Much of the substance of governance economics is about marginal decision making affecting operations in the short-run time frame. Most of the rest of these segments elaborate the marginal criteria for short-run decision making; however immediately I am going to devote to long-run decision considerations and the analysis of risk.

In addition to the differences noted in previous posts between long and short runs, a major distinction remains to set the long-run decision problem apart from short-run decision making. Since the effects of the long-run decision can be expected to impact the enterprise in the future, some recognition must be made of the remoteness of those effects. The sense of the problem is that the expectation of a benefit to be realized in the future is worth less to the decision maker than an equivalent benefit received immediately. Specialists in finance often refer to this phenomenon as the “time value of money,” but the phenomenon would exist even in a barter economy (one which does not use money). The phenomenon is described by the ancient adage that “a bird in the hand is worth two in the bush.” The problem pertains to costs as well as to benefits. In addition, costs which must be paid at some future time are also less meaningful to the decision maker than those which must be paid today, although the wise decision maker should plan and make careful arrangements to cover expected future costs.

Since future possibilities are worth less than present realities, economists have acknowledged this phenomenon by discounting the expected future values at an appropriate rate. This rate is usually taken to be the best market rate of interest for which the enterprise can qualify. The interest rate is used as a discount rate on the premise that the equivalent of the expected future value, less the cost of interest, can be had at present by borrowing the future sum. This relationship should be true whether the borrowed principle and the interest to be repaid are expressed in barter or monetary terms. If we let the symbol i stand for the interest rate which will serve as discount rate, the present value of the expected future outcome can be expressed as PV as the “present value” of an expected future income stream, V as a predicted future net income (or return) in each of n future periods (it is “expected” if it is a probability-weighted average of all possible outcomes which may occur). The value of V is taken to be the net of the difference between the future benefit, b, and the cost of realizing it, c, or V = (b – c). PV is less than the sum of the Vs because each V is divided by a number greater than 1, i.e., 1 plus the discount rate i.

If there are no risk considerations to be taken into account, the appropriate decision procedure is to first compute, using formula (1), the present values of the expected future net benefits for each of the k outcome possibilities for each of the decision alternatives. Then the expected values of possible outcomes of each decision alternative can be computed as their probability-weighted averages using previously described formulas into which the computed present values, PV, are substituted for the outcomes, V. The proper decision criterion is to choose the alternative with the largest present expected value of the possible outcomes.

In the present value formula (1), values for V and i are known or estimated, and the value of PV is computed. An alternative version of the present value formula permits computing the so-called internal rate of return,

In formula (2), K is the capital outlay required to acquire and install an investment opportunity (since it is known today, it is the opportunity’s “present value”), and r is the internal rate of return on the investment opportunity. In this approach, the value of K and the values for V are known (or can be estimated), but the value of r is to be computed. Actually, equation (2) cannot be easily solved for value r, but r may be estimated by successive approximation from annuity tables.

If we may abstract from the possibility of a scrap value of the capital at the end of its useful life, n, the conceptual sense of r is the discount rate which would be just sufficient to make the sum of the returns, V1…Vn, just equal to the capital outlay, K. The discount rate, r, is interpreted as a rate of return because if all of the net amounts represented by V were invested at an interest rate equal to r, they and their interest earnings would add up to the capital outlay, K. The investment criterion which justifies undertaking the investment opportunity is that its rate of return, r, is at least as great as the best market interest rate, i, for which the enterprise can qualify, or r >= i.

If we may assume that the predicted net returns, V1…Vn, can be estimated, the internal rates of return can be computed for each prospective investment opportunity currently under consideration by the enterprise’s management. For example, suppose that the management of an enterprise is considering five prospective investment opportunities, designated A through E, which require the capital outlays and promise the internal rates of return. These opportunities have already been arrayed in descending order of internal rates of return. When the capital outlays are “stacked” from left to right on a set of coordinate axes with capital expenditures on the horizontal axis and internal rates of return on the vertical axis, the plotted points A through E constitute a downward sloping path which John Maynard Keynes called the “marginal efficiency of capital” (The General Theory of Employment, Interest, and Money, Harcourt, Brace & World, Inc., 1964, p. 135). Suppose that the enterprise can borrow funds from the capital markets at an interest rate i = 8 percent, represented by the horizontal dashed line. The marginal investment criterion then is to undertake additional investment opportunities in descending order of rates of return as long as the rates of return are at least as high as the interest rate, i, or r >= i. Investment opportunities A, B, and C ought to be undertaken; opportunities D and E ought to be rejected because their rates of return would not be sufficient to pay the interest on borrowing to finance them.

We should note that this long-run investment decision criterion is appropriate even if the enterprise can finance its capital outlays from internal sources. The rationale is that funds accumulated internally by depreciation allowances and retaining earnings have been (or could have been) “invested” on financial capital markets earning interest rate, i, which must now be foregone if the funds are used to finance the prospective investment opportunities instead.

**This series is a lot of parts that I am quasi-using pieces of for a academic research paper stance so bear with me if it gets too esoteric. Or read the other governance articles available within the SharePoint Security category within the main site (available through the parent menu).**