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  • Novalis_97 Novalis_97 Aug 16, 1998 6:17 PM Flag

    The intrinsic value of Pepsi

    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 =

    PV = C / (r - g) = $1 mil. / (0.10 - 0.06) = $1 mil.
    / 0.04 = $1 mil. / (1/25) = $1 mil. * 25 = $25

    In the second case, when g has been reduced to

    PV = C / (r - g) = $1 mil. / (0.10 - 0.00) = $1 mil.
    / 0.10 = $1 mil. / (1/10) = $1 mil. * 10 = $10

    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

    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

    �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

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