Investment Risks and Discounted Cash Flow Applications
You are the company accountant with a medium sized, privately owned company. The company has surplus funds which it does not believe it will be able to invest in company operations for at least five years. The majority shareholders are also the directors of the company and they do not wish the surplus finds to be distributed as dividends. A board meeting has, therefore, been called to discuss the proposal that the funds be invested in a portfolio of medium to long term securities. Three of the directors have recently attended a short course at the local university on "Investment and the Management of Risk". They make the following comments at the meeting, based on their interpretations of what they have learned on the course: "If we hold a portfolio of stocks we need only consider the systematic risk of the securities" "As a cautious investor we must always consider total risk" "We should not buy anything if the expected return is less than the market as a whole and certainly not if it is below the return on the risk free asset". Question 1(i): Explain to the members of the board the meaning of systematic, unsystematic and total risk and advise them about how all three types of risk can be measured. Reasons for Dissecting Risk
Investing in securities is an inherently risky proposition (unless one invests in the risk free asset). Prudent investors are risk-averse (Damodaran 2002, pp. 70), and as such they need methods to quantify the risk associated with potential investments, in order to make informed investment decisions corresponding with their risk tolerance and objectives for return. Thus, the concept of "risk" needs to be reduced into separate elements which can be calculated. Total, Systematic, and Unsystematic Risk
The total risk involved in holding any security has two distinct components: systematic risk and unsystematic risk. Systematic risk refers to the risk of holding securities in general, and is also known as "market risk" (Ross, Westerfield, & Jaffe 2005 pp.275). This is the risk associated with macroeconomic variables beyond the control of any one company, and this risk measure serves as a "floor" for the amount of risk in a portfolio of stocks that can be eliminated by diversification (McAlister, Srinivasan, & Kim 2007, pp. 39). When an investor's portfolio is properly diversified, this is the level of risk that such an investor should concern themselves with (Howard 2006, pp. 29). Unsystematic risk refers to the level of risk associated with a particular security, which can fluctuate greatly depending on the underlying value of the assets which the security represents (Howard 2006, pp. 30). For instance, while the economy may be rather steady at any given time (and a diversified portfolio would reflect such stability in its measures of systematic risk), an individual company may be undergoing dramatic changes which cause the company valuation to fluctuate wildly. Unsystematic risk is the portion of total risk that an investor in a diversified portfolio seeks to minimize. To illustrate the difference between systematic and unsystematic risk, one helpful analogy is the schism in physics between the smooth "macro-level" curvature of space-time at cosmic scales predicted by General Relativity, and the chaotic and unpredictable "micro-level" fluctuations of space-time at infinitesimally small scales predicted by Quantum Physics. At the scale of space-time discussed by Einstein's General Relativity equations, the effects of small-scale fluctuations are ultimately balanced out, and the picture of space-time is one of a smoothly curving space-time accentuated bent according to the gravitational effects of large masses. At the scale of space-time addressed in Quantum Physics, however, space-time fluctuates in such an unpredictable and chaotic manner that predictions become difficult, if not impossible (Feynman 1985, pp. 5). This corresponds to the "macro-level" systematic risk of the market, in which the volatility of individual securities is balanced out, leaving only the risk of the market as a whole, compared to the violent variances of individual companies at the "micro-level" which is measured by unsystematic risk. Total risk is a combination of systematic and unsystematic risk. Since unsystematic risk decreases asymptotically as stocks are added to a portfolio (meaning that the level of risk approaches, but never quite equals, the level of systematic risk), investors with properly diversified portfolios are most concerned with systematic risk as a measure of their total risk (Howard 2006, pp. 29). Investors with less diversified holdings should add the market level of systematic risk to the level of unsystematic risk associated with the securities held to compute total risk. Computation of Total, Systematic, and Unsystematic Risk
Systematic risk, or non-diversifiable market risk, can be calculated as the average covariance of the securities in the portfolio (in this case, the "portfolio" should be considered to be a basket of stocks representing the entire market) (Ross, Westerfield, & Jaffe 2005, pp. 273). Total risk is the average variance of the security in the portfolio, and by definition (total risk = systematic risk + unsystematic risk), the unsystematic risk of any security in the portfolio is the average variance of the individual security minus the average covariance of the portfolio (Ross, Westerfield, & Jaffe 2005, pp. 275). Question 1(ii): Discuss the directors' comments "If we hold a portfolio of stocks we need only consider the systematic risk of the securities"
This comment by the directors holds true, if the portfolio is sufficiently and adequately diversified. As mentioned above, a properly diversified portfolio creates a scenario in which the unsystematic risk asymptotically approaches 0, leaving only the systematic or market risk in the calculation of total risk. However, this assumes that the stocks selected in the portfolio are sufficiently diverse (Damodaran 2002, pp. 735). For an example, a diversified portfolio that includes a broad cross-section of securities from many industries can be considered more "properly" diversified than a portfolio which gives extra weight or emphasis to specific industries. Otherwise, there is an industry-specific level of risk that remains in the unsystematic risk of the entire portfolio. As a more concrete example, consider a portfolio that consists of a group of energy stocks and a group of petrochemical companies. No matter how many stocks are added to this portfolio from the group, the risk associated with petroleum price shocks has not been removed via diversification (while it is true that petroleum price shocks would affect the market at large, they would disproportionately affect industries in which petroleum is the critical input). The stocks in the portfolio must be sufficiently diverse for the effects of diversification to be realized as a reduction in unsystematic risk. However, if the stocks in the portfolio are assumed to be sufficiently diverse to account for a truly diversified portfolio, the statement made by the directors certainly coincides with financial theory, and should be applauded a sound understanding of the concept of diversification and its relation to investment and risk management. "As a cautious investor we must always consider total risk"
This statement certainly rings true for the investment decisions of the directors, and demonstrates an understanding of both the impacts of diversification and the demarcation between the different types of risk involved in the total risk of an investment (Howard 2006, pp. 29). To support this statement by the directors, three scenarios will be used to illustrate the importance of a focus on total risk. In the first scenario, a hypothetical investor has no information regarding any of the components of total risk. The hypothetical investor has little knowledge of the inherent risk factors of the current market (no understanding of current levels of systematic risk), and has randomly selected a single security (perhaps by using the "dart toss" stock selection scheme). This investor may not understand that the market as a whole is in an upswing or decline, and has no information to understand how any random stock in the market at large should perform, on average. Thus, the investor has no information on systematic risk. This investor also selected the security at random, so the investor has no information regarding the proclivity of the particular security to fluctuate in value. Here, the investor has no way to deduce total risk, since the investor cannot arrive at a conclusion regarding either the systematic risk or the unsystematic risk. Any profits made by the investor in this scenario can only be regarded as the fortuitous results of chance. In the second scenario, a hypothetical investor has performed a thorough analysis on a particular company, and thus has a solid understanding of the company's earnings potential and "true" valuation relative to its market capitalization. However, the investor has not performed an analysis on the economy as a whole, and as such has no information as to whether macroeconomic conditions support or invalidate a decision to purchase the particular security in question. So, while the investor feels confident that they understand the unsystematic risk associated with the security, they have no information regarding the systematic risk of the market as a whole, and thus the investment decision based on their research may be ruined by a change in overall market conditions. Finally, in the third scenario, the final hypothetical investor has performed an analysis of macroeconomic conditions to concoct an investment decision. This investor, however, has performed no analysis of the particular securities they plan to purchase (even to see if they form a "properly diversified portfolio"). Thus, even though this investor potentially understands the systemic risk portion of their investment, they have no way of determining if they have eliminated the unsystematic risk in their holdings. They may very well be correct regarding the market's overall risk level, but if they do not eliminate the unsystematic risk associated with individual securities, their efforts will also be in vain as they are still subject to potential volatility and additional risk based on fluctuations in the securities held. "We should not buy anything if the expected return is less than the market as a whole and certainly not if it is below the return on the risk free asset".
The first portion of this statement is incorrect, unless the board has decided that the return on the market as a whole is equivalent to their required rate of return. The level of expected return on the investment should be a function of the risk tolerance of the investors. If the risk of the market as a whole (systematic risk) is higher than the risk tolerance of the investors, the investors should seek to invest in the risk free asset, or at least include the risk free asset in the portfolio to achieve the level of total risk that best suits the risk tolerance of the investors (Ross, Westerfield, & Jaffe 2005, pp. 300). The directors have here made a very easy mistake: equating the expected return on the market as a whole with the minimum acceptable return, without considering that even the systematic risk may be more risk than they are willing to tolerate. For instance, a troubling political climate or unexpected macroeconomic events may create levels of price fluctuations in the market as a whole which amount to risks that the investors are not willing to take. At such a point, the investors should seek to lessen their exposure by investing some portion of their holdings in the risk free security (to "park" their funds until the systematic risk of the market more closely mirrors their own risk tolerance) (Damodaran 2002, pp. 155). The second statement is correct. Since the return on the risk free asset is, by definition, devoid of either systematic or unsystematic risk, this is the minimum return that the investors should demand for their resources (Damodaran 2002, pp. 204). Any additional expected return should be balanced by the systematic risk associated with placing funds in risky securities. Investors in properly diversified portfolios should not expect any returns above market average, unless they are willing to assume some level of unsystematic risk as well. Question 2 (i): Why is it important to discount future cash flows? The Relevance of Discounted Cash Flows Valuation Models
The notion that future cash flows should be discounted back to "today's value" by a factor equal to the opportunity cost of capital is central to the concept of the Time Value of Money. By discounting future cash flows by the opportunity cost of capital, we recognize the very real impact of financial decision-making (Ross, Westerfield, & Jaffe 2005, pp. 195). Cash flows in the future are worth less because if they were available in the present, they could be earning a return equal to the opportunity cost of capital (which is always greater than zero based on the existence of the risk free asset). A dollar held today is worth more than a dollar held in the future, because today's dollar could (at the very least) be invested in the risk free asset and be worth more in the future. Whereas if we have to defer our receipt of cash until the future, we should expect compensation relative to the opportunity cost of not receiving the money up front. This is the basis of interest payments, the time value of money, and ultimately this concept is the crux of all financial theory (Damodaran 2002, pp. 11). To forego discounting future cash flows is to assume that there is no time value associated with cash, and that there are no investments with positive returns (Ross, Westerfield, & Jaffe 2005, pp. 901). If future cash flows are not discounted, it becomes easy to lose sight of the potential returns that were missed based on the allocation of cash for a project. This will also skew the decision-making process and distort the perceived profitability of a project. The net present value (NPV) model allows investors to determine if a project makes financial sense based on their expected rates of return or opportunity cost of capital (Damodaran 2002, pp. 13). If the cash flows were not discounted, a project may look profitable in the initial feasibility study for the project, even though the project returns less over time than is expected by the investors, and the money would be better invested in other projects with a higher or positive net present value. Thus, discounting future cash flows allows quantitative models to presume that capital has other potential uses, and that a project should at least meet certain requirements for return over time before it is considered. As an example, consider a project which costs A£100, and is expected to generate A£150 in year 1. A similar project costs A£100 but will generate A£150 in year 2. Without discounting the deferral of cash flows in the project, they both appear to generate A£50, and both look equally profitable. In truth, however, the first project is more profitable, since the real profit over the time period in question is equal to the A£50 plus any profits that could be generated over the next year at the company's required rate of return. Thus, it is vital that future cash flows are discounted to make accurate decisions through financial analysis, or the opportunity cost of capital will be omitted from the final decision. Question 2(ii): Susie Lee owns the Lotus Blossom Bar and Restaurant. She is considering the following investment to upgrade the existing facilities. The cash flows for the investment are estimated as follows: End of Year Cash Flow (A£)
Assuming the opportunity cost of capital is 12 percent
, calculate the investment's net present value. Based on your calculations advise Susie if she should undertake the investment project? Net Present Value of Upgrading the Lotus Blossom Bar and Restaurant
Net present value is calculated as the sum of future cash flows discounted by the opportunity cost of capital (here, 12%) (Damodaran 2002, pp. 12). In this example, a A£10,000 investment yields five years of positive cash flows (A£10k year 1, A£20k in year 2, A£40k for year 3, A£50k for year 4, and a final cash flow of A£30k in year 5). All of these cash flows must be discounted to today (year 0), and if the sum of the discounted cash flows is greater than the A£10k cost of the project, the project will have a positive net present value and will make a sound investment for the Lotus Blossom Bar and Restaurant. The following table illustrates the present value calculations as performed on the cash flows, and summarizes by adding all of the project's cash flows to arrive at the project's net present value.
|Initial Investment (Year 0)
|Net Present Value: Sum of DCF
Even after considering Susie Lee's opportunity cost of capital by discounting her expected future cash flows from the project, the net present value of the upgrade is overwhelmingly positive, and she is strongly advised to undertake the investment project (Boyes 2004, pp. 235). This project generates revenues well beyond her required rate of return. Generating A£150,000 in 5 years from a A£10,000 up-front investment is a very solid investment at a 12% required rate of return. In fact, the investment is incredibly profitable using the Internal Rate of Return (IRR) methodology, which yields the rate of return at which the project yields a NPV of 0 (Damodaran 2002, pp. 866). Solving for a zero value for net present value yields the following result:
|Initial Investment (Year 0)
|Net Present Value: Sum of DCF
In other words, until Susie Lee requires a 265.18% rate of return on her capital, this upgrade represents an extremely solid investment (Collis, Montgomery 1998, pp. 88). Works Cited:
Boyes, W. The New Managerial Economics. Houghton Mifflin Company. Boston, Massachusetts. 2004. Collis, D. and Montgomery, C. Corporate Strategy: A Resource-Based Approach. Irwin/McGraw Hill. Boston, Massachusetts. 1998. Damodaran, A. Investment Valuation: Tools and Techniques for Determining the Value of Any Asset. Second Edition. John Wiley & Sons, Inc. New York. 2002. Feynman, R. QED: The Strange Theory of Light and Matter. Princeton University Press. New Jersey. 1985. Howard, M. “Accounting for Unsystematic Risk”. Financial Management. Sep. 2006. McAlister, L., Srinivasan, R., & Kim, M. “Advertising, Research and Development, and Systematic Risk of the Firm”. Journal of Marketing. January 2007. Ross, S., Westerfield, R., and Jaffe, J. Corporate Finance. Seventh Edition. McGraw-Hill Companies. New York. 2005.
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