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WRAPPING UP GEOTHERMAL

We now turn one last time to Jo Ann Cox and Geothermal`s proposed expansion. We want to make sure that she ¤and you ¤know how to use the weighted-average cost of capital. Remember that the proposed expansion cost $30 million and should generate a perpetual cash flow of $4.5 million per year. A simple cash-flow worksheet might look like this:3

Note that these cash flows do not include the tax benefits of using debt. Geothermal`s managers and engineers forecast revenues, costs, and taxes as if the project was to be all-equity financed. The interest tax shields generated by the project`s actual debt financing are not forgotten, however. They are accounted for by using the after-tax cost of debt in the weighted-average cost of capital. Project net present value is calculated by discounting the cash flow (which is a perpetuity) at Geothermal`s 11.4 percent weighted-average cost of capital:

Expansion will thus add $9.5 million to the net wealth of Geothermal`s owners.

CHECKING OUR LOGIC Any project offering a rate of return more than 11.4 percent will have a positive NPV, assuming that the project has the same risk and financing as Geothermal`s business. A project offering exactly 11.4 percent would be just break-even; it would generate just

enough cash to satisfy both debtholders and stockholders.

Let`s check that out. Suppose the proposed expansion had revenues of only $8.34 million and after-tax cash flows of $3.42 million: With an investment of $30 million, the internal rate of return on this perpetuity is exactly

11.4 percent: Rate of return = 3.42 = .114, or 11.4% 30 NPV is exactly zero: NPV = Ј30 + 3.42 = 0 .114

When we calculated Geothermal`s weighted-average cost of capital, we recognized that the company`s debt ratio was 30 percent. When Geothermal`s analysts use the weighted-average cost of capital to evaluate the new project, they are assuming that the $30 million additional investment would support the issue of additional debt equal to 30 percent of the investment, or $9 million. The remaining $21 million is provided by the shareholders.

The following table shows how the cash flows would be shared between the debtholders and shareholders. We start with the pretax operating cash flow of $5.26 million:

Project cash flows before tax and interest are forecast to be $5.26 million. Out of this figure, Geothermal needs to pay interest of 8 percent of $9 million, which comes to $.72 million. This leaves a pretax cash flow of $4.54 million, on which the company must pay tax. Taxes equal .35 ГЧ 4.54 = $1.59 million. Shareholders are left with $2.95 million, just enough to give them the 14 percent return that they need on their $21 million investment. (Note that 2.95/21 = .14, or 14 percent.) Therefore, everything checks out.

If a project has zero NPV when the expected cash flows are discounted at the weighted-average cost of capital, then the project`s cash flows are just sufficient to give debtholders and shareholders the returns they require.

2 Financial managers often use ¬equity ­ to refer to common stock, even though a firm`s equity strictly includes both common and preferred stock. We continue to use requity to refer specifically to the expected return on the common stock. 3 For this example we ignore depreciation, a noncash but tax-deductible expense. (If the project were really perpetual, why depreciate?)