How to calculate Return on Equity?

[Snoopy]

I have been trying to calculate ROE. I am getting confused with various balance sheet items in annual reports. so ROE is…

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ROE
Return on Equity. An indicator of corporate profitability, widely used by investors as a measure of how a company is using its money. There are two ways of calculating ROE: the traditional formula and the DuPont formula. The traditional approach divides the company's net profit after taxes for the past 12 months by stockholders' equity (adjusted for stock splits). But this fails to account for the effect of borrowed funds, which can magnify the returns posted by even a poorly managed company. An alternative approach, developed by the DuPont Corporation, links return on investment (ROI) to financial leverage (use of debt).

Traditional Formula:
ROE = Net Profit After Taxes ÷ Stockholders' Equity

DuPont Formula:
ROE = ROI x Equity Multiplier
ROE = (Net Profit After Taxes ÷ Total Assets) x (Total Assets ÷ Stockholders' Equity)
For example, using the traditional formula, a company with $18,000 in net profit after taxes and $45,000 in stockholders' equity would have an ROE of 40%. The DuPont formula takes the analysis one step further by factoring in the contribution of borrowed funds. Using the previous example, if the company has total assets of $100,000, then $55,000 of the company's capital is supplied by creditors and its equity multiplier is 2.22.
ROE = ($18,000 ÷ $100,000) x ($100,000 ÷ $45,000)
ROE = 18% x 2.22
ROE = 40%
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ok. so lets take a real life example. We look at Telecom New Zealand 2007 annual report.
http://annualreport07.telecom.co.nz/...eport-2007.pdf

I get these figures from pages 31 and 32.

Net earnings /(loss) attributable to shareholders =3024
Total assets =8276
Total equity attributable to equity holders of the company=3598

ROE=(3024/8276) x (8276/3598) =0.840%

Is this calculation correct?

Good question Jackie. These buzzword terms are bandied about on this forum often enough and IMO there probably is not enough discussion on demystifying them. Also thanks for your references which makes it clear where you are pulling your data from so it is easy to follow.

On my paper edition of the Telecom 2007 Annual Report 'The net earnings attributable to shareholders' appears on page 29 as $3,024m. Total equity attributable to equity holders of the company is $3,598m.

Using the traditional definition of:

ROE= Net Profit After Taxes ÷ Stockholders' Equity

I get $3,024m/$3,598m = 0.84 which is 84% (when expressed in percentage terms)

Using the Dupont definition, we also work in the 'total assets' as found on page 31 of the annual report ($8,276m)

ROE= ROI x Equity Multiplier
= (Net Profit After Taxes ÷ Total Assets) x (Total Assets ÷ Stockholders' Equity)
= ($3,024/$8,276)x($8,276m/$3,598m)
= (0.3654)x(2.300)
= 0.84 = 84% when expressed in percentage terms

Both formulae give the same answer (which is no surprise), which is the same as your answer Jackie. Well done, you have nailed it!

So why bother with the two different formulae if they both give the same answer?

The Dupont formula makes it clear that the 'Return on Invested Capital' (ROI) is 0.3654, or 36.5%. That is less than the 'Return on Shareholders Equity' (ROE) finally calculated out at 84%. And that shows that a large reason the ROE is so high is because of Telecom's borrowings. The Dupont formula does not give a different answer. It just gives you a better feel for why the answer is the way it is.

Finally, any formula is only as good as the numbers you put into it. That $3,024m profit is made up from the profit from normal operations *plus* the profit made by the 'Yellow Pages' group sale. Once the Yellow pages group is sold it is sold, Telecom cannot sell it again. That is why Halebop has used the 'Adjusted Net Earnings' on page 20 of the annual report of $955m in his calculations, and why he gets a different answer to you. Usually it is the ongoing operational profitability (and by implication 'Ongoing operational ROE') we are interested in.

SNOOPY

[jke_brown]

thanks Halebop for your great input while eating squid and snoopy for clearing up the diffrence between "Return on Shareholders Equity" and "Return on Invested Capital"

I worked out ROE for last 7 years.

2001	2002	2003	2004	2005	2006	2007	Year
							
643	191	704	775	806	2656	3024	Net profit after taxes
614	670	709	775	806	820	955	Adjusted net earnings
5403	5537	5199	5360	5605	5555	5582	Operating Revenue
7421	7500	7755	8246	8972	6203	8276	Total assets
2003	1328	1776	2617	2612	1062	3604	Total Equity
							
30.65%	50.45%	39.92%	29.61%	30.86%	77.21%	26.50%	ROE (du point)
							
32.10%	14.38%	39.64%	29.61%	30.86%	250.09%	83.91%	ROE

so telecom nz been doing well in terms of ROE over the years? Surely better than having the money in the bank looking at ROE?

Other thing I am not sure about is the dividends. How do I go about including dividends in the formula?

[Snoopy]

I worked out ROE for last 7 years.

2001	2002	2003	2004	2005	2006	2007	Year
							
643	191	704	775	806	2656	3024	Net profit after taxes
614	670	709	775	806	820	955	Adjusted net earnings
5403	5537	5199	5360	5605	5555	5582	Operating Revenue
7421	7500	7755	8246	8972	6203	8276	Total assets
2003	1328	1776	2617	2612	1062	3604	Total Equity
							
30.65%	50.45%	39.92%	29.61%	30.86%	77.21%	26.50%	ROE (du point)
							
32.10%	14.38%	39.64%	29.61%	30.86%	250.09%	83.91%	ROE

So telecom nz been doing well in terms of ROE over the years? Surely better than having the money in the bank looking at ROE?

There are a couple of things you need to bear in mind Jackie, that makes the return, from an investor perspective, not as attractive as it might casually appear.

If you buy shares in Telecom you become a shareholder and you get your slice of shareholders equity - that's true. However you cannot buy shareholders equity on its own. You also have to buy your fair share of shareholder debt which is included in the purchase price of the Telecom shares you buy. You have to buy the shareholders equity AND debt, which together add up to the sum of the company assets, as part of one purchase package.

So? you say. That only means I get the Du Pont return instead of the 'classic' ROE return. The Du Pont return may be less than the classic (84% in this case) return, but it is still much better than the bank return, so buying in is still a good deal - right?

I am sorry to inform you that most of those financial types who graze on the sharemarket for a living have figured this out before you. So let's say your Dupont ROE return for Telecom is 26.5%. Let's say our sharemarket punter has their money in the bank at 9%. On paper it looks like an easy swap. Take your money invested at 9% out of the bank. Put your money into Telecom and voilà your income has more than doubled!

In practice you can't more than double your return by doing this. That's because 'the market' ensures that an arbitrage adjustment on the Telecom purchase price exists. Let's say you want to buy $10,000 worth of Telecom. The market will ensure that instead of paying $10,000 for this 'investment package' you will actually pay around:

$10,000 x (26.5%/9%) = $29,444.

Thus even though you are getting 26.5%, you have to pay more than the nominal coupon rate (called 'the market price') to get it. Thus your $10,000 will buy far less shares than you thought reducing your investment yield to 9%, the same as you were getting from the bank.

OK I am simplifying things a bit here. The market does price in risk. An investment in Telecom is seen as riskier than a term deposit. So that means you will get slightly more by way of a Telecom dividend than from interest by investing in the bank. But the point I am making is that the amount 'extra' that you get is actually quite small. You won't get a return of 26% just by buying Telecom shares on market!

Other thing I am not sure about is the dividends. How do I go about including dividends in the formula?

Ah now there is an important question, and there is no one answer.

There is a school of thought that dividends are a bad thing. Why? Because any money paid out in dividends *reduces* shareholder equity. The lower the shareholder equity, for a given ROE, the lower your return is likely to be. That's because:

Total Return= (Shareholder Equity)x(ROE)

And, for a constant ROE, reducing shareholder equity will reduce your return in the future- not a good thing

Either the company will keep the money they earn OR distribute it to you as dividends. But they can't use the same money to pay you a dividend AND build up shareholder equity. The company management has to *choose* what they will do.

If a company can earn a superior return on the equity they retain from normal earnings, than you can get by investing that same money, then (in theory) you do not want them to pay a dividend. But if they can't do that, then paying you the money as a dividend is the best use of the cash they are generating.

SNOOPY

[jke_brown]

Snoopy I guess the next thing to work out is the intrinsic value.
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from http://en.wikipedia.org/wiki/Benjamin_Graham_formula

The Graham formula proposes to calculate a company’s intrinsic value V* as:

V: Intrinsic Value
EPS: the company’s last 12-month earnings per share
8.5: the constant represents the appropriate P-E ratio for a no-growth company as proposed by Graham
g: the company’s long-term (five years) earnings growth estimate
4.4: the average yield of high-grade corporate bonds in 1962, when this model was introduced
Y: the current yield on AAA corporate bonds

To apply this approach to a buy-sell decision, each company’s relative Graham value (RGV) can be determined by dividing the stock’s intrinsic value V* by its current price P:

An RGV of less than one indicates an overvalued stock and should not be bought, while an RGV of greater than one indicates an undervalued stock and should be bought.
>>>>>>

so again with telecom nz

g: the company’s long-term (five years) earnings growth estimate= 2007 ernings -2003 ernings / 5=8%

from http://www.nzx.com/market/debt_summaries
4.4: the average yield of high-grade corporate bonds in 2007= 8.61
Y: the current yield on AAA corporate bonds= 8.56

so then we have...

2001	2002	2003	2004	2005	2006	2007		
643	-188	704	775	806	2656	3024	Net profit after taxes	
614	670	709	775	806	820	955	Adjusted net earnings	
5403	5537	5199	5360	5605	5555	5582	Operating Revenue	
7421	7500	7755	8246	8972	6203	8276	Total assets	
2003	1328	1776	2617	2612	1062	3604	Total Equity	
								
30.65	50.45	39.92	29.61	30.86	77.21	26.50	ROE (du point)	
32.10	-14.16	39.64	29.61	30.86	250.09	83.91	ROE	
								
0.364	-0.101	0.376	0.392	0.47	0.22	1.58	EPS	
0.08	0.08	0.08	0.08	0.08	0.08	0.08	g	
8.56	8.56	8.56	8.56	8.56	8.56	8.56	y	
8.61	8.61	8.61	8.61	8.61	8.61	8.61	4.4	
								
3.17	-0.88	3.28	3.41	4.09	1.92	13.76	V	
4.17	4.66	4.93	5.67	5.92	4.35	4.47	Share Price (01 sep)	
								
0.760	-0.189	0.664	0.602	0.692	0.441	3.079	RGV

I am not sure how accurate this method is, but I guess it gives a relative valuation that one can compare against the share price and ROE.

What other methods available to do similar valuation?

[Snoopy]

What other methods available to do similar valuation?

Hold on! I wouldn't give up on ROE just yet.

I stand by everything I said about 'the market' reducing your return to well below ROE from an investor perspective by bidding up the price of shares to more than they are 'nominally worth', thus reducing your return for any new shares you buy 'on market'.

But there is still one thing you can do with ROE to 'beat the market'. You have to look for a company with high ROE that does not pay all of its income out as dividends. Why? Because if they can.

1/ Retain some shareholder equity AND
2/ invest that new equity at an historic high rate

(NOTE: these are two pretty big 'ifs')

then the effect of that new bit of equity is often *not* arbitraged away by Mr Market, if you consider a long term time horizon. This is exactly Warren Buffett's strategy as espoused by Mary Buffett.

Effectively Warren considers buying a company on his ten year time horizon, as buying a (roughly) fixed rate of return investment (if you select your company carefully) with what Warren terms an 'expanding coupon' caused by the 'new retained earnings' growing the incrementally expanding business at well above treasury bond rates.

That means that 'high ROE' is not a sufficient criterion for the likes of Warren to make an investment. Warren also requires the company he is considering to be able to retain some of that ROE and invest it wisely. The general market will very likely steer clear of bidding up these investments because in a classical sense this can involve buying a share with a very high PE ratio, which with a one or two year time horizon looks hard to justify. To the likes of Warren however, such an investment can make perfect sense.

SNOOPY

[jke_brown]

1/ Retain some shareholder equity AND
2/ invest that new equity at an historic high rate

SNOOPY

good point. lets look at retained earnings. so how do you know if the company is using that retained earnings to make higher return at a historic high rate?

Lets look at dividend paid by telecom nz from 2002 to 2007. during that period total EPS was $3.038 (from my table above)

From that $1.975 was paid in dividend. (from http://www.telecom.co.nz/content/0,8...,00.html?nv=sd)

So telecom nz retained $1.063. During that period share price moved from $4.66 to $4.47.
gain of -0.19 dollars

so assuming all of the retained equity used increase earnings.

return percentage= (-0.19/1.063)*100= -17.87%

But looking at dividend payments and earning per share over the same period.

So dividend return = dividend/eps = 1.975/3.038= 65%

This value seems very high. I am sure I did the calculation correct. So Telecom nz has outstanding dividend return over the same period but negative growth from retained equity.

with a one or two year time horizon looks hard to justifySNOOPY

this make sense as investors who were not in for the long term didn’t get the high dividend return.

Snoopy, how can one relate ROE to the share price ('nominally worth') mathematically?

As you say market will “bidding up the price of shares to more than they are 'nominally worth', thus reducing your return for any new shares you buy 'on market'

In 2007.
Dollar equity in telecom nz is creating 26c in return.
Dollar equity invested in ASB bank term deposit is crating 8.5c in return.

Dollar invested in the bank has a fixed value, where as dollar equity in telecom nz has a “variable value” due to market dynamics.

My previous post attempted to calculate the fair value, is that accurate?

Most of Warrens concepts like competitive advantage etc are easy to apply but in terms of calculating the nominal value I haven’t found an appropriate equation/method by him.

[Snoopy]

good point. lets look at retained earnings. so how do you know if the company is using that retained earnings to make higher return at a historic high rate?

Lets look at dividend paid by telecom nz from 2002 to 2007. during that period total EPS was $3.038 (from my table above)

From that $1.975 was paid in dividend. (from http://www.telecom.co.nz/content/0,8...,00.html?nv=sd)

So telecom nz retained $1.063. During that period share price moved from $4.66 to $4.47.
gain of -0.19 dollars

so assuming all of the retained equity used increase earnings.

return percentage= (-0.19/1.063)*100= -17.87%

We are talking cross purposes here Jackie. What you have calculated out is 'earnings' from an 'investor perspective'. This is largely uncorrelated with retained earnings from a 'company perspective', which is what is important for company performance.

But looking at dividend payments and earning per share over the same period.

Yes that is what you should be doing. We are back on the same wavelength.

So dividend return = dividend/eps = 1.975/3.038= 65%

This value seems very high. I am sure I did the calculation correct.

I don't think you have included the recent capital return per share. That's because it wasn't on the dividend table because a capital return is not a dividend!
If you include that, the percentage profit paid out will rise to even higher than 65%. But I'm not sure why you consider that high. Telecom have a stated policy of paying out some 90% of earnings as dividends.

BTW....

Retained Earnings = Earnings Per Share - Dividends Per Share

So Telecom nz has outstanding dividend return over the same period

Yes

but negative growth from retained equity.

You can't say that because you haven't worked out what the retained equity was over five years yet. The fact that the share price declined over five years is not relevant to the calculation.

Snoopy, how can one relate ROE to the share price ('nominally worth') mathematically?

Most of Warrens concepts like competitive advantage etc are easy to apply but in terms of calculating the nominal value I haven’t found an appropriate equation/method by him.

You probably need to get hold of one of the Mary Buffett books on Warren's methods. I think the latest is "The New Buffettology."

Suffice to say, briefly, that if a company pays out all of their earnings as dividends then ROE and share price are virtually unrelated. But if the company saves all of their earnings and reinvests them back into the company then you will find quite a strong correleation between ROE and share price. Provided that is the reinvestment program is successful!

My previous post attempted to calculate the fair value, is that accurate?

You mean the Ben Graham formula? Yes it is accurate up to a point, depending on how well you agree with the somewhat arbitrary way Ben calculates what the PE 'should be'. I think it is fair to say that Telecom is worth at least what that Ben Graham formula tells you it is worth.

SNOOPY

[Snoopy]

Snoopy I guess the next thing to work out is the intrinsic value.

The Graham formula proposes to calculate a company’s intrinsic value V* as:
<snip>

To apply this approach to a buy-sell decision, each company’s relative Graham value (RGV) can be determined by dividing the stock’s intrinsic value V* by its current price P:

An RGV of less than one indicates an overvalued stock and should not be bought, while an RGV of greater than one indicates an undervalued stock and should be bought.

I am not sure how accurate this method is, but I guess it gives a relative valuation that one can compare against the share price and ROE.

I want to say something on the Ben Graham formula , even though it is tangential to the topic of this thread, before I move on.

If you are looking for some share valuation formula where you can stick in some values, crank the handle and get out an 'accurate value' at the other end then I think you will end up disappointed. Any formula based on historical inputs will only give a meaningful answer if those historical numbers you are feeding into it have meaning today and in the future.

In the case of Telecom the industry rules have changed (thanks to the government unbundling announcements). We now have the retail/wholesale 'split' to deal with. Furthermore the way Telecom operates their business model units has changed as well. Telecom have 'repackaged' their businesses into customer focussed 'Consumer' and 'Business' units. The old 'technology packaged' mobile, local service, calling and Broadband/Internet business units are no more (for reporting purposes). Off hand I cannot think of a more radical change for any company I have been a shareholder of, over such a short period of time. Whether the historic Telecom results of even five years ago have any meaning in today's terms is debatable.

Moving to specifics the 'V' value of over 13 you have calculated for FY2007 derives from using an 'eps' figure of $1.58 which includes the one off profit from the Yellow Pages sale. This result while 'accurate' (which means you made no obvious mistakes in the calculation) is also meaningless. That's because the Yellow pages division can only be sold once and the effect of that sale has already been reflected in the share price. (You should have used the adjusted net earnings of $955m instead.) What you have calculated Jackie, is that Telecom is an absolute steal (having an RGV of 3) provided they can sell the Yellow Pages Group again this financial year. A true statement, but one that is of no use to us as investors looking forwards.

Turning to the mechanics of Ben Grahams formula, the core of what Ben is doing is taking 'earnings per share', multplying that number by a predetermined 'Price Earnings Ratio' of 10.1 (calculated by using a typical PE ratio for zero growth, incrementally increased to allow for what real growth the company has demonstrated in the past).

Earnings x Price/Earnings = Price

That is where your valuation (V) share price comes from. Personally I think this formula will underestimate the value of a utility share quite seriously. I think that when earnings from Telecom stabalise (whenever that might be) it should trade in a PE of around 15, given the very strong market position the company has. Grahams formula does not allow for different PEs across different industries.

The formula then tweaks the above result by recognising that valuations are also affected by interest rates. Thus the PE result is 'scaled' by a factor to take this into account by dividing the base timeframe 'long term interest rates' by today's timeframe 'long term interest rates' of comparable quality. If todays long term interest rates are substantially higher than the base case long term interest rates then the value of the PE, and consequently the shares themselves, is proportionately reduced.

The problem we face by using this formula in New Zealand is that it was set up by Graham in the US, for US markets. I notice Jackie that you have replaced the "US base case rate" of 4.4&#37; by

"the average yield of high-grade corporate bonds in 2007= 8.61%".

I do not believe that is a valid substitution, because it is not obviously an historical base case average, like the 4.4 was. However you have divided into that 8.61%

"the current yield on AAA corporate bonds"

That is effectively exactly the same thing. Were you not suspicious when the numbers were virtually identical? Any number divided by itself is one.

So really for 'V' in your spreadsheet you have gone back to Ben's original formula

Price = Earnings x Price/Earnings

or as Ben writes it

Price = Earnings x (8.5+2g)

where g=0.08 (8%)

On the subject of adjusted earnings for Telecom, you may wish to cross reference the work I have already done on the subject.


http://forum.sharechat.co.nz/showthread.php?t=192


SNOOPY

[patsy]

If you buy shares in Telecom you become a shareholder and you get your slice of shareholders equity - that's true. However you cannot buy shareholders equity on its own. You also have to buy your fair share of shareholder debt which is included in the purchase price of the Telecom shares you buy. You have to buy the shareholders equity AND debt, which together add up to the sum of the company assets, as part of one purchase package.

SNOOPY

Snoopy - If a competitor took over Telecom as a company, your assertion is correct. But if you buy its equity, or a share of its equity, then you are not buying its respective debt. There is a distinction between the "value of the firm" versus the "value of equity" - the difference between both being the "value of debt". When you apply your Buffet spreadsheets to a company to reach a suggested share price, you are purely valuing the equity. ROE is the indicator that allows to do that. ROE does not lead you by itself to reach to the value of the firm.

[Snoopy]

When you apply your Buffet spreadsheets to a company to reach a suggested share price, you are purely valuing the equity. ROE is the indicator that allows to do that. ROE does not lead you by itself to reach to the value of the firm.

Quite correct

Snoopy wrote:
If you buy shares in Telecom you become a shareholder and you get your slice of shareholders equity - that's true. However you cannot buy shareholders equity on its own. You also have to buy your fair share of shareholder debt which is included in the purchase price of the Telecom shares you buy. You have to buy the shareholders equity AND debt, which together add up to the sum of the company assets, as part of one purchase package.


Snoopy - If a competitor took over Telecom as a company, your assertion is correct. But if you buy its equity, or a share of its equity, then you are not buying its respective debt. There is a distinction between the "value of the firm" versus the "value of equity" - the difference between both being the "value of debt".

I may have been a bit loose with my words here.

Think of it this way. A company has no debt and you buy say 10% of its shares on the sharemarket. That means you now own 10% of the shareholders equity as well and none of the debt (because there is no debt). I trust we agree so far.

Now lets say there is a company with $100m in assets which was initally funded through shareholders equity of $50m and a bank loan of $50m. Once gain you buy 10% of the shares in this company 'on the market'. What do you consider you have actually bought?

Well, you have 10% of the company with shareholders equity of $50m. So you now control

0.10 x $50m = $5m

of shareholders equity. I hope we still agree up to this point.

Whatever you do as a shareholder does not affect the bank loan. The bank is still owed $50m no matter who the shareholders are. I think this is the point you were making Patsy(?)

However, who do you think is responsible for ultimately paying back this loan? It is the shareholders isn't it? No matter who the shareholders are at any particular time? What I am trying to say is this.

When you buy shares in a company you are buying a 'slice of a pie'. That pie contains two ingredients: shareholders equity and an obligation to pay back your owners share of the bank loan. You are correct Patsy in saying that when you buy shares you do not actually buy a share of the bank loan. The bank continues to own that. But you *do* buy into the obligation to pay off that loan, in proportion to your shareholding. If this wasn't true then I can present you with an excellent money making proposition, courtesy of ten of your friends.

Let's say you own a nice house valued at $1m in which you have $100k in equity and funding from a $900k bank loan. You decide to float it on the sharemarket as 'Patsy House Ltd.' You find 10 keen friend shareholders all of who can see the value of the house and all agree to put up $100k each for a 10% share. You take the $1m in payment for your house from the ten new shareholders, and you are out of there. You buy a yacht with the proceeds and set sail for your new home in Monaco. Now the bank decides to call the loan in. There are now ten owners on the title deed (the new shareholder owners). Who do you think the bank will ask to pay the loan money back? Do you expect the bank to set sail and come after you? Do you think that because the 10 shareholders who bought your house only put up equity themselves they now 'own the house outright' and the bank will just write off the $900k loan you put in place when you set up 'Patsy House Ltd.'?

SNOOPY