Discounting is the most common calculation in municipal finance. A rather mundane use of discounting is to convert bond prices into yields.

Much more important is to assess the present value of future cash flows. It makes sense to report the benefit of a refund transaction by summing the present values of the future savings, rather than summing the undiscounted savings – the latter would certainly overestimate the true benefit.

Despite its importance, the actual choice of discount rate receives little attention in municipal finance. This is clear from the terminology: to begin with, instead of a single discount rate, we should refer to the term structure of discount rates. Provided that the long-term rates are higher than the short-term rates, the far cash flows must be discounted at higher rates than the nearby ones. An unfortunate custom in municipal finance is to discount every cash flow at the same rate, namely by the yield of the redemption issue.

This underestimates the value of nearby savings and overestimates the value of savings far in the future.

But let’s leave the discussion of the term structure of interest rates for another day and assume that the yield curve is flat. However, even under this simplification, we are faced with another question: should we really discount tax-exempt cash flows with a tax-exempt rate? Using a tax-exempt discount rate certainly seems reasonable. But consider a municipal issuer that has both taxable and tax-exempt bonds outstanding.

With the issuance of taxable prepayment bonds, this situation is becoming quite common. To keep things simple, let’s assume the bonds are optionless and identical in all other respects. The market values of these bonds would certainly be different, depending on the tax considerations of the respective investors. However, we consider these obligations from the point of view of the municipal issuer.

The cash flows generated by identical taxable and exempt bonds are unmistakably identical. Therefore, the present values of the generated cash flows must also be the same. **Thus, the discount rate applicable to the cash flows should also be the same**. The question is whether this discount rate should be based on the issuer’s taxable or exempt lending rate.

In an article co-authored with Bruce Tuckman entitled “Subsidized Borrowing and the Discount Rate…” in the Winter 1999 issue of the Municipal Finance Journal, we argue that **the discount rate should be based on the municipality’s taxable borrowing rate**. The core logic is that because the tax rate is not capped, excess cash flow can be invested at that rate. On the other hand, the tax-exempt subsidized rate is only applicable to tax-exempt loans.

The taxable discount rate correctly determines the market price of a taxable bond and underestimates the market price of a tax-exempt bond. For example, consider a 10-year 2% tax-exempt bond sold at par, where the issuer’s tax rate is 3%. The PV of the 2% bond at a 3% discount rate is 91.42%. The difference of 8.58% between the nominal market value and the 91.42% liability of the municipal issuer is **a measure of the federal subsidy**. This approach can be applied to the entire liability portfolio of the municipality, to determine its present value. One caveat is to use the term structure of discount rates, rather than a single discount rate, as in the example above.

More generally, using the “tax discounting” approach, we can estimate the overall subsidy provided by the federal government to tax-exempt bond issuers. According to a calculation at the bottom of the envelope, the federal subsidy is currently around $500 billion.

As noted above, issuers should use their taxable borrowing rate to discount the cash flows generated from their tax-exempt liabilities. But how do you deal with refundable tax-exempt bonds? In this case, the value of the underlying cash flows depends on taxable rates, while the value of the call option depends on tax exempt rates. This is a tricky problem that we plan to solve in the future.