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Berkshire Hathaway Inc. Message Board

  • spameggsspamandspam spameggsspamandspam Dec 11, 2003 4:40 PM Flag

    PV of Future Cash Flow

    In the book The Warren Buffett way, author Hagstrom calculates the present value of a company's future cash flow by dividing a year's earnings by the yield on the 30-year Treasury bond.

    Can someone explain this to me? Why, in theory, does the PV of future cash flow equal earnings / 30-year rate?

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    • Present value is extrapolated backward from the projected future, and compared against the long term T-bill yeild, two reasons there - is it better yield than the bond, and long term inflation expectations in a normally functioning market.
      We do not have a normally functioning market when inflation expectations are low and commodities have risen by 60%!
      The value of future earnings are less when inflation takes hold, so as in the 1970's the market sells off and P/E multiples crash fro >30 to less than 14, purely because inflation robs you of the expected future income stream.
      The

    • Yeah, swusc's point is extremely important & hopefully Hagstrom mentions this as well. All this stuff is jam-packed with land mines.

      The current 30 year rate would give a P/E of 20x for a company with steady earnings. In reality nobody wants to pay that much for anything but treasuries, because they feel that the payments may not actually arrive. So folks talk about a P/E of 10x or 14x or something for companies whose earnings might reasonably be expected to continue without growing or shrinking.

      Opinion:
      To help make all this more incomprehensible, people also use the phrase "discounted cash flow analysis" to mean "we ran lots of spreadsheets before we picked a PE".

    • Well, the highest (so most conservative) yet (hopefully) risk-free interest rate out there is the dreaded Long Bond. Call that rate R.

      NPV of a stream of $1 payments that will arrive in your mailbox at 1-year intervals is

      NPV = $1 [now] + $1*(1-R) [y/e 2004] + etc.

      The future payments are worth less than the immediate payment, because you could take your $1 now, put it in bonds, and get R. From there it's an algebra trick to show that NPV = 1/R.


      I'm a former techie so I'll grind it out for exercise ... please skip the following if
      you value your time
      -----------------------------------------
      We know that
      NPV = 1 + (1-R) + (1-R)^2 + (1-R)^3 + ... (A)

      so we can multiply by (1-R) on both sides:
      NPV*(1-R) = (1-R) + (1-R)^2 + (1-R)^3 + ...
      add one to both sides:
      NPV*(1-R) + 1 = 1 + (1-R) + (1-R)^2 + (1-R)^3 + ...
      But the right-hand side of the last expression is just the same as our formula (A) for NPV above. So we can set
      NPV = NPV*(1-R) + 1
      Then we solve for NPV:
      NPV*(1-(1-R))=1
      NPV*(R) = 1
      NPV = 1/R.
      -----------------------------------------


      Finally, Buffett warns people to be real careful when quantifying the future cash flows themselves, for several reasons. Graham has much more to say about that in "The Intelligent Investor."

    • Well he is using 30yr as the discount rate. I would never do that and Buffett isnt doing it either. Or he would have a lot to buy right now.

      The reason it equals is this.

      If you want to make say 8% and the company is make $1 with no growth rate. Then you should be willing to pay 12.5$ Because you would get 8% or $1 a year. 1/0.8

      If you have a growth rate of 2% and same discount rate. You use the next years earnings/(discount rate-growth rate)

      1.02/.06=$17

      Why? You need to make 8% off $17 or 1.36. You have 1.02 but where does the extra .34 come from? Well since earnings are growing then the value of the stock should grow as well. 2% of $17 is 34c.

      I said i wouldnt do anymore math today, so if any figures are wrong. I am sorry. my math isnt working so well today. Which isnt good since I took a tax exam at 9AM

      SWUSC

    • That makes no sense, sorry.

 
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