a certain course of action A real option is a course of action that usually – Improves financial results under certain conditions – Exists in a real, physical business sense – Frequently occurs in capital budgeting – Generally increases a project's expected NPV 25 The Abandonment Option ... called sensitivity analysis 10 Concept Connection Example 12- 1 Scenario Analysis 11 Concept Connection Example 12- 1 Scenario Analysis 12 Decision Tree Analysis Decision Tree: A graphic representation... Interpretation of results is subjective 14 Figure 12- 4 Results of Monte Carlo Simulation for NPV 15 Figure 12- 5 A Simple Decision Tree 16 Concept Connection Example 12- 2 Decision Tree Analysis The Wing Foot... Connection Example 12- 3 More Complex Decision Trees The NPV for the new upper path is 21 Concept Connection Example 12- 3 More Complex Decision Trees 22 Concept Connection Example 12- 3 More Complex