San José State University
Department of Economics

applet-magic.com
Thayer Watkins
Silicon Valley
USA

The Systematics of an Investment Decision

An investment project usually has a product and the expected sales of that product over time. The quantity produced and sold, along with the price, determine revenue and the cost of production. A positive difference leads to a profit and a tax liability. The future after tax profits are discounted to the present time and the compared to the capital investment. If the present value of the future after tax profits is greater than the capital investment then the project is worthwhile, if not then the project is not worthwhile.

It must be noted that in situations in which a change in personal tax rates is expected the after tax profit should mean the income to a corporation's stockholders after personal taxes rather than profit after corporate taxes.

The present value of a gain of G, t years in the future, is G/(1+r)t, where r is the discount rate. The value of r depends upon the interest rate but it may also involve a risk premium to take into account the riskiness of the project. Thus an increase in uncertainty about the outcome of a project is effectively like an increase in the interest rate in its effect on investment.

## A Project's Rate of Return

The rate of return (ROR) for a project is that discount rate which makes the project exactly break even; i.e., the present value of the future net profits exactly matches the investment cost. One might tabulate a distribution of investment projects by their rate of return. Such a distribution might look like the following.

However the number of investment projects for a given rate of return is not the relevant variable. The capital required for the investment project is what is relevant; e.g.,

The amount of investment that occurs comes from a comparison of the rate of return. The worthwhile investment projects are the ones such that their rates of return are greater than the risk adjusted cost of capital. This comparison is shown below. The capital for the projects that are worthwhile are shown in green.

If something increases the uncertainty about investment in general there is a high risk premium added to the cost of capital. This results in the capital investment for the shown in yellow ochre being cancelled.

## Conclusion

A typical investment project involves an initial outlay for equipment, structures and other requirements to start the project. These initial outlays have to be justified by the future after tax profits of the project. Such profits depend upon the volume of sales, the price of the product, the operating costs and taxes. Not all of the future variables are known with certainty so risk is also a consideration for a project. The effect of increased uncertainty and hence risk is equivalent to an increase in the interest rate because the investment decision depends upon a risk premium associated with a project.