Question

Project Evaluation. Aguilera Acoustics, Inc. (AAI), projects unit sales for a new seven-octave voice emulation implant as follows:

Production of the implants will require $1,500,000 in net working capital to start and additional net working capital investments each year equal to 15 percent of the projected sales increase for the following year. Total fixed costs are $1,450,000 per year, variable production costs are $230 per unit, and the units are priced at $355 each. The equipment needed to begin production has an installed cost of $24,000,000. Because the implants are intended for professional singers, this equipment is considered industrial machinery and thus qualifies as seven-year MACRS property. In five years, this equipment can be sold for about 20 percent of its acquisition cost. AAI is in the 35 percent marginal tax bracket and has

a required return on all its projects of 18 percent. Based on these preliminary project estimates, what is the NPV of the project? What is the IRR?

Answer 1

Under normal circumstance projects usually have a set of cash flows for a limited time horizon. To take up or not to take up an investment depends upon the NPV of such investment.

However, in certain cases the cash flows are assumed to be infinite i.e. the returns are expected to continue till perpetuity.

For the given problem the cash flows can be summarized as follows:

For the given set of constantly growing perpetual cash flows NPV is represented as:

(a)

In the above formula, ‘R’ is the required rate of return i.e. 13% and ‘g’ is the annual growth in cash flows i.e. 6%. Thus,

Growth rate percent 6

At the given rate of return of 13% the NPV is negative and hence the company should not undertake the new business.

(b)

What is required here is a value of ‘g’ if the cash flows are same. Also, the break-even would result in a nil NPV.

Based on this, the above formula can be rewritten as:

Required rate of return is 13 percent.

By trial and error the value of ‘g’ can be found as 6.5135%. At this growth rate, the NPV is approximately $0 resulting in break even for the business.