Tuesday, July 12, 2011

The Many Faces of PE - DCF

A lot of people like to say that PE is not robust enough. Ultimately a company is the present value of its future cashflow and how does one simple ratio determine it? We need to have a full model of all it's future cashflow, discount it back to today's earnings, add it up and we have the true value of the firm. How can one simple no. like PE determine the true value of a company?

Well, actually, it kinda does a great job at that.

PE is actually not that different with DCF.

Let's start with DCF. DCF is basically discounted cashflow of a firm:

Discount rate: 6%, Growth: 2%

Yr 0 EPS $1.00 - DCF to Yr 0 = $1
Yr 1 EPS $1.02 - DCF to Yr 0 = $0.96
Yr 2 EPS $1.04 - DCF to Yr 0 = $0.93
Yr 28 EPS $1.74 - DCF to Yr 0 = $0.34
Yr 29 EPS $1.78 - DCF to Yr 0 = $0.33

The calculations above shows you that this firm earns $1 per share and increases it by 2% every year, and will continue to do so for 30 years. To calculate the value of the firm, we need to discount these future cashflow back to today. So you can see that in Yr 1, ie next yr, it is actually making only $0.96 in today's dollar, Yr 2 it's $0.93 and in Yr 29 it's $0.33 in today's dollar.

Now adding these up gives you $18, which should be the intrinsic value of the firm.

Incidentally, if you think of the inverse of PE, which is the earnings yield and compare it against the discount rate of 6%, you can say that the right PE for the firm is 1 divided 0.06 which is 17x.

Using this to calculate the intrinsic value, we use next yr's EPS of $1.02 multiply by 17x, which gives you $17.4, not so different from the $18 calculated using the complicated discount cashflow.

In fact, if we know that the firm will continue to grow 2% for 30 years, we should be using a higher EPS, maybe say a Yr 2 EPS, which will give you $17.7 intrinsic value, just 2% different with the DCF calculated value of $18.

So PE while simple, gives you a quick but somewhat accurate way to calculate the intrinsic value of a stock.

Of course, there are a few caveats here:

1. Why 30 yrs? Shouldn't a company exist forever?

Yes in the example above, DCF lasted only 30 yrs but in reality companies can exist longer than that. In fact, we need to do DCF for 100 years in order for the last few years to become small enough such that it doesn't matter. Alternative, most people will actually stop after 5 or 10 yrs, and put in a terminal value and discount that back to today. But in doing so, basically, we are applying the PE methodology on the terminal value, and this value actually constitutes a larger part of the final intrinsic value. So essentially, we are still using PE this way.

2. Shouldn't a company grow faster than 2%?

Yes that is true, but with our example, when we put in a high growth rate for 30 yrs, the no.s become astronomical and can't be justified rationally. This is the power of compound interest which we have also discussed. For example, if we put in 8% growth, intrinsic value becomes $40 after 30 yrs, that's 40x PE based on next yr's earnings. Hence for very long periods, like 30 yrs, we have to assume that the average growth is small.

3. What if we change the discount rate?

The discount rate is the most sensitive part of the whole DCF methodology, changing it slight would alter the picture significantly. For example, changing the discount rate from 6% to 4% brings the intrinsic value to $23 from $18. Which is why most people doing DCF usually put in a sensitivity table showing how the intrinsic value changes as discount rate changes.

Putting this altogether, I think the main message is: you can use DCF if you have a good grasp of the various assumptions going into it, ie the growth rate, discount rate and how things changes over the next 5, 10, 30 years. Now if someone can really get all these right, then perhaps he should be doing something greater, like save the world and be the next Messiah or something. Why bother investing money, which really doesn't add value to the society?

Well if all you want is to get a quick answer to a ballpark intrinsic value, using a ballpark EPS multiplied by a rational PE multiple (between 10-18x) would suffice in most cases.
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