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1. Risk and Capital Budgeting
1. Definition of Risk. One of the most essential areas in a business firm that must be managed is risk as it relates to both the firm's financial assets and the projects it accepts. It is defined as ____(Key Term). Risk occurs in decision-making when there is a wide range of possible outcomes.
2. Investors and Risk. Neither firm management nor investors like risk. They are generally risk-averse. See What is Risk? (60.0K) . They have to take some risk in order to earn a higher return for the firm. However, they require an increased rate of return, or risk premium, to compensate them for taking on this additional risk. See Slide 2 (32.0K) . The more variable the returns, the higher the risk.
2. Measurement of Risk
1. Probability Distributions. Risk can be measured using the statistical concepts of expected value and standard deviation and developing a table of possible outcomes such as Slide 3 (30.0K) . First, for any project, the expected value is calculated by multiplying the outcomes by their likelihood of occurrence or probability. Next, the standard deviation is calculated. The larger the standard deviation, the greater the risk. In order to standardize the risk measure and compare projects, we then calculate the coefficient of variation (). To calculate coefficient of variation, you divide the standard deviation of an investment by its expected value. The higher the coefficient of variation, the higher the risk. See Slide Statistical Measures of Risk (65.0K) .
2. Beta. Beta is used as a measure of risk if you are calculating risk for securities held in a portfolio, instead of in isolation. Beta Measures _________. The market index has a beta of 1. Any stock with a beta greater than that of the market index is riskier than the market. Conversely, any stock with a beta less than that of the market index is less risky than the market. See Slide 5 (43.0K) for a listing of sample companies and their betas. See Slide Beta (66.0K) .
3. Risk and Capital Budgeting
1. Risk-Adjusted Discount Rate. In capital budgeting, we must take the risk of individual projects in to account. To do this, we can use risk-adjusted discount rates. The discount rate for the firm is determined based on the firm's cost of capital plus a ____ to account for the riskiness of a single project(Critical Concept). See Slide 10 (35.0K) . Risk increases over time as returns become more uncertain. See Slide 11 (51.0K) for an example of the risk-adjusted discount rate.
2. Qualitative Measures of Risk. Firm management can also use qualitative, or subjective, factors in determining the risk-adjusted discount rate and determine this rate based on the relative risk of projects within their specific firm.
3. Simulation Models. Simulating situations in the real world is another way of measuring risk for the purposes of capital budgeting. Simulation uses a number of random variables as inputs for analyzing risk. See Slide 14 (39.0K) .
4. Decision Trees. A decision tree is a graphical picture of the decision process of choosing between different investment choices. See Slide 16 (44.0K) .
4. The Portfolio Effect

A. Portfolio Risk. Firms generally have a portfolio of projects rather than one single project. Portfolio risk depends to some degree on how highly correlated the projects are. The correlation coefficient for two projects indicate the degree to which their returns move in the same direction. + 1 means they move exactly together with -1 meaning they move inversely. See Slide Coefficient of Correlation (65.0K) . In order for a firm to diversify and lower its risk, it should take on projects that have the lowest correlation coefficient possible.

5. The Efficient Frontier

A. Objectives of Firm Management. Firm management has two objectives. One is to achieve the highest possible return at the lowest possible risk level. The other is providing the lowest possible risk to shareholders while achieving the highest possible return. Graphically, this relationship is illustrated by the efficient frontier. See Slide Efficient Frontier (67.0K) .