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.