This is the last in a series of four blogs featuring key excerpts from the writings of our founder and past president, Richard Zerbe. His insights shaped the foundation of our association and remain relevant to today’s challenges. We hope these selections offer valuable perspectives to all members.

The Combined Approach

Issues concerning discount rates span the history of Cost Benefit Analysis (CBA) and Benefit-Cost Analysis (BCA) and have long bedeviled the economics profession.  The debate now is primarily between rates consistent with the Social Rate of Time Preference (SRTP) on the one hand (societal, long-term, and often sustainability-focused) and the Opportunity Cost of Capital (OCC) (private market, short-term, and efficiency-focused) on the other hand. Should decisions be guided by private market returns, though allowing for private consumption displacement (OCC) as suggested by Hargerger, or social welfare over time)? I predict that over time a solution will lie in the realization that both play a role. This combined approach, developed by Szekeres 2024, uses the SRTP after accounting for the cost of capital benefits are used to pay costs down if it pays to do so, as long as the OCC > SRTP. This approach recognizes the value of paying down capital costs is of greater value than the current consumption of benefits, and, for the same reason, encourages doing this as quickly as possible.  An example is given in the Table below in which both the OCC and SRTP are each used separately and together in the combined approach. The example assumes the OCC is 7% and the SRTP is 2%.

Table1: Solutions Compared

In Table 1, project benefits are 50 per period and capital costs in period zero are 100. The costs are amortized over the life of the project and are subtracted from benefits with the resulting cash flows discounted at 2% to give an NPV_AMT of 162.  This is the NPV when costs are amortized over project life. This is for illustrative purposes only as the better approach is to pay down costs as quickly as possible as this is the efficient thing to do to avoid the 7% interest charge. The result is shown by the NPV_CE. When this is done the NPV is necessarily higher at 172.  In this example, costs are able to be paid down from benefits received.  Otherwise, the NPV would be negative.  Thus, the hurdle rate for the project is the OCC.  Simply put, a desirable project must meet its opportunity costs. A way to envision the comparison of the SRTP and OCC approaches is to envision a project that always yields a positive NPV when discounted at the OCC; such a project is paying down government debt.

Not surprisingly the two factor NPVs are between the higher NPV determined by the SRTP and the OCC.  Yet, as long as benefits cover capital costs fully, the NPV_SRTP and the NPV_CE will both be positive.  The important point remains: if costs are not covered, the SRTP can yield a false positive NPV, but neither the two rate test nor the OCC will yield this error.

Incorrect Objections to the Combined Approach

This objection (Spackman) supposes that the effects of private funding are different from those of public funding, as public funding can be from taxes. This, however, is incorrect. Even if, say, 100 percent of public spending is covered by taxes (making the AVERAGE cost of funds equal to the cost of raising taxes, the MARGINAL cost of funds is the cost of borrowing. This puts the government in the same position as a private corporation; they both have the same social cost of funding. Suppose, for example, I plan to build a wall around my property which would reduce damage to my property by an amount greater than the costs of the wall. The government, however, taxes me an amount equal to the cost of the wall, and uses the funds to build another wall elsewhere.  Now to build my wall I borrow the money that I had saved before it was taxed away so that the wall project involves borrowing. In addition, the government could also use my tax money to pay down government debt which again represents the costs of borrowing so that if the government wall yields less than paying down its dept, its project is inefficient.

The Ramsey equation cannot be used, inter alia, for choosing a rate when its derivation of the Ramsey equation already assumes a rate.

No agreement will be reached on the discount rate (that is, if one is forced to choose). A rate of zero which has been proposed on the grounds of concern for future generations will instead punish those generations by depriving them of the fruits of more productive investments.