Sensitivity Analysis Estimates of cash flows are based on assumptions about the economy,

Sensitivity Analysis Estimates of cash flows are based on assumptions about the economy,

competitors, consumer tastes and preferences, construction costs, and taxes, among a host of other possible assumptions. One of the first things managers must consider about these estimates is how sensitive they are to these assumptions. For example, if we only sell 2 million units instead of 3 million units in the first year, is the project still profit- able? Or, if Congress increases the tax rates, will the project still be attractive?

We can analyze the sensitivity of cash flows to change in the assumptions by reestimating the cash flows for different scenarios. Sen- sitivity analysis, also called scenario analysis, is a method of looking at the possible outcomes, given a change in one of the factors in the analy- sis. Sometimes we refer to this as “what if” analysis—“what if this changes,” “what if that changes,” and so on.

To see how sensitivity analysis works, let’s look at the Williams 5 &

10 cash flows we determined in Chapter 12, where the detailed calcula- tions were shown in Exhibit 12.4 of that chapter. The net cash flow for each year is:

Year Net Cash Flow

+460,946 Now let’s play with the assumptions. Suppose that the tax rate is

not known with certainty, but instead the tax rate may be 20%, 30%, or 40%. The tax rate that we assume affects all the following factors:

■ The expected tax on the sale of the building and equipment in the last year; ■ The cash outflow for taxes from the change in revenues and expenses; and ■ The cash inflow from the depreciation tax shield.

Each different tax assumption changes the project’s net cash flows as follows:

LONG-TERM INVESTMENT DECISIONS

Net Cash Flow

Year Tax rate = 20% Tax rate = 30% Tax rate = 40%

+489,987 We can see that the value of this project, hence any decision made based

on this value, is sensitive to what we assume will be the tax rate. We could take each of the “what if” tax rate assumptions and re- calculate the value of the investment.

If the ... the net present value using tax rate is ...

a cost of capital of 5% is ...

But when we do this, we have to be careful—the net present value requires discounting the cash flows at a rate that reflects risk—but that is what we are trying to figure out! So we shouldn’t be using the net present value method in evaluating a project’s risk in our sensitivity analysis.

An alternative is to recalculate the internal rate of return under each “what if” scenario.

If the ... the internal tax rate is ... rate of return will be ...

16.32% And this illustrates one of the attractions of using the internal rate

of return to evaluate projects. Despite its drawbacks in the case of mutually exclusive projects and in capital rationing, as pointed out in Chapter 13, the internal rate of return is more suitable to use in assess- ing a project’s attractiveness under different scenarios and, hence, that

Capital Budgeting and Risk

project’s risk. Why? Because the net present value approach requires us to use a cost of capital to arrive at a project’s value, but the cost of cap- ital is what we set out to determine! We would be caught in a vicious circle if we used the net present value approach in sensitivity analysis. But the internal rate of return method does not require a cost of capital; instead, we can look at the possible internal rates of return of a project and use this information to measure a project’s risk.

If we can specify the probability distribution for tax rates, we can put sensitivity analysis together with the statistical measures of risk. Suppose that in the analysis of the Williams project it is most likely that tax rates be 30%, though there is a slight probability that tax rates will

be lowered and a chance that tax rates will be increased. More specifi- cally, suppose the probability distribution of future tax rates and, hence the project’s internal rate of return, is:

that the and hence the internal Probability is ... tax rate will be ... rate of return will be ...

Applying the calculations for the statistical measures of risk to this distribution,

Expected internal rate of return = 17.433% Standard deviation of possible internal rates of return = 1.148% Coefficient of variation

= 0.066 We could then judge whether the project’s expected return is suffi-

cient considering its risk (as measured by the standard deviation). We could also use these statistical measures to compare this project with other projects under consideration.

Sensitivity analysis illustrates the effects of changes in assumptions. But because sensitivity analysis focuses only on one change at a time, it is not very realistic. We know that not one, but many factors can change throughout the life of a project. In the case of the Williams project, there are a number of assumptions built into the analysis that are based on uncertainty, including the sales prices of the building and equipment in five years and the entrance of competitors no sooner than five years. And you can use your imagination and envision any new product and the attendant uncertainties including the economy, the firm’s competi- tors, and the price and supply of raw materials and labor.

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