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.

Before There Was The Motely Fool, There Was The Sane Investor

On this one topic.

There was an article that recently graced the front page of the Motley Fool, talking about how big Apple (AAPL) is compared to its brethren on the S&P 500. It's interesting, because I wrote practically the same article more than a month ago on this subject.

I'm definitely not trying to cite any sort of "copying" (they probably didn't read my article), but it did feel good to have a major investing website run with the same tag line that I recently wrote a piece on.

I'm sorry about the complete absence of content for this blog...I've been really busy. But I will say that I'm happy to be employed now (yay!) although still weighing out two offers I received. Hopefully not having to find a job will give me more time to write on the site.

Is Apple Really the Fourth Most Valuable Company in the United States?

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Upon glancing at the top holdings in the SPDR S&P 500 ETF (SPY), I must admit I was very surprised to see that Apple Inc. (AAPL) was the fourth most heavily held company in the index. Smack between Proctor and Gamble (PG) and Johnson and Johnson (JNJ), as I looked at the list I started to wonder whether the assumptions behind AAPL's valuation might be a little rosy.

To do this analysis, I used the financial information from Apple's most recent 10-K to build a discounted cash flow valuation model. My goal was to see whether the assumptions built in to AAPL's stock price were realistic. After really digging in to the numbers I feel confident that Apple, especially with a one year target price from analyst estimates of $248.33, is in a bubble.

Looking At the Numbers

From a price to earnings perspective, Apple (at 19.64) is somewhat overvalued. Exxon Mobil (XOM) trades at a P/E of 16.56, Microsoft (MSFT) at 15.85 and Proctor and Gamble (PG) at 15.11 (these are the only other companies in the S&P 500 more highly valued than AAPL). If one were to take an average of these three, and infer from this Apple's stock price, one would get a price of $162.68, $38.99 less than what it closed at on Friday.

But price to earnings ratio comparison would be a ridiculous way to value Apple, since obviously its shareholders believe there is still some growth to be had for the company. To see what these growth assumptions are, I projected out through 2015 a balance sheet and income statement for Apple and then did sensitivity analysis with a discounted cash flow to see how operating profit margins and sales growth rates impacted the company's valuation.

>To schedule out the balance sheet, I looked at Apple's ratio of either the various line items to sales or the line items to cost of sales from 2008 and 2009. I then used the average of these two ratios to infer the future values for the line items. While this is a relatively simplistic way of doing this and will no doubt not occur as projected in reality, I wanted to see how Apple would perform if they ran the company much like they have been doing in the recent past.

Looking at Apple's income statement, I tied R&D as a ratio to sales based on recent historical levels and cost of sales based on an operating profit margin. Looking at Apple's recent history, it becomes quite apparent that this company has been immensely profitable and successful based on its extremely high operating margins (40% in 2009) and robust sales growth, with 34% in 2008 and 13% in 2009.

For my DCF valuation, I just did a simple 10% discount rate. Looking at the sensitivity analysis, it becomes quite evident that Apple's future valuation is pricing in consistently strong sales growth and operating margins:

Based on Apple's current market valuation, it appears as though the market is presuming that Apple is going to maintain operating profit margins of 40% in perpetuity and that sales growth would be 14-15% next year tapering off to a terminal growth rate of 4% in 2015.

Since I thought that 40% operating margins in perpetuity was a little much, I looked at what would happen if it tapered off to a terminal level. In my opinion, I feel like it'd be very difficult to constantly stay ahead of the curve and provide products that were just so downright amazing so as to justify a 40% operating profit margin for the life of the company. To find this terminal rate, I took Dell's operating margin from their most recent 10-K and added 5% for good measure:

The valuations under these assumptions are no where near that of the market, which leads me to believe that this stock might be in a bubble.

Conclusion

Of course some of the assumptions I used in this model were a bit simplistic and if I had a little more time I could go in to more detail, but from my simple analysis I feel comfortable saying that the market has absurd expectations for Apple. Does this mean that I don't think Apple is a great company? Of course not. But I do feel like it's overvalued right now, and the analyst estimates seem downright ridiculous, putting it at a market capitalization of $225 billion one year from now.

When the very best case scenario is what seems to be driving the stock price I think it's time to look for greener pastures.

You can download my model below and play with the numbers if you like.

AAPL DCF Valuation