Friday, 5 July 2013

Valuation - The Cash Flows

Just a preamble: if you are unfamiliar with discounted cash flow analysis, I anticipate much of the following discussion will be about as clear as mud, so don't get too concerned if I don't sound very coherent here.

Whilst DCF analysis is often used to value income producing assets like shares, it does have a number of flaws or weaknesses that individuals must be aware of. Most of these stem from the accuracy required in making predictions about the future and the sensitivity of DCF analysis to relatively small adjustments. As the popular saying goes, 'It is difficult to make predictions, especially about the future'. Hence, unless you have enough confidence to make reasonable guesses about the future of a business, one should just put it in the 'too hard' basket and move on.

There are however, a couple of remedies for the inherent sensitivity of DCF valuations. By testing a range of assumptions instead of just one scenario, investors can get a feel for the best case and worse case scenarios. If even under the worse case scenario, the valuation doesn't seem too bad, then you might decide to buy. Alternatively, some like to be very conservative in all their assumptions and thus while they may miss out on opportunities for being overly cautious, they also avoid buying overvalued businesses.

I'd just like to discuss something that has bothered me about the way many professionals go about DCF valuations but is rarely pointed out. Many will tell you that you need to discount 'free cash flows' (essentially operating cash flow minus capital expenditure), I beg to differ. Firstly, if you want to get the true cash flows that a business earns, then you need to subtract the capital expenditure required to maintain the business. Capital expenditure for growth is lumped together with maintenance capital expenditure in the financial statements, making it difficult to determine maintenance capex for businesses that are growing (which is the majority of businesses), and unfortunately management rarely estimate it for investors. In most cases, that's too hard, so the total capital expenditure figure is used, or otherwise earnings are used as a proxy for free cash flow.

More importantly, even if you can get this free cash flow figure, it doesn't make mathematical sense. Let's look at an example of a hypothetical scenario. Suppose a business earns a return on equity of 10% and continues to earn 10% on any retained earnings. It starts out with $10,000 of equity and therefore earns $1000 in the first year (also assume that for this business, free cash flow = earnings). If there are 1000 shares on issue, that equates to earnings per share, or free cash flow per share of $1.00. If it pays out 50% of its earnings as a dividend, earnings will increase at a rate of 5% per annum (so will equity, dividends and intrinsic value) as you can see in the table below.

Assume also that the discount rate, or required return of the investor is 10% (I'll discuss this further in my next post). If I discount the earnings per share every year as you can see in the 'Discounted earnings' column, they eventually approach zero. To come up with an intrinsic value, one just needs to add all of these discounted earnings into infinity, in this table, I've just used the Gordon growth model explained in the previous post to keep things short (only 10 years are displayed) and easily calculate an intrinsic value for each year. In the first year, we come up with an intrinsic value per share of $21.00. Sounds fairly reasonable.

Now, what if we discounted not earnings or free cash flow, but dividends as some investors advocate? Since the dividends are half of this business' earnings, dividends per share in the first year are $0.50 in the new table below. Reapplying the discounting process to the dividends, we get an intrinsic value of just $10.50 (incidentally, this is equal to the equity per share at the end of the first year). So which one is the correct value?

To sort this conundrum out, let's say we have investor A, who buys 400 shares of this business at the end of year 0, when he calculates the value of the business as $21.00, for an initial investment of $8400. Investor B does the same, but at her calculated value of $10.50, for an initial investment of $4200. At the end of the first year, they both receive their dividend, and decide to invest that money at their required return of 10%. While they could invest it anywhere else at 10% and the end result would be the same, let's also conveniently assume that the share price always trades at its intrinsic value (which should give a return of 10% if the intrinsic value is correct) and both investors decide to purchase more shares each year with their dividends.

As is visible in the two tables above, at the end of year 10, investor A ends up with 506 shares and would be sitting on an investment of $17,313, up from his $8400. This is a return of 7.5% per year, an unwelcome surprise after expecting a return of 10%. Happily, investor B ends up with 637 shares, and an investment of $10,894, for an annualised return of precisely 10%.

Thus, it is evident that discounting free cash flows or earnings overestimates intrinsic value, whilst discounting dividends produces the mathematically logical answer. This is because unless those free cash flows are paid out to the investor as a dividend, the investor cannot treat it as theirs yet, and therefore cannot discount them yet. Those retained earnings are used to boost future dividend payments so discounting free cash flows or earnings is double counting. If you're still unconvinced, consider what happens if this business only paid out 5% of its earnings as a dividend, not 50%. The free cash flow model produces an absurdly high valuation of $219.00, while the dividend discount model remains reasonable at $10.95. No sane investor would pay $219.00 per share for a business that earned $1.00 per share in the last year.

In what seems like an endless circle of problems, discounting dividends is difficult to do for a business that doesn't pay any dividends yet. In this situation, investors may skip the business entirely, try to guess at future dividend payments, or simply discount earnings if that is too hard. But as I've pointed out, discounting earnings or free cash flows overestimates intrinsic value, so it's advisable to add an extra layer of conservatism on top if taking this approach. And what if there are no earnings either? Again, either skip the business, guess at future earnings, or approach the valuation from an equity or net tangible assets (NTA) perspective, which I'll cover more in my next post. Finally, in Australia, not all businesses pay the same level of franking credits so to account for that I would suggest incorporating franking credits into the dividend figures (a little research online will show how).

A few interesting conclusions can be drawn about the DCF model from the example above and by examining how its inputs affect intrinsic value:
  1. The further in the future cash flows are, the less important they are to the valuation, even though they may be rising in nominal terms (exhibiting the time value of money concept). Therefore, the job of predicting the future is made a little easier: the most important predictions to make are the ones closest to the present. 
  2. As briefly hinted at, a business that perpetually earns a return on equity that is equal to the discount rate/required return is worth exactly the value of the equity itself. This can be useful to approximate intrinsic value for certain businesses in your head. 
  3. A business that can earn a return on equity above the discount rate should ideally retain earnings to reinvest them rather than giving into pressure to pay dividends. This produces the highest intrinsic value (which is above the value of its equity). On the other hand, businesses that earn a low return on equity and have no good prospects of raising this should pay out all of their earnings as a dividend to maximise intrinsic value (which is below equity). Management that ignore these principles may show ignorance in 'maximising shareholder value', as they so often espouse. 
In summary: I believe that while some other methods produce similarly rational valuations, discounting dividends is the most mathematically correct way to calculate intrinsic value, but it is very dependent on putting the right numbers in. The next, and final post about valuation (for now at least) will explore the discount rate a little more, other valuation methods, and end with my thoughts on valuation in practice. 

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