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  • Novalis_97 Novalis_97 Aug 14, 1998 11:19 PM Flag

    The intrinsic value of Pepsi

    I don't think Hagstrom is far off the mark. In
    the 1991 Letter to Shareholders, Buffett used 10% as
    his discount rate in an example to find the intrinsic
    value of a newspaper, but at year-end 1991, the 30-yr
    bond rate was 7.7%. So Buffett was additing 2.3% to
    the discount rate at the time to do the discounting.

    Remember what the discount rate is used for: it's used as
    the discount rate in the perpetual annuity formula,
    PV = C / (r - g). A perpetuity's coupons are paid
    yearly FOREVER, so you want to make sure the discount
    rate, r, accurately reflects what the discount rate
    will be not just now but from now until

    Buffett made comments a few months ago saying that if
    both interest rates stayed low and ROE's stayed high,
    current high stock prices could be justified. But he said
    it's not likely that either of these conditions will
    continue to be true in the future, so to be on the safe
    side, you should jack up the discount rate. 10% is good
    (and even higher than Hagstrom's) because Buffett
    himself used it in his 1991 Shareholder letter example
    (see the section entitled, "Some Valuation Math.")

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    • I understand your logic and I appreciate your
      reply to my message. However, you are off the mark a

      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.
      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

      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.

      • 2 Replies to AynRand23
      • Forgot to include it in the title again.

      • 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

    • One of the problems with using the perpetuity
      formula for anything during times of very low interest
      rates, (such as now, as the long bond is at the lowest
      rates since being issued in the 70's), is that prices
      can quickly approach infinity. This is due to the
      convex nature of a bond's yield. I am sure most of you
      are familiar with basic bond math, so suffice it to
      say that it takes a correspondingly greater increase
      in the price of a bond to go from 6% to 5% than from
      10% to 9%.

      Let's say that we are now in a
      period where interest rates will remain permanently low,
      due to, say, massive global oversupply, Asia's
      recession, whatever. Now, if you were to use the long bond's
      yield of 5.537% to discount your growth rate of 5%, the
      prices approach absurd levels. At these rates, every
      dollar of earnings would be valued at over 186 dollars!
      The same dollar using a discount of 7% would be worth
      50 dollars, still not cheap. And as rates go lower,
      the problem becomes worse, especially when you
      consider what happens if (when) rates start to rise again.
      These astronomically high valuations quickly plummet to
      earth, causing massive asset devaluations.

      if you have a company expected to grow at 5%
      forever, and rates continue to go lower, how do you use
      this equation effectively??? Even if you use the 50%
      of intrinsic value method, you still are paying high
      prices for stocks.

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