When municipalities consider whether to refinance debt, the industry standard is to pull the trigger if savings exceed 3%.

Why 3%? Why not 8%, or 2%, or 13%? The answer: just because.

In 1995, the Government Finance Officers Association published "Analyzing an Advanced Refunding," a document urging issuers to sell refunding bonds if savings exceed 3% to 5%.

Today that benchmark is cited almost universally by municipalities and financial advisers, most of whom freely admit it is nothing more than custom.

"My rule of thumb, which I think is pretty common, is at least 3% present-value savings," said Lucien Calhoun, president of Calhoun, Baker Inc., an adviser in Pennsylvania. "It's just a rule of thumb. There's no magic."

"It's more convention than anything else," said Scott Nash, managing director at JNA Consulting Group of Boulder City, Nev "In Nevada, many governments have debt policies that prescribe when they should consider refundings. Most, if not all, target 3%."

Some doubt the rectitude of this tradition, saying other factors - such as sacrificing the call option and the term structure of the debt - might outweigh the importance of dollar savings.

Even if they do not, the targeted level of savings is contrived. Phil Ferrand, president of Ferrand Consulting Group, who used to be a senior vice president in Bear, Stearns & Co.'s public finance division, calls it an "artificial threshold."

"For years, we've understood on an intellectual level that percentage savings is not a good way" to judge the wisdom of refinancings, said Ferrand, who makes software that helps municipalities decide when to refinance. "It's bizarre, but the standards for selecting advanced refundings are not based on sound financial practice or theory."

When issuers say 3% savings, they mean dollar savings realized discounted to present value, expressed as a percentage of the refinanced debt.

This presents the next quantitative problem in refundings: what interest rate should a municipality use to calculate the present value of savings? An issuer must select the appropriate magnitude by which $1 today is worth more than $1 tomorrow.

Many issuers calculate the "true interest cost" of the refunding issue, or a single discount rate that equates what the issuer is borrowing now to what it is paying later. This number is the same concept as the yield to maturity.

The issuer assumes this rate is its cost of capital, and therefore the rate at which money loses value over time. That rate is then applied to the dollars saved at each maturity to determine present value.

This method can distort savings when maturities are extended or contracted, Ferrand said, because long-term debt usually carries a higher rate than short-term debt.

Say a municipality refinances long-term bonds with a shorter-term refunding issue. The new bonds will come at a lower interest cost because they have shorter maturities.

If this municipality calculates savings using that lower interest rate, the money saved on longer maturities will appear to be greater, since the present value of future money is higher when the interest rate is lower.

That means municipalities can think they have saved money when all they have done is agreed to pay off debt sooner.

"If you really want to be logically consistent, what you really ought to do is use a different discount rate for every maturity," Ferrand said. "In practice, what most issuers do is, they use a single discount rate."

Ferrand said much of what municipalities do is rooted in the days before the average workaday financial adviser had a computer. Computing the cost or savings from a refunding using different discount rates for scores of maturities and coupon and principal payments on a handheld calculator is an unenviable task.

Now that a college freshman could probably calculate net present value on his cell phone, though, Ferrand said the old ways do not make much sense.

"It's just tradition and politics," he said. "If that's the way people have always done it, then it's very hard to swim against that."

Ferrand sees another reason refinancing techniques remain outmoded. Because the old ways often inflate calculated savings, municipalities are not so eager to embrace new methods - and bankers are not so eager to persuade them to.

Joseph Starshak, a principal at Starshak Winzenburg & Co. in Chicago, puts it bluntly: "Investment bankers are always looking for reasons to refinance."

Carlos Desmaras, managing director at MFR Securities Inc., said one way some municipalities waste money is exercising call options when they are worth too much.

The option to redeem bonds is valuable. How valuable it is depends on the likelihood rates will fall, and how far.

In order to achieve savings by refunding, an issuer must forfeit the value of the option by exercising it, losing the right to refund if interest rates continue to fall.

An option's value consists of the "intrinsic" value - or the cash realizable immediately through conversion - as well as "time" value, or the potential for even greater savings should interest rates fall more.

"Turning it into cash, you're going to realize the intrinsic value of the option and you're going to do away with the time value," Desmaras said.

He contends any savings achieved through refunding should be measured against the value of the option forgone, and he said most issuers don't gauge their options' values.

Andrew Kalotay, president of Andrew Kalotay Associates, argues issuers don't save as much as they think because they often squander the time value of their options.

He advocates using a method called refunding efficiency to evaluate a possible refunding.

Refunding efficiency is the net present-value savings divided by the value of the sacrificed option. It conveys whether the issuer is saving enough to justify refinancing.

If a bond has an embedded call option worth $1 million and the issuer saves $800,000 by exercising it, the issuer is refunding at 80% efficiency - it is collecting in cash only 80% of the option value it is giving up. For each $1 of option value, the issuer cashes in 80 cents of intrinsic value and bestows 20 cents of time value back to the bondholder. Kalotay advises against refunding below 90% efficiency.

At The Bond Buyer's request, Kalotay analyzed a refunding issue by the Ohio Turnpike Commission.

The commission in May sold $137.2 million of refunding bonds to refinance its 1998 Series B bonds ranging in maturity from 2010 to 2018, plus part of that issue's 2024 maturity.

The Turnpike also refinanced its 2001 Series A bonds' maturities through 2024.

James Steiner, chief financial officer at the OTC, said the Turnpike saved $7.5 million net present value through this transaction, representing savings of 5.3%. Advised by Fifth Third with Morgan Stanley as its banker, the commission used the guideline of 3% to 5% savings, Steiner said.

Kalotay does not bother with percentage savings.

He calculates the value of the call options in all these bonds based on the yield curve, which describes the likely path of interest rates, and on the bond market's implied volatility, or the likely deviations from that path.

He concluded the Ohio Turnpike refunded its 1998 Series B bonds at 100% efficiency - meaning it converted its option into cash at 100 cents on the dollar. The entire value of the option was intrinsic, and holding on to it for more time did not confer additional value. Wise move.

Kalotay found refunding the 2001 bonds was not as wise.

The refunded bonds had options he valued at $2.6 million, based on the yield curve and assumed 9% volatility, which Kalotay assures is a generously placid assumption.

The OTC saved $2.1 million in the 2001 component of the refunding, for an efficiency of 79.4%. That is to say, for every 79 cents the Turnpike saved, it would have saved 21 cents more just by doing nothing and keeping its option.

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