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Discounted Cash Flow Madness

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By TMFKMHinson
June 6, 2008

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I've been racking my brain for the last few days trying to reconcile the fact that when I use different methods of valuation, I can come up with wildly different results even when using identical inputs. That should not be the case, and it clearly means I'm introducing an error somewhere. I've put in some serious time thinking about it, and even if I can't numerically reconcile the various methods, I've at least tried to understand the reason for the error and make my choice of preferred approach accordingly.

The questions about what to do DCF on that I've answered in my own mind (at least until you guys start poking holes and showing me my errors) are the following...

1.) FCFF versus FCFE
2.) Capitalize leases versus don't capitalize leases
3.) Apply a terminal multiple to earnings versus projecting earnings out indefinitely

Bonus question I'm not yet sure about - Maintenance cash flow versus depreciation.

1.) FCFF versus FCFE

This shouldn't matter. Theoretically, if I'm using the same starting point and the same assumptions about the future, whether I value a company using FCFF to FCFE should make no difference. But it does. Not usually a big difference, but there is a delta.

For all my examples, I'm going to use Joseph A Bank FY2007 numbers as my starting point, and to keep things simple I'm going to assume flat store count, flat margins, no working capital changes, 3% comps indefinitely and a 10% discount rate. Unrealistic assumptions to be sure, but this is solely for me to have a baseline scenario to work with.

[See post for table]

So doing a DCF on FCFF (10.5% of revenues), applying a 10X multiple on year 6 cash flows and adding in net cash (leases are not capitalized here, and I'm ignoring options outstanding for simplification) gives a fair value of $45/share. A DCF on FCFE (10.7% of revenues), applying a 10X multiple on year 6 cash flows yields $41/share, or 9% lower.

Maybe my made up 10X multiple is screwing things up and something's not linear... Besides, if someone is willing to pay 10X FCFE in year 6, they'd be willing to pay a higher multiple of FCFF because of its lower absolute number and it's the same company. Accounting for that difference still gives approximately the same result though, so if instead I skip applying a multiple and project those cash flows out at a 3% growth rate indefinitely and discount it all I get $56/share using FCFF and $52/share using FCFE. This closes the gap a little, providing a 7% difference. This isn't huge considering the magnitude of the changes when I vary margins or growth by a mere +/-1%, but if I can exorcise as many structural complications in my process as possible ahead of time, I think my valuations will give me more useful results.

My conclusion... why estimate the value of cash/debt on the balance sheet by projecting future interest payments on it and discounting it back. The process seems much cleaner to me by subtracting the impact of interest from earnings, projecting that pre-interest number out, and then simply valuing cash and debt at face value. The alternative of including interest payments, and adjusting the discount rate appropriately all so I value $100 in cash as $100 and don't do something goofy like project out 3% interest payments in perpetuity, discount it back at 10% and value that $100 on the books as $30. Yes I can adjust the discount rate appropriately, but it just seems easier to value $100 as $100, and simply make sure somewhere else in my process that return on capital is good and debt is used judiciously.

Winner: FCFF + net cash over FCFE

2.) Capitalize leases versus don't capitalize leases

Here again, the decision made should be irrelevant... but it's not. Whether I capitalize leases, move the implied interest payments below NOPAT (giving us a higher margin), lump in increases in implied lease purchases into cap ex, and then subtract capitalized lease debt out at the end... or whether I simply leave leases alone giving us a lower NOPAT margin since 100% of lease payments remain an operating expense, but we don't have to subtract capitalized lease debt out at the end... the result should be the same, and the pluses and minuses should balance out exactly.

Keep in mind, I'm not arguing against capitalizing leases when looking at a company, it's capital structure, its debt coverage, etc. I'm simply arguing that it does not matter whether I do it when valuing a company, yet I come up with different results... so which method will give me the least likelihood of introducing user error?

Above, when I didn't capitalize leases and applied a 10X multiple to FCFF, I got a fair value of $45.

�[See post for table]

Using these numbers, which capitalized leases using a 6.3% interest rate across the board and had $244 million in lease debt at the end of 2006 (which I'm carrying forward at 3% growth per year assuming no growth in store count over year-end 2007 numbers)... and I get a fair value of $36/share... a full 20% difference.

Now consider this... if I change the interest rate used to capitalize leases from 6.3% to 9%... the fair value changes again and moves to $30.


These numbers should all be the same, and they're not. Why?

A few things cross my mind... First that debt burden introduced by capitalized leases is huge. It's probably not as bad as true on balance sheet debt since they could break leases or sublet their space if they went out of business. But ignoring that... If the company really bought the real estate outright, as capitalizing leases suggests, then one benefit that would help offset the big debt number subtracted at the end is the fact that in about 30 years they wouldn't have to pay rent on that real estate anymore. In 2007 rent payments was > 7% of revenue, whereas terminal cash flow margins are in the ballpark of 10%. That means in 25-30 years, the company's margins would shoot up ~ 70%. That goes a long way towards reconciling the two numbers (when I project it out and bump margins by 70% on the 6.3 model in year 26, it actually boosts fair value 16% and covers quite a bit of the 20% gap... but it's an extra level of complexity to the model, and there's still the matter of the impact of interest rate fluctuations in the lease capitalization... and that interest rate variability isn't even really there since leases are already negotiated.... so if they should come out with the same number regardless of which method I use, I'm in favor of the one with the least moving parts and the least complexity.

Winner: Not capitalizing leases for valuation purposes.

3.) Apply a terminal multiple to earnings versus projecting earnings out indefinitely

First off... to clear things up since I'm dazed and my terminology is wonky... when I say "project earnings out indefinitely" I just mean I don't apply a terminal number... I instead continue growing that FCF number out at 3% per year for some large number of years and discount it all back. In theory, I could figure the multiple implied by this process and simply apply it. I get to that in a second.

I see a lot of people do this (apply a terminal multiple at the end of the explicit forecast period). Right now I'm Vitaliy Katsenelson super fan #1 (you'll notice I'm using JOSB as my example, right?) and he models valuations out for an explicit period of time and then applies a multiple. I've seen Tom G do this a lot. It must be good! But... I just don't seem to have an intuitive sense for what multiple should be applied. In "Active Value Investing" Katsenelson gives some qualitative adjustments to absolute P/Es based on growth/dividends to think about and work with, and I like the approach... but I can't apply it, at least not yet. I've looked at 10 year average P/Es and P/FCFFs to try and get an idea of what range to use... FCF is lumpy in general and too low for growing companies to get a useful multiple from history... and the multiple of net income isn't directly applicable to FCFF. Add in the fact that if we're in a range bound market, we've got the headwind of P/E erosion on higher multiples (though we could account for that... I think the avg. is 4% erosion of the growth premium per year according to the man I can't stop referencing in this post)... But MOST IMPORTANTLY... if I'm looking for a beaten up company/industry... or I'm looking at a company/industry that's been overvalued for some time or has had inflated margins for some time... I'm undermining my quest for value by expecting future values to be similar to the past... and if I'm looking to exploit inefficiencies, it doesn't serve me well to model those same inefficiencies in my future expected valuations. (Of course I have to have a catalyst for why those inefficiencies will be wrung out if I think past valuations are too low... but that's a topic for another post.)

So... where I got a fair value of $45/share using a 10X forward multiple at the end of year 5 (see item #1)... if I skip applying the multiple, and simply carry out that 3% growth indefinitely, my fair value jumps to $56. The implication here is that investors would be willing to pay 14X FCFF of this perpetual 3% grower at the end of year 5, which initially seems high. But consider this company at that stage... it's spinning off $75 million a year in cash and has no debt and no growth opportunities in this scenario... while it may not be growing absolute earnings at more than 3% per year, it's yield is 7%. Whether that's applied to share buybacks (ramping up earnings per share growth to as high as 10%) or paid out as a massive dividend, or some combination of the two, I don't think that implied 14X multiple is out of the question (though there's some circular math in here... making conclusions based on the numbers implied by the scenario I'm testing... but I still think this is justified).

The bottom line... I'm more likely to introduce error making up terminal P/Es, so instead I'll project earnings out indefinitely and discount them back and simply do a common sense check on my implied multiples 5 years out or so.

Winner: not making up P/E multiples for terminal conditions.

Bonus Question - Maintenance cash flow versus depreciation

This one I'll just kind of throw out there. In the past I've always looked at maintenance capex and modeled it as increasing until it equals depreciation at some point down the line, assuming that for a growing company with young assets maintenance capex will increase with time. (note: I subtract out all capex in valuation, but I categorize it as maintenance and growth since those have to be modeled differently as growth changes) This may be true, but I think I have been overly pessimistic in this approach and wanted to get some feedback. It also just occurred to me that as a company ages it may continue to utilize fully depreciated assets and thus maintenance capex and depreciation may converge and split the difference somehow. I wondered how other folks here look at these two things, depreciation and maintenance capex, on a young company and model their changes over time as the company matures. It may be pointless, since maintenance capex may rise, but margins may increases as well and it's either all a wash or it's all too difficult to model explicitly... but I like thinking about the components that cause margins to change as a company matures rather than blindly saying... "they stay the same" or "they go up as sales increase and they lever fixed costs" or some blanket statement like that.

So... how do you guys... wait, is anybody still reading? Probably not... but if you are, how do you model depreciation and maintenance capex as a young company matures?

Anyway... with pages of scrawled out thoughts and worksheet after worksheet of models... I think I've settled on my approach (for now). Not sure if this was helpful for anybody, or if I've gotten so lost in the numbers that I've posted something absolutely absurd that my common sense filter missed... I'm a bit dazed, but I wanted to share and get feedback from anybody who's interested.

Thanks for listening.