## 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.

1. P/E and DCF is obviously different.

P/E ratio depends on earnings.
DCF depends on free cash flow. Free cash flow means operating cash flow minus capital expenditure.

A company with rising earnings may not result in rising free cash flows.

Using 30 years for calculation may result in an expensive valuation. I prefer to use a conservative 10 years.

As for the growth rate, we can use past history growth rate as a guide. Problem is most companies do not have consistent growth rate. So we have only apply DCF to company that has consistent growth rate like Boustead, OCBC, DBS, Raffles Medical etc.

Discount rate of 6% is too low in my view. Discount should be based on equity premium. Most stocks have discount rate of 8% to 12%.

2. Hi,

Great Post. Could you please explain how you use the discount rate and calculate prices in layman's term. I am not a finance student and it would be easier for me.
Your value investing ideas are useful for new investors like me. Thanks.

Jereme

3. Send an email to me at metal.commodity@tradingeducationprogram.org.

I will send you my spreadsheet which I had used to calcuate DCF.

Value Investor

4. Hi Value Investor

Spot on the discount rate, yes it should be higher at 8-12% for most co.s

My argument was trying to protray that using a discount rate of 6% is essentially the same as applying a PE of 17x which gives you roughly 6% earnings yield.

As to whether it is appropriate to use 10 or 30 yrs, the true answer is that it really doesn't matter, bcos at the end of it, we still need a terminal value.

The terminal value determines the bulk of the intrinsic value anyways.

So in order for the DCF to be really accurate, we need to know all the inputs for the next 30 yrs.

Wouldn't it be easier to apply a PE and EPS methodology then?

That was the point I tried to make.

5. Hi Jereme,

The point that I am trying to make is that applying a PE and EPS methodology is very much similar to DCF, which uses the discount rate.

As a simple example, if the average EPS of the stock is \$1 for the last 10 yrs with little volatility, what is the fair value of the stock?

The answer is an art form, not science.

If we apply 10x PE, the fair value is \$10.

At 15x PE, the fair value rises to \$15.

The insight here is that applying different PE is also the same as applying different discount rates for the firm.

PE is just the inverse of the discount rates.

So when we apply very high PE on stocks, like 50x PE. Essentially we are saying that the discount rate of is 2% - which is lower than long term Singapore govt bond yield.

What are the chances that we overpay then?

Yes, very high.

As a rule of thumb, I would usually buy stocks with PE not higher than 18x.