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?
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.
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.
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*(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."
I understand! Thank you! (wow, I learned something on the internet)
But how did you do this step?
NPV = NPV*(1-R) + 1
I had to go
NPV = NPV*(1-R) + 1
NPV-(NPV*(1-R)) = 1
NPV-NPV+R(NPV) = 1
NPV = 1/R
Also, I wish earnings was "E" instead of 1. I assume that when you added one to both sides, you were really adding E, which in the example just happens to be $1.
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)
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