Risk and Capital Budgeting 13 Risk and Capital Budgeting Block, Hirt, and Danielsen Foundations of Financial Management 16th edition

Definition of Risk in Capital Budgeting Risk defined in terms of variability of possible outcomes from given investment Risk is measured in terms of losses and uncertainty Assets (real or financial) which have a greater chance of loss are considered more risky than those with a lower chance of loss. Risk may be used interchangeably with the term uncertainty to refer to the variability of returns associated with a given asset.

Types of Risk

Risk Preferences Most investors and managers are risk-averse Prefer relative certainty as opposed to uncertainty Expect higher value or return for risky investments Investors require a higher expected value or return for risky investments

Risk of a Single Asset Norman Company, a custom golf equipment manufacturer, wants to choose the better of two investments, A and B. Each requires an initial outlay of $10,000 and each has a most likely annual rate of return of 15%. Management has estimated the returns associated with each investment. The three estimates for each assets, along with its range, is given on next slide. Asset A appears to be less risky than asset B. The risk averse decision maker would prefer asset A over asset B, because A offers the same most likely return with a lower range (risk).

Risk of Single Asset

Risk of Single Asset The wider the range of returns the more risky the investment

Actual Measurement of Risk Basic statistical devices used to measure the extent of risk in any given situation Expected value: 𝐷 = 𝐷𝑃 Standard deviation: σ= (𝐷− 𝐷 ) 2 𝑃 Coefficient of variation: 𝑉= 𝜎 𝐷

Probability Distribution with Differing Degrees of Risk Larger standard deviation means greater risk

Calculation of Standard Deviation Step 1 – Calculate the Expected Return

Calculation of Standard Deviation Step 2 – Calculate the Variance and Std Dev.

Figure 13-4 Probability Distribution with Differing Degrees of Risk Direct comparison of standard deviations not helpful if expected values of investments differ Standard deviation of $600 with expected value of $6,000 indicates less risk than standard deviation of $190 with expected value of $600

Actual Measurement of Risk Coefficient of Variation (V) Size difficulty can be eliminated by introducing coefficient of variation (V) Formula: 𝑉= 𝜎 𝐷 Project A = 600/6000 = .10 Project B = 190/600 = .31 The larger the coefficient, the greater the risk

Risk-Adjusted Discount Rate Different capital-expenditure proposals with different risk levels require different discount rates Project with normal amount of risk should be discounted at cost of capital Project with greater than normal risk should be discounted at higher rate Risk assumed to be measured by coefficient of variation (V)

Increasing Risk over Time Accurate forecasting becomes more difficult farther out in time Unexpected events Create higher standard deviation in cash flows Increase risk associated with long-lived projects Figure 13-6 Risk over time Depicts the relationship between risk and time

Figure 13-6 Risk Over Time

Qualitative Measures and Table 13-3 Setting up risk classes based on qualitative considerations Raising discount rate to reflect perceived risk Table 13-3 Risk Categories and associated discount rates

Table 13-4 Capital Budgeting Analysis Investment B preferred based on NPV calculation without considering risk factor

Capital-Budgeting Decision Adjusted for Risk— Example Assume Investment A calls for addition to normal product line, assigned 10% discount rate Investment B represents new product in foreign market, must carry 20% discount rate to adjust for large risk component NPV A at 10% Required Rate = $180.32 NPV B at 20% Required Rate = $-1493.70

Simulation Models Deal with uncertainties involved in forecasting outcome of capital budgeting projects or other decisions Computers enable simulation of various economic and financial outcomes using number of variables Monte Carlo model uses random variable for inputs Rely on repetition of same random process as many as several hundred times

Simulation Models Have ability to test various combinations of events Used to test possible changes in variable conditions included in process (real world) Allow planner to ask “what if” questions Driven by sales forecasts, with assumptions to derive income statements and balance sheets Generate probability acceptance curves for capital budgeting decisions

The Portfolio Effect An investment portfolio is any collection or combination of financial assets. If we assume all investors are rational and therefore risk averse, that investor will ALWAYS choose to invest in portfolios rather than in single assets. Investors will hold portfolios because he or she will diversify away a portion of the risk that is inherent in “putting all your eggs in one basket.” If an investor holds a single asset, he or she will fully suffer the consequences of poor performance. This is not the case for an investor who owns a diversified portfolio of assets.

Portfolio Risk Investment may change overall risk of firm depending on relationship to other investments Highly-correlated investments move in the same direction in good and bad times, do not diversify against risk Negatively-correlated investments move in opposite directions and are a greater risk reduction Uncorrelated investments provide some risk reduction

Coefficient of Correlation Represents extent of correlation among various projects and investments May take on values anywhere from -1 to +1 Real world will produce a more likely measure, between -0.2 negative correlation and +0.3 positive correlation Risk can be reduced Combining risky assets with low-risk or negatively correlated assets

Table 13-7 Measures of Correlation Diversification is enhanced depending upon the extent to which the returns on assets “move” together. This movement is typically measured by a statistic known as “correlation” as shown in the figure below.

Figure 13-9 Levels of Risk Reduction as Measured by the Coefficient of Correlation

Types of Risk

Types of Risk

Types of Risk

CAPM If you notice in the last slide, a good part of a portfolio’s risk (the standard deviation of returns) can be eliminated simply by holding a lot of stocks. The risk you can’t get rid of by adding stocks (systematic) cannot be eliminated through diversification because that variability is caused by events that affect most stocks similarly. Examples would include changes in macroeconomic factors such interest rates, inflation, and the business cycle.

CAPM In the early 1960s, finance researchers (Sharpe, Treynor, and Lintner) developed an asset pricing model that measures only the amount of systematic risk a particular asset has. In other words, they noticed that most stocks go down when interest rates go up, but some go down a whole lot more. They reasoned that if they could measure this variability—the systematic risk—then they could develop a model to price assets using only this risk. The unsystematic (company-related) risk is irrelevant because it could easily be eliminated simply by diversifying.

CAPM To measure the amount of systematic risk an asset has, they simply regressed the returns for the “market portfolio”—the portfolio of ALL assets—against the returns for an individual asset. The slope of the regression line—beta—measures an assets systematic (non-diversifiable) risk. In general, cyclical companies like auto companies have high betas while relatively stable companies, like public utilities, have low betas. The calculation of beta is shown on the following slide.

Beta as a Measurement of Risk To measure the amount of systematic risk an asset has, they simply regressed the returns for the “market portfolio”—the portfolio of ALL assets—against the returns for an individual asset. The slope of the regression line—beta—measures an assets systematic (non-diversifiable) risk. Measures volatility of returns on individual stock relative to returns on stock market index In general, cyclical companies like auto companies have high betas while relatively stable companies, like public utilities, have low betas. A common stock with a beta of 1.0 is said to be of equal risk with the market

Beta

Security Market Line The required return for all assets is composed of two parts: the risk-free rate and a risk premium. The risk premium is a function of both market conditions and the asset itself. The risk-free rate (RF) is usually estimated from the return on US T-bills

Security Market Line The risk premium for a stock is composed of two parts: The Market Risk Premium which is the return required for investing in any risky asset rather than the risk-free rate Beta, a risk coefficient which measures the sensitivity of the particular stock’s return to changes in market conditions.

Security Market Line

Security Market Line rZ = 7% + 1. 5 [11% - 7%] rZ = 13% Benjamin Corporation, a growing computer software developer, wishes to determine the required return on asset Z, which has a beta of 1.5. The risk-free rate of return is 7%; the return on the market portfolio of assets is 11%. Substituting bZ = 1.5, RF = 7%, and rm = 11% into the CAPM yields a return of: rZ = 7% + 1. 5 [11% - 7%] rZ = 13%

Shifts in the SML Inflation Shifts SML Risk Aversion Shifts SML

Final Comments on CAPM & SML The CAPM relies on historical data which means the betas may or may not actually reflect the future variability of returns. Therefore, the required returns specified by the model should be used only as rough approximations. The CAPM also assumes markets are efficient. Although the perfect world of efficient markets appears to be unrealistic, studies have provided support for the existence of the expectational relationship described by the CAPM in active markets such as the NYSE.