Economic evaluation of investment projects
Investing one million to receive 300 thousand per year for five years yields an internal rate of return of 15.2 %: it is worthwhile if capital costs 12 %, with a net present value of 81 thousand, and stops being worthwhile if it costs 20 %.
01The time value of money
A peso today is worth more than a peso a year from now, because it can be invested and because the future is uncertain. To compare amounts from different moments they are brought to the same date with an interest rate \( k \): an amount \( F_t \) received \( t \) periods from now is equivalent today to its present value:
02The cash flow
Evaluating a project —a production line, a test fixture, a new product— starts with its cash flow: year by year, what comes into and goes out of the cash box because of doing the project, compared with not doing it.
| Item | What it includes |
|---|---|
| Investment | Equipment, installation, initial working capital |
| Revenues | Additional sales or cost savings |
| Outflows | Additional variable and fixed costs, as seen in costs |
| Taxes | On profit; depreciation is not a cash outflow, but it reduces the tax |
| Residual value | What the project is worth at the end, and the recovery of working capital |
03The decision criteria
The net present value adds up all the flows brought to the present; if it is positive, the project yields more than the cutoff rate and adds value. The internal rate of return is the rate that makes it zero: the project’s own profitability, which is compared with the cutoff rate. The payback period is the time in which the flows return the investment; it is an indicator of risk and liquidity, not of profitability.
A project with an initial investment and a constant annual flow for n years, with no residual value. The curve is the net present value as a function of the cutoff rate; it crosses zero at the internal rate of return. The yellow dot is the chosen rate.
Since future flows are estimates, the analysis is completed with sensitivity —how much the NPV changes if sales, costs or investment depart from what was forecast— and with pessimistic, likely and optimistic scenarios.
04In the laboratory
Build in a spreadsheet the cash flow for the purchase of a surface-mount assembly machine, with labor savings, maintenance, taxes and residual value, and calculate NPV and IRR with the spreadsheet functions.
Calculate how much the savings can fall before the NPV turns negative.
Sketch the cash flow of the product of the degree’s final project.
05Common mistakes
- Adding up flows from different years without discounting them. A peso five years from now is not worth a peso today.
- Mixing nominal flows with a real rate, or the other way around. The result makes no sense.
- Treating depreciation as a cash outflow. It matters only through its effect on the tax.
- Choosing between mutually exclusive projects by the IRR. A small project with a high IRR can add less value than a large one.
06Self-assessment
What NPV does investing one million to receive 300 thousand per year for five years have, at 12 %?
About ARS 81,400.
What is its internal rate of return?
Around 15.2 %.
And its simple and discounted payback period at 12 %?
3.3 years simple and about 4.5 years discounted.
What does a negative NPV indicate?
That the project yields less than the cutoff rate: the alternative is preferable.
07Further reading
- Nassir Sapag Chain and Reinaldo Sapag Chain. Preparación y evaluación de proyectos. McGraw-Hill. (In Spanish.) The most widely used text in the region for building and evaluating cash flows.
- Leland Blank and Anthony Tarquin. Engineering Economy. McGraw-Hill. (Spanish edition: “Ingeniería económica”.) The time value of money and the decision criteria, with exercises.
- Richard A. Brealey, Stewart C. Myers and Franklin Allen. Principles of Corporate Finance. McGraw-Hill. (Spanish edition: “Principios de finanzas corporativas”.) The cost of capital and the foundations of net present value.