Foundations of Financial Management: An Analysis (part 52)

“If you have trouble imagining a 20% loss in the stock market, you shouldn’t be in stocks.” 

– John Bogle

Risk and Capital Budgeting (part C)

by

Charles Lamson

Simulation Models

Computers make it possible to simulate various economic and financial outcomes, using a large number of variables. Thus simulation is one way of dealing with the uncertainty involved in forecasting the outcomes of capital budgeting projects or other types of decisions. A Monte Carlo simulation model uses random variables for inputs. By programming the computer to randomly select inputs from probability distributions, the outcomes generated by a simulation are distributed about a mean, and instead of generating one return or net present value, a range of outcomes with standard deviations is provided. A simulation model relies on repetition of the same random process as many as several hundred times. Since the inputs are representative of what one might encounter in the real world, many possible combinations of returns are generated.

One of the benefits of simulation is its ability to test various possible combinations of events. This sensitivity testing allows the planner to ask "what if" questions, such as: What will happen to the returns on this project if oil prices go up? Go down? What effect will a 5 percent increase in interest rates have on the net present value of this project? The analysts can use the simulation process to test possible changes in economic policy, sales levels, inflation, or any other variable included in the modeling process. Some simulation models are driven by sales forecasts with assumptions to derive income statements and balance sheets. Others generate probability acceptance curves for capital budgeting decisions by informing the analyst about the probabilities of having a positive net present value.

Decision Trees

Decision trees help lay out the sequence of decisions that can be made and present a tabular or graphical comparison resembling the branches of a tree, which highlights the differences between investment choices. In Figure 8 we examine a semiconductor firm considering two choices: (a) expanding the production of semiconductors for sale to end users of these tiny chips or (b) entering the highly competitive personal computer market by using the firm's technology. The cost of both projects is the same 60 million dollars (column 4), the net present value (NPV) and risk are different. 

Figure 8 Decision tree

If the firm expands its semiconductor capacity (Project A), it is assured of some demand so a high likelihood of a positive rate of return exists. The market demand for these products is volatile over time, but long-run growth seems to be a reasonable expectation. If the firm expands into the personal computer market (Project B), it faces stiff competition from many existing firms. It stands to lose more money if expected sales are lower low than it would under option A, but it will make more if sales are high. Even though Project B has a higher expected NPV than Project A (last column and Figure 8), it's extra risk does not make for an easy choice. More analysis would have to be done before management made the final decision between these two projects. Nevertheless the decision tree provides an important analytical process.

The Portfolio Effect

Up to this point, we have been primarily concerned with the risk inherent in an individual investment proposal. While this approach is useful, we also need to consider the impact of a given investment on the overall risk of the firm---the portfolio effect. For example, we might undertake an investment in the building products industry that appears to carry a high degree of risk---but if our primary business is the manufacture of electronic components for individual use, we may diminish the overall risk exposure of the firm. Why? Because electronic components sales expand when the economy does well and falter in a recession. The building products industry reacts in the opposite fashion---performing poorly in boom periods and generally reacting well in recessionary periods. By investing in the building products industry, an electronic components manufacturer could smooth the cyclical fluctuations inherent in its business and reduce overall risk exposure.

Portfolio Risk

Whether or not a given investment will change the overall risk of the firm depends on its relationships to other investments. If one airline purchases another, there is very little risk reduction. Highly correlated investments---that is, projects that move in the same direction in good times as well as bad---do little or nothing to diversify away risk. Projects moving in opposite directions (building products and electronic components) are referred to as being negatively correlated and provide a high degree of risk reduction. 

Finally, projects that are totally uncorrelated provide some overall reduction in portfolio risk---though not as much as negatively correlated investments. For example, if a beer manufacturer purchases a textile firm, the projects are neither positively or negatively correlated but; the purchase will reduce the overall risk of the firm simply through the law of large numbers. If you have enough unrelated projects going on at one time, good and bad events will probably even out.

The extent of correlation among projects is represented by a new term called the coefficient of correlation---a measure that may take on values anywhere from -1 to +1. Examples are presented in Table 6.

Table 6 Measures of correlation

In the real world, few investment combinations take on values as Extreme as -1 or +1, or for that matter exactly 0. The more likely case is a point somewhere between, such as -.2 negative correlation or +.3 positive correlation, as indicated along the continuum in Figure 10.

Figure 10 Levels of risk reduction as measured by the coefficient of correlation

The fact that risk can be reduced by combining risky assets with low or negatively correlated assets can be seen in the example of Lamson, Inc., in Table 7. Lamson has fairly average returns and standard deviations of returns. The company is considering the purchase of one of two separate but large companies with sales and assets equal to its own. Management is struggling with the decision since both companies have a 14 percent rate of return, which is 2 percentage points higher than that of Lamson, and they have the same standard deviation of returns as that of Lamson, at 2.82 percent. This information is presented in the first three columns of Table 7.

Table 7 Rates of return for Lamson, Inc., and two merger candidates

The Share Price

The firm must be sensitive to the wishes and demands of shareholders. To the extent that unnecessary or undesirable risks are taken, a higher discount rate and lower valuation may be assigned to the stock in the market. Higher profits, resulting from risky ventures, could have a result that is the opposite from that intended. In raising the coefficient of variation, or beta, we could be lowering the overall valuation of the firm.

The aversion of investors to unpredictability (and the associated risk) is confirmed by observing the relative valuation given to cyclical stock versus highly predictable growth stocks in the market. Metals, autos, and housing stocks generally trade at an earnings multiplier well below that for industries with level, predictable performance, such as drugs, soft drinks, and even alcohol or cigarettes. Each company must carefully analyze its own situation to determine the appropriate trade-off between risk and return. The changing desires and objectives of investors tend to make the task somewhat more difficult.

*MAIN SOURCE: BLOCK & HIRT, 2005, FOUNDATIONS OF FINANCIAL MANAGEMENT, 11TH ED., PP. 394-402*

end