## Numeric Models Profit Profitability

As noted earlier, a large majority of all firms using project evaluation and selection models use profit/profitability as the sole measure of acceptability. We will consider these models first, and then discuss models that go well beyond the profit test for acceptance.

Payback Period The payback period for a project is the initial fixed investment in the project divided by the estimated annual cash inflows from the project. The ratio of these quantities is the number of years required for the project to repay its initial fixed investment. For example, assume a project costs \$100,000 to implement and has annual cash inflows of \$25,000. Then

This method assumes that the cash inflows will persist at least long enough to pay back the investment, and it ignores any cash inflows beyond the payback period. The method also serves as an inadequate proxy for risk. The faster the investment is recovered, the less the risk to which the firm is exposed.

Average Rate of Return Often mistakenly taken to be the reciprocal of the payback period, the average rate of return is the ratio of the average annual profit (either before or after taxes) to the initial or average investment in the project. Because average annual profits are not equivalent to net cash inflows, the average rate of return does not equal the reciprocal of the payback period. Assume, in the example just given, that the average annual profits are \$15,000:

Neither of these evaluation methods is recommended for project selection, though payback period is widely used and does have a legitimate value for cash budgeting decisions. The major advantage of these models is their simplicity, but neither takes into account the time value of money. Unless interest rates are extremely low and the rate of inflation is nil, the failure to reduce future cash flows or profits to their present value will result in serious evaluation errors.

Discounted Cash Flow Also referred to as the present value method, the discounted cash flow method determines the net present value of all cash flows by discounting them by the required rate of return (also known as the hurdle rate, cutoff rate, and similar terms) as follows,

F, = the net cash flow in period t, k = the required rate of return, and

A0 - initial cash investment (because this is an outflow, it will be negative).

To include the impact of inflation (or deflation) where pt is the predicted rate of inflation during period t, we have

where n

Early in the life of a project, net cash flow is likely to be negative, the major outflow being the initial investment in the project, A0. If the project is successful, how-

ever, cash flows will become positive. The project is acceptable if the sum of the net present values of all estimated cash flows over the life of the project is positive. A simple example will suffice. Using our \$100,000 investment with a net cash inflow of \$25,000 per year for a period of eight years, a required rate of return of 15 percent, and an inflation rate of 3 percent per year, we have

\$25,000

Because the present value of the inflows is greater than the present value of the outflow—that is, the net present value is positive—the project is deemed accept-able.

PsychoCeramic Sciences, Inc. (PS1), a large producer of cracked pots and other cracked items, is considering the installation of a new manufacturing line that will, it is hoped, allow more precise quality control on the size, shape, and location of the cracks in its pots as well as in vases designed to hold artificial flowers.

The plant engineering department has submitted a project proposal that estimates the investment requirements as follows: an initial investment of \$125,000 to be paid up-front to the Pocketa-Pocketa Machine Corporation, an additional investment of \$100,000 to install the machines, and another \$90,000 to add new material handling systems and integrate the new equipment into the overall production system. Delivery and installation is estimated to take one year, and integrating the entire system should require an additional year. Thereafter, the engineers predict that scheduled machine overhauls will require further expenditures of about \$15,000 every second year, beginning in the fourth year. They will not, however, overhaul the machinery in the last year of its life.

The project schedule calls for the line to begin production in the third year, and to be up-to-speed by the end of that year. Projected manufacturing cost savings and added profits resulting from higher quality are estimated to be \$50,000 in the first year of operation and are expected to peak at \$120,000 in the second year of operation, and then to follow the gradually declining pattern shown in the table at the end of this box.

Project life is expected to be 10 years from project inception, at which time the proposed system will be obsolete and will have to be replaced. It is estimated that the machinery will have a salvage value of \$35,000.

PSI has a 12 percent hurdle rate for capital investments and expects the rate of inflation to be about 3 percent over the life of the project. Assuming that the initial expenditure occurs at the beginning of the year and that all other receipts and expenditures occur as lump sums at the end of the year, we can prepare the Net Present Value analysis for the project shown in the table.

The Net Present Value of the project is positive and, thus, the project can be accepted. (The project would have been rejected if the hurdle rate were 14 percent.)

lust for the intellectual exercise, note that the total inflow for the project is \$759,000, or

\$75,900 per year on average for the 10 year project. The required investment is \$315,000 (ignoring the biennial overhaul charges). Assuming 10 year, straight line depreciation or \$31,500 per year, the payback period would be