Sunday, March 21, 2010

When People Forget to Implement Present Value Adjustments

In a recent New York Times piece by Op-Ed Contributor Douglas Holtz-Eakin, entitled: The Real Arithmetic of Health Care Reform, the author points out several "gimmicks" employed in the proposed health care legislation that supposedly reduce the Federal Budget deficit.

I'm not an expert in this field. I couldn't precisely tell you how the Congressional Budget Office (CBO) works, or what methodology is employed. What I can tell is when an author is failing to discount to present value.

Take his first gimmick: "the bill front-loads revenues and backloads spending. That is, the taxes and fees it calls for are set to begin immediately, but its new subsidies would be deferred so that the first 10 years of revenue would be used to pay for only 6 years of spending."

Now if you sum up the benefits and the costs, you may very well get what the author is talking about. However, if you employ present value in your analysis, you might arrive at a very different conclusion.

If you were to ask someone if they'd rather have a dollar today or a dollar a year from now, they would say the dollar today. Why? Because they could spend it now, or invest it and earn some sort of return. So how much would you have to give someone a year from now to make them indifferen between the dollar today and the sum a year from now? Well if it's a sure thing they'll get that sum from you, that's essentially the risk-free rate of return. If there's a risk that they'll get that amount from you, the rate should be the risk-free rate plus the risk premium you represent.

Typically, people look at Treasury bills and bonds as the risk free rate. So right now, the one year Treasury bond is yielding 0.41%. So if you knew you would get the sum a year from now, you would demand $1.0041 a year from now to make you indifferent between that and a dollar today (part of the reason this is so low is because interest rates are at record lows right now).

So to determine the real cost of a project, you have to discount the yearly costs and payoffs by (1 + discount rate)^(t), where "t" is the time that has passed in years (presuming the discount rate is an annual rate). If there is no risk in the payoff and costs, then you discount by the risk free rate. If there is risk, it's the risk free rate plus the risk premium.

So what does this all mean? Essentially, even though when you do a strict summation the project might net zero or a negative value, when you employ discounting it could very well be positive. By the nature of the plan identified by the author (payoffs early on, costs later), I'm extremely skeptical about his conclussion since he doesn't note employing any type of present value adjustements. I'd guess the CBO does. I think I'll side with what the CBO says.

Sorry Doug.

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