I understand your logic and I appreciate your reply to my message. However, you are off the mark a little.
First, the Buffett example about the newspaper valuation was not supposed to be an exact example of how he does it. He was using that as an example of how the market values stocks generally. I've read that section about 50 times and nowhere does he specifically come out and say that's how he does it or how he figures out the discount rate. I have read quotes by him, however, in which he says you should not use any risk premium, but use a margin of safety when estimating future growth in earnings. Come to think of it, even the Hagstrom book quotes Buffett as saying that. The reason Hagstrom's valuations all came out so low (i.e. for Disney, Coke, ABC, etc.) is because Hagstrom didn't cut 50% off the intrinsic value as an acceptable buy price. He just took the full I.V. using the 9% rate as the buy price, which of course was higher than the current market price of those stocks. Almost ANY stock has an I.V. higher than the market price if you do it this way. Go ahead and discount Coke's earnings out right now using a 12% growth rate for 10 years and 5% after that, and a 9% discount rate. You'll see what I mean. It gives an I.V. higher than today's market price. Would you then conclude that Coke is undervalued at 51 times earnings? Of course not. You have to discount Coke's earnings out at about 7%, and then take 50% of the I.V. as an acceptable buy price. Even then, it's overvalued.
If you try to predict earnings AND future interest rates, you're trying to do the inhuman. No one can predict future interest rates more than a few months out.
In 1991, if rates were 7.7% when Buffett wrote his piece and he used a 10% discount rate, that would be a 30% premium over the then current long bond rate. Today's long bond rate is 5.6%, and 30% above that is about 7.25%. You have to use the percentage premium he used, not the absolute number. Otherwise, the logic is flawed. So I guess maybe I should be using 7.25% instead of 7%, but again the Buffett example was not meant to be that specific.
I still say you can't predict something like interest rates, whether they'll go up or down, and so the only thing you can do is use the current rate and go off that. It's hard enough to predict future earnings. Use a margin of safety for that. If interest rates go down from here (they just might), you may be using a margin of safety on your discount rate that prevents you from buying some great stocks at bargain prices.
The purpose of the newspaper example was to show how an estimate for intrinsic value can dramatically change if the assumption for earnings growth rate changes. He's saying that if the newspaper's earnings growth rate changes from 6% to 0%, the intrinsic value estimate changes dramatically from $25 mil. to only $10 mil. He's definitely using the "perpetual annuity (aka perpetuity)" formula. He says, "(in the past) ownership of a media property could be construed as akin to owning a perpetual annuity set to grow at 6% a year." Look at the math and you'll see that he really is using the perpetuity formula.
In the first case, when g = 6%:
PV = C / (r - g) = $1 mil. / (0.10 - 0.06) = $1 mil. / 0.04 = $1 mil. / (1/25) = $1 mil. * 25 = $25 mil.
In the second case, when g has been reduced to 0%:
PV = C / (r - g) = $1 mil. / (0.10 - 0.00) = $1 mil. / 0.10 = $1 mil. / (1/10) = $1 mil. * 10 = $10 mil.
There's no debate that Buffett uses the perpetual annuity formula to calculate intrinsic value. In the 1992 Shareholder Letter, Buffett states that in his book, "The Theory of Investment Value," John Burr Williams set forth the "equation for value." And what is this equation? It's the equation for a perpetuity! Go look it up yourself! Except that Williams uses dividends as C, while Buffett in his 1986 Annual Report stated he uses "owner earnings."
In the newspaper example, Buffett doesn't give a reason for why he uses 10%. He just uses it. He says, "Say that a discount rate of 10% was used to determine the present value of that earnings stream." I've already pointed out that this is higher than the 7.7% long-bond yield at the time. If Buffett uses it, it's good enough for me!
If you recognize what a perpetuity is, that its coupons are paid out FOREVER, you'd want to make sure your discount rate, r, reflects what the interest rate is not just now (or in the past several years) but out until Judgment Day. If you're using 7% as your discount rate, you're saying that, on average, the discount rate from now until Judgment Day will stay at 7%. But you don't know this and, furthermore, it's not likely to stay at 7% in the future. Essentially, you're making a prediction about future interest rates but, as you said yourself, no one knows what future interest rates will be. Just because interest rates have been low in recent years doesn't mean they will continue to be low in the future.
To be on the safe side -- not because I or Buffett can predict future interest rates -- you want to use a conservative (i.e., higher) discount rate. If Buffett uses 10% -- which is the historical average -- then people who want to calculate intrinsic value like he does should use it, too. By using 10%, you aren't using an unrealistically conservative discount rate, either. You're just using a rate that, over time, will likely better reflect future rates than 7%, based on history. As a result, your IV calculation based on 10% is likely to be accurate rather than an underestimate. On the other hand, the danger of using 7% is that your IV estimate is likely to be an overestimate and, even if you cut that IV by 50%, you're not going to end up truly buying a company for 50% of its true IV.
Here's what Buffett said not too long ago at the Univ. of Washington:
�There�s no magic to evaluating any financial instrument...If every financial asset were valued properly, they would all sell at a price that reflected all of the cash that would be received from them forever until Judgment Day, discounted back to the present at the same interest rate. There wouldn�t be a risk premium, because you�d know what coupons were printed on this �bond� between now and eternity. That method of valuation is exactly what should be used whether you�re in 1974 or you�re in 1998.�
We want to use a discount rate that reflects not just recent years but will reflect what the likely rate will be from now until Judgment Day.