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Discount rates


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1. Say you are valuing company X using a discounted cash flow model. What is the appropriate discount rate to use?

 

2. Say you now are the only person who knows the annual free cash flow of company X with certainty to perpetuity. Assume further that all FCF will be paid out to shareholders annually. What is the appropriate discount rate to use and why?

 

3. If your answer to 2. was the long term risk free rate, does it mean that the reason for using a discount rate that is higher to the risk free rate when valuing company X is to adjust for uncertainty in its future FCF?

 

4. If your answer to 3. was yes, why do we not adjust the numerator (FCF) instead of the denominator (discount rate).

 

5. Or am I just wrong to think in this way and that DCF models are next to worthless for valuing companies given its many flaws

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Maybe there isn't a correct discount rate?

 

However, there might be arbitrage opportunities available.  Sometimes the implied discount rates don't make sense.  The prices of assets often vary wildly in a single year... in practice, it often makes sense to take advantage of these mood swings.

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1. Whatever rate of return you want, or expect on the next-best investment.  I use 10% because over very long periods this beats the nominal return on the stock market. 

 

2. 10%, because it is the rate of return I want.

 

3. Yes.  It is called the equity risk premium.

 

4. I do.  I try to discount at 10% using a conservative estimate of future cash flows.

 

5. DCF models have no flaws...it's the assumptions that go into them that have flaws.  So make conservative assumptions, use a conservative discount rate, buy at a discount to the price that the DCF gives for intrinsic value, and you should have a good margin of safety.

 

Just my methods - there are no right answers!

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1. The risk-free rate or anything above it.

 

2. Same as 1

 

3. I want to earn more than the risk-free rate. In order to do that I either have to buy below PV of future cash (margin of safety) or use a higher discount rate.

 

4. I share Buffett's view that DCF is the only logical way to measure the relative attractiveness of assets.

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How do you reconcile your statement attributed to Buffett vs the claims that he has rarely (never?) used a DCF model...do you think (as I do) that it simple a mental framework in which to analyze an investment?

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How do you reconcile your statement attributed to Buffett vs the claims that he has rarely (never?) used a DCF model...do you think (as I do) that it simple a mental framework in which to analyze an investment?

 

"We don't formally have discount rates. Every time we start talking about this, Charlie reminds me that I've never prepared a spreadsheet, but I do in my mind. We just try to buy things that we'll earn more from than a government bond - the question is, how much higher?" -WEB

 

I believe him when he says he doesn't write them out. Can he do them mentally? 1) We're talking about a man who can calculate compound annual return figures in his head; I think the mental math ability is there. 2) I am not suggesting the DCF is done with precision. He's noted before that others would be surprised at just how imprecise he is.

 

The more I do these DCF calculations in Excel the more mental shortcuts I find. With enough practice I don't think doing these without Excel is so far fetched.

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You can come up with mental models pretty easily using a simplified PE method.

 

For a 5 time horizon:

 

D = Discount Rate

GR = Growth Rate

PEt= Terminal PE

r = Discounted PE ratio

PEd = Discounted PE

 

r = D^5/PEt

 

PEd = GR^5/r

 

Example:

 

Coke

 

D = Discount Rate = 10%

GR = Growth Rate = 8%

PEt= Terminal PE = 16

r = Discounted PE ratio

PEd = Discounted PE

 

r = D^5/PEt = (1.1^5)/16 = .1

 

PEd = GR^5/r = (1.08^5)/.1 = 14.7

 

This implies the estimated DCF for KO is 14.7 x 1.91 (earnings) = $28

 

Now for the compound growth problem made easier

 

use the formula-

 

n= number of years

r= rate of growth

 

1+(n-1)r/72

 

for n=5 years:

1+r/18

 

for n=10 years:

1+r/8

 

If you decide on a conservative PEt to look at companies and set your own discount rate. You can simplify the math greatly. For instance:

 

PEt = 10

D = 10%

 

PEd =  6.25 + .34*GR

 

PEt = 12

D = 10%

 

PEd = 7.5 + .41*GR

 

PEt = 14

D = 10%

 

PEd = 8.75 + .48*GR

 

PEt = 16

D = 10%

 

PEd = 10 + .55*GR

 

 

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  • 1 year later...

How do you reconcile your statement attributed to Buffett vs the claims that he has rarely (never?) used a DCF model...do you think (as I do) that it simple a mental framework in which to analyze an investment?

 

"We don't formally have discount rates. Every time we start talking about this, Charlie reminds me that I've never prepared a spreadsheet, but I do in my mind. We just try to buy things that we'll earn more from than a government bond - the question is, how much higher?" -WEB

 

I believe him when he says he doesn't write them out. Can he do them mentally? 1) We're talking about a man who can calculate compound annual return figures in his head; I think the mental math ability is there. 2) I am not suggesting the DCF is done with precision. He's noted before that others would be surprised at just how imprecise he is.

 

The more I do these DCF calculations in Excel the more mental shortcuts I find. With enough practice I don't think doing these without Excel is so far fetched.

 

Example...

 

It's 2011 and he is sitting in his bathtub thinking about how even with a middle-of-the-road management team BAC will earn a consistent 13% ROTCE in a few years.  He only has to multiply 0.13 times $14 and he's got $1.82 in earnings.  That's a 26% yield on $7 price tag.  Does he need a spreadsheet?  No, this is basic math stuff that can be approximated in your head even if you can't calculate $1.82 precisely.  He knows that there might be no yield for 3 years (going to cleaning up the mess), so he knows that $1.82 is still a fine yield on $9.50 stock (approximating a 10% return for the first few years before earning the yield on top of that).

 

It takes more effort to dig up Moynihan's phone number.

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I read a quote from one of the old guys (Charlie or Warren) about this subject a while ago. Something along the lines of: "Our discount rate is the expected rate of return on our second-best idea". This struck me at the time as a valuable insight. There is no 'correct' discount rate, your analysis only makes sense in comparison with alternative investments.

 

When faced with uncertainty I prefer to calculate an expected value over multiple scenarios instead of adjusting the discount rate upwards by an arbitrary amount. Because in thatt case you force yourself to make explicit your assumptions.

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I read a quote from one of the old guys (Charlie or Warren) about this subject a while ago. Something along the lines of: "Our discount rate is the expected rate of return on our second-best idea". This struck me at the time as a valuable insight. There is no 'correct' discount rate, your analysis only makes sense in comparison with alternative investments.

 

When faced with uncertainty I prefer to calculate an expected value over multiple scenarios instead of adjusting the discount rate upwards by an arbitrary amount. Because in thatt case you force yourself to make explicit your assumptions.

 

Weren't they talking about their return on capital invested?

 

BeerBaron

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How do you reconcile your statement attributed to Buffett vs the claims that he has rarely (never?) used a DCF model...do you think (as I do) that it simple a mental framework in which to analyze an investment?

 

"We don't formally have discount rates. Every time we start talking about this, Charlie reminds me that I've never prepared a spreadsheet, but I do in my mind. We just try to buy things that we'll earn more from than a government bond - the question is, how much higher?" -WEB

 

I believe him when he says he doesn't write them out. Can he do them mentally? 1) We're talking about a man who can calculate compound annual return figures in his head; I think the mental math ability is there. 2) I am not suggesting the DCF is done with precision. He's noted before that others would be surprised at just how imprecise he is.

 

The more I do these DCF calculations in Excel the more mental shortcuts I find. With enough practice I don't think doing these without Excel is so far fetched.

 

Example...

 

It's 2011 and he is sitting in his bathtub thinking about how even with a middle-of-the-road management team BAC will earn a consistent 13% ROTCE in a few years.  He only has to multiply 0.13 times $14 and he's got $1.82 in earnings.  That's a 26% yield on $7 price tag.  Does he need a spreadsheet?  No, this is basic math stuff that can be approximated in your head even if you can't calculate $1.82 precisely.  He knows that there might be no yield for 3 years (going to cleaning up the mess), so he knows that $1.82 is still a fine yield on $9.50 stock (approximating a 10% return for the first few years before earning the yield on top of that).

 

It takes more effort to dig up Moynihan's phone number.

 

+1

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Guest longinvestor

How do you reconcile your statement attributed to Buffett vs the claims that he has rarely (never?) used a DCF model...do you think (as I do) that it simple a mental framework in which to analyze an investment?

 

"We don't formally have discount rates. Every time we start talking about this, Charlie reminds me that I've never prepared a spreadsheet, but I do in my mind. We just try to buy things that we'll earn more from than a government bond - the question is, how much higher?" -WEB

 

I believe him when he says he doesn't write them out. Can he do them mentally? 1) We're talking about a man who can calculate compound annual return figures in his head; I think the mental math ability is there. 2) I am not suggesting the DCF is done with precision. He's noted before that others would be surprised at just how imprecise he is.

 

The more I do these DCF calculations in Excel the more mental shortcuts I find. With enough practice I don't think doing these without Excel is so far fetched.

 

Example...

 

It's 2011 and he is sitting in his bathtub thinking about how even with a middle-of-the-road management team BAC will earn a consistent 13% ROTCE in a few years.  He only has to multiply 0.13 times $14 and he's got $1.82 in earnings.  That's a 26% yield on $7 price tag.  Does he need a spreadsheet?  No, this is basic math stuff that can be approximated in your head even if you can't calculate $1.82 precisely.  He knows that there might be no yield for 3 years (going to cleaning up the mess), so he knows that $1.82 is still a fine yield on $9.50 stock (approximating a 10% return for the first few years before earning the yield on top of that).

 

It takes more effort to dig up Moynihan's phone number.

 

+1

 

"We would rather multiply with 3 than with pi" - WEB.

 

He probably does this all day. The 0.14159265359 difference allows him to be more conservative as well.

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Weren't they talking about their return on capital invested?

 

BeerBaron

 

At this years annual meeting someone asked what their cost of capital is and Buffett answered,

"Our cost of capital is the production of our second-best ideas. I have listened to so many nonsensical cost-of-capital discussions. I have heard CFOs talk about it, but nobody knows what it is. The real test is whether the capital that we retain generates more in market value than is retained. The real test is whether the capital that we retain generates more in market value than is retained."

 

He's also said it in relation to the risks of deploying capital into buying whole companies, "The cost of a deal is relative to the cost of the second best deal."

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2. Say you now are the only person who knows the annual free cash flow of company X with certainty to perpetuity. Assume further that all FCF will be paid out to shareholders annually. What is the appropriate discount rate to use and why?

 

3. If your answer to 2. was the long term risk free rate, does it mean that the reason for using a discount rate that is higher to the risk free rate when valuing company X is to adjust for uncertainty in its future FCF?

 

 

My answer to #2 would be the lowest rate of long term, non-MTM funding I could get to borrow heavily against this investment. That would probably be higher than the risk free rate.

 

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