The first step in the “Greenwald” approach is to remember that there are two ways to go about determining whether a stock is trading at an attractive price. We tend to, by default, think that we have to figure out what price the stock should be (intrinsic value) and compare that to what the stock is currently trading at. But we can also estimate what return we think we’ll get if we purchase at today’s price. It’s sort of net present value (NPV) versus internal rate of return (IRR).
I see Greenwald’s technique as a hybrid between the two, but mostly IRR. We are estimating rate of return, but as you will see, part of that computation requires an NPV calculation. The Good News about this approach though, is that small errors in your best guesses at your inputs only cause small errors in your estimate of expected return. As a bonus, the valuation equation is transparent. You can see how much each part contributes to the whole, so if you’re a little unsure about one of the terms, you can mentally say “if this terms ends up being 0% instead of what I think it is, how does that
change my expected return?”
I’ll give you the equation soon. Then we’ll talk about the terms. First, let me just say that this is not meant to be a mathematically airtight equation for exactly what return you’ll get. It’s more putting a rough equation around common sense – storyboarding – in order to see whether the price is attractive.
4 factors will contribute to what return we get from purchasing a stock:

(1) the % of earnings the company gives us via dividends
(2) the % of earnings the company “gives” us via buybacks
(3) the % earnings grow from the company reinvesting some earnings
(4) the % earnings grow just due to increases in demand
The first two terms, Greenwald refers to as “cash return”. The last two terms are growth, with one being active (think, opening new stores or developing new product lines) and the other being organic (think, same stores sales growth or selling more of an existing product just due to increases in demand).
Let’s begin to form the equation for our expected return:
As we develop the equation, we’ll add some meat on these bones. And we might as well use real numbers for the analysis, so let’s examine a stock I was recently asked to take a look at. Today (November 13, 2013) IBM is trading at $182 and a forward P/E of 10. It was 20% higher at $215 earlier this year. Is it a bargain?
How would this equation apply to Google when it IPO?
I think there is zero value from factors 1 and 2. About factor 4, I dont know how much the overall demand has increased. But maybe 10% a year?
Google has compounded about 30% a year since its IPO. Which suggests that 20% value has been generated from factor 3 (and 10% from factor 4). But this calculation doesnt work, because Google IPO around 50 P/E. So the IRR was 2% (1/50). Even if all the earnings were reinvested, it wouldn’t be able to generate 20% return.
Can you explain?
Michael – what a great question.
First let me say that I’ve never heard Greenwald talk about using this with IPO’s. In fact the only thing I can remember him saying re: IPOs is something like “The insiders KNOW what the business is worth since they know the future cash flows (or presumably can estimate them better than you can). And now on the IPO date, they’re willing to let you in on the action for a price. Who do you think is getting the better deal?!? Ha ha ha…”
However, if you put a gun to my head and told me I HAD to prove that the equation worked with Google, I might try to weasel my way out with the following logic:
#1: This site shows how # of internet users has grown over time. In 2004 (Google’s IPO) it was about 900M. Today (12 yrs later) it’s about 3500M. That’s about a 12% p.a. growth rate. If you’d magically called that number right back then, and assumed Google maintained the same % of market share, you’re already starting with 12% organic growth.
#2: Now say you assumed Google had a cost of capital of about 10% and a return on capital of 30%. With the P/E of 50 that contributes 1/50 x 30 / 10 = 6% of active growth.
#3: Greenwald says not to do the math to get what return you expect to actually make. Do the math to answer a YES/NO question: is it cheap? Well, 12% + 6% = 18% which is above the 1315% hurdle for “cheap”, so it could easily have been a buy depending upon your margin of safety.
Does that make sense or am I grabbing for straws. 🙂
yes, your calculation makes total sense. its exactly what I did in too.
but as i mentioned, google in fact did about 30% return annualized.
the calculation predicted 18%. why does the equation not account for the extra 12%? (not to mention the p/e has even contracted)
I just think that the calculation (a) is a rough approximation (b) assumes an infinite time (c) doesn’t account for how differently the market may value something at a future date vs. what it’s worth and (d) requires a correct estimation of cost of capital.
The only way I know of to get an EXACT equation for total return requires you to include the growth in some metric and the change in the multiple on that metric.
Return = (1 + EPSgrowth) x (1 + P/E change) – 1
I don’t have Google’s #’s dating back to the IPO – but let me just do what’s in front of me now. Lululemon (LULU):
Price on 12/31/2010 = $34.21
Price on 12/31/2015 = $52.47
Return = (52.47 / 34.21) ^(1/5) – 1 = 8.9% p.a.
EPS on 12/31/2010 = $0.79
EPS on 12/31/2015 = $1.86
EPS growth = (1.86 / 0.79) ^(1/5) – 1 = 18.7% p.a.
P/E on 12/31/2010 = 34.21 / 0.79 = 43.3x
P/E on 12/31/2015 = 52.47 / 1.86 = 28.2x
P/E change = (28.2 / 43.3)^(1/5) – 1 = 8.2% p.a.
So the 8.9% price return we saw above comes from (1+.187) x (1 – .082) 1 = 8.9%
You could use an equation like this to estimate your expected return instead of the Greenwald equation, but you have to make a guess at future P/E in addition to EPS growth. I’ve often used this as a check on the Greenwald equation, assuming for example that the P/E will return to its 5 or 10year historical median.
Hi,
You said “#2: Now say you assumed Google had a cost of capital of about 10% and a return on capital of 30%. With the P/E of 50 that contributes 1/50 x 30 / 10 = 6% of active growth.”
My question 1 is, how can you estimate out Google’s future return on capital?
A) If you just use the current or historical ROC, how would you know how much of the earnings growth is from their actual reinvesment and how much is just from the free organic growth? For example, if their current ROC (earnings/capital) is 30%, that earnings number includes all the free organic growth. So it isn’t purely earnings from invested capital.
2) You could also take retained earnings from 2014 compared to the earnings growth in 2016. So something like (2015 earnings minus 2014 earnings) / retained earnings from 2014. But again, the earnings growth would also include organic growth that Google got for free.
Also another question 2 I have is, if you use Greenwald’s IRR equation:
E[R] = DividendYield + BuybackYield + ActiveGrowth + OrganicGrowth
This does not include any R&D or capital invested in Google’s past. Maybe they invested money in 2014 that takes 5 years before it will see a return. The “ActiveGrowth” part of the equation takes into account current reinvestment, but does not consider past investment that may add value. Has Greenwald addressed this issue, or do you have any thoughts on how to address it?
I very much understand as I ran into the same problem myself since I often rely upon historical growth rates from which to estimate the future. You can’t tell which parts of growth came from where.
We’re way off the Greenwald reservation but here’s how I handle it.
Let’s say you’re looking at a company – it’s at a P/E of 18 and you think its cost of equity is ~10%.
First, examine EPS and dividends over some time period (say 5 or 10 yrs). Add up all EPS “earned” but not paid out as a dividend. These are retained earnings. Compute the change in EPS over that time period divided by those retained earnings. You now have Return on Retained Earnings. Let’s say it works out to 20%. That’s the combined result of active growth, passive growth, and net buybacks.
Next look at what their dividend policy has been recently. Let’s say 30% of EPS is generally paid out as a dividend (the Dividend Payout Ratio).
I say the Greenwald formula can be roughly simplified to:
Expected Return = E/P x (DPR + (1DPR) x RORE / COE)
or,
Expected Return = 1/18 x (0.30 + 0.70 x .20 / .10)
It’s a little sloppy since it ignores debt, but maybe that’s fine if you’re investing in generally low debt companies. Otherwise you need to do a more complete Return on Retained Capital and use Cost of Capital instead of Cost of Equity. Also it’s purely extrapolating RORE from the past whereas Greenwald says you want to use numbers based on new (marginal) capital they’re deploying today along with its associated risk (who knows where you’d get that unless you could sit down with management).
Now there’s one thing not accounted for. Like you mentioned, maybe the company made some investments some time long in the past that they’re still reaping benefits from today. For that reason I compute RORE a little differently than I described above. I add the starting book value per share in the denominator to all retained EPS. If you divide current EPS by starting book value plus retained EPS, you (theoretically) get an RORE than includes all equity invested and retained prior to the year where you started adding up EPS’s and subtracting dividends. I can point you to a book I got this from if you’re interested.
Does that make sense? Let me know what you think.
Hello!
Thanks for your response again!
The first part of your answer makes sense. I think you’re right to basically merge the passive growth in the active growth (since you can’t determine what was passive and what was active in the past). On a side note, my guess is Greenwald uses the expected PE for the next 12 months from the present moment? Or does he use the trailing 12 month PE?
About the 2nd part of your answer, I see how you are trying to calculate the RORE. But I think that the equation still breaks down in some cases. Take for example an extreme case:
Imagine today is December 31st, 2014. Apple has invested 100% of retained earnings into iCar from 20102014 (5 years) with 0% dividends. 2014 EPS was $10. The iCar is set to launch in January 1st, 2016, and is expected to generate $20 a share in EPS with the stock trading at $100.
Assume Apple 2015 EPS will s has a 20% RORE,
Using the IRR equation at the end of 2014, Expected Return = $10/$100 x (1 x .20 / .10)
The 5 years of investment in iCar doesn’t show up into the equation, and the $20 EPS from iCar also doesn’t show up into the equation. So in this situation, the IRR would dramatically undervalue Apple. Do you know if Greenwald has talked about this problem?
Also, does Greenwald use the reported P/E for the IRR calculation?
Or does he use an adjusted owner’s earnings?
If he were to use the owner’s earnings, all the investment into iCar would not be recorded as an expense, and the EPS would be much higher.