Differential Costs of Capital Theory and Practice

There is no doubt that projects must be discounted by their project-specific cost of capital. Yet, Graham and Harvey found in their 2001 survey (the same survey you saw in Chapter 1) that just about half of surveyed CFOs always—and incorrectly—use the firm's overall cost of capital, rather than the project-specific cost of capital! And even fewer CFOs correctly discount cash flows of different riskiness within projects. The easy conclusion is that CFOs are ignorant—and though some CFOs may indeed use a uniform cost of capital because they are ignorant, some intelligent CFOs are doing so quite deliberately.

In practice, a good number of firms do not use differential costs of capital.

348 ■ Chapter 13 THE CAPITAL ASSET PRICING MODEL

Getting project costs You already know that it is very difficult to correctly estimate the cost of capital. In theory, you of cap¡ta| ¡s diffkult:. just know the market-beta of every project and the other CAPM inputs. In practice, you do not.

1. Even the historical betas of publicly traded corporations are not entirely reliable and indicative of the future. Different estimation methods can come up with different numbers. This is why you may want to use the market betas of similar, publicly traded comparables or the market beta of an entire industry. But many of your projects may be so idiosyncratic, so unusual, or in such far-away locales that no comparable may seem particularly suitable.

You could try to estimate your own market beta. To do so, you would need a time-series of historical project values, not just historical project cash flows. This is because you cannot rely on historical cash flow variation as a substitute for historical value variation. You already know that the market values themselves are the present discount value of all future cash flows, not just of one period's. Here is an example how this can go awry. Consider a firm whose cash flows are perfectly known. Therefore, its appropriate true discount rate would be close to the risk-free rate. However, if its cash flows occur only every other month ($200, $0, $200, etc.), this firm would have infinite monthly cash flow volatility (-100% followed by +~%). Its percent changes in cash flows would not be indicative of its value-based rates of returns. Plus, almost surely, it would have an extreme market-beta estimate, indicating a wrong cost of capital. In order to estimate your market-beta, you would need to somehow obtain a time series of estimated market values from the known time series of cash flows. Of course, you already know that it is difficult to estimate one market value for your firm—but estimating a time-series of how this market value changes every month is entirely beyond anyone's capability. (When only cash flows but not market-values are known, your estimates must necessarily be less accurate. The best way to estimate an appropriate cost of capital relies on the certainty equivalence formula explained in Appendix A.)

Many firms may not have any historical experience that you can use, not just for market values, but even for cash flows. There would be nothing you could verifiably and credibly use to estimate in the first place.

Betas are often difficult to estimate, equity premium estimates are very uncertain, and the CAPM is not a perfect model. These uncertainties may not only distort the overall corporate cost of capital, but also the relative costs of capital across different projects. Quite simply, you must be aware of the painful reality that your methods for estimating the cost of capital are often just not as robust as you would like them to be.

Consequently, the problem with assigning different costs of capital to different projects may now become one of disagreement. Division managers can argue endlessly about why their projects have a lower cost of capital than the company's. Is this how you want your division managers to spend their time? Managers could even shift revenues from weeks in which the stock market performed well into weeks in which the stock market performed poorly in order to produce a lower market-beta. The cost of capital estimate itself becomes a piece in the game of agency conflict and response—all managers would like to convince themselves and others that a low cost of capital for their own divisions is best. What the overall corporation would like to have in order to suppress such "gaming of the system" would be one immutable good estimate of the cost of capital for each division that cannot be argued with. In the reality of corporate politics, however, it may be easier to commit to one and the same immutable cost of capital for all divisions than it would be to have immutable but different costs of capital for each division. This is not to argue that this one cost of capital is necessarily a good system, but just that there are cases in which having this one cost of capital may be a necessary evil.

Flexible costs of capital can cause arguments and agency conflicts.

And finally there is the forest. You know that each component must be discounted at its own discount rate if you want to get the value and incentives right. However, if you want to value each paper clip by its own cost of capital, you will never come up with a reasonable firm value—you will lose the forest among the trees. You need to keep your perspective as to what reasonable errors are and what unreasonable errors are. The question is one of magnitude: if you are acquiring a totally different company or project, with a vastly different cost of capital, and this project will be a significant fraction of the firm, then the choice of cost of capital matters and you should differentiate. However, if you are valuing a project that is uncertain, and the project is relatively small, and its cost of capital is reasonably similar to your overall cost of capital, you can probably live with some error. It all depends—your mileage may vary!

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