A firm is considering a project that will result in initial aftertax cash savings of $5 million at the end of the first year. These savings will grow at the rate of 5 percent per year.

Question

A firm is considering a project that will result in initial aftertax cash savings of $5 million at the end of the first year. These savings will grow at the rate of 5 percent per year. The firm has a debt-equity ratio of .5, a cost of equity of 29.2 percent, and a cost of debt of 10 percent.
The cost-saving proposal is closely related to the firm’s core business, so it is viewed as having the same risk as the overall firm. Should the firm take on the project?

Accepted Answer

Assuming a 34 percent tax rate, the firm should take on this project if it costs less than $30 million. To see this, first note that the PV is:

PV=[latex]\frac{\$5 million}{W ACC - .05} [/latex]

This is an example of a growing perpetuity as discussed in Chapter 6. The WACC is:

WACC=[latex](E/V)×R_{E}+(D/V)×R_{D}×(1-T_{C})[/latex]

=2/3×29.2%+1/3×10%×(1-.34)

=21.67%

The PV is thus:

PV=[latex]\frac{\$5 million}{.2167 - .05} [/latex]= $30 million

The NPV will be positive only if the cost is less than $30 million.

Question 14.5: A firm is considering a project that will result in initial ...

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