How to calculate Return on Equity?

[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

[patsy]

Snoopy – In your example of purchasing shares in a leveraged company ($50M equity, $50M debt), 10% of equity means, as you say, “owning” $5M of the company’s equity. In other words, you “own” $5M worth of assets. So far, so good.

However, owning $5M of assets or equity does not imply that you (as a shareholder) are responsible for paying the debt. Neither does the bank have any recourse on you as a shareholder for unpaid debt. The only entity that is responsible for debt repayment is “the firm” – that’s a principle of limited liability. The only big caveat is when shareholders have provided a personal guarantee to a lender; this is common in small entrepreneurial companies. With this particular exception, you as a shareholder have no responsibility to repay the debt.

However, company debt impacts a shareholder in various ways:

1) Company earnings are reduced by interest and principal repayments to lenders (cashflows to lenders) thus reducing dividends (that is, cashflows to shareholders). This is so because lenders rank at a higher priority than shareholders
2) ROE is a strict function of the “equity beta” (the company risk premium), which in turn is dependent on the level of debt. The more debt a firm takes on, the higher the beta will be of the equity in that business. Debt creates a fixed cost, interest expenses, that increases exposure to market risk.
3) Point (2) does NOT mean that you as a shareholder are taking responsibility for the debt of the company. Rather, that the return you should expect as a shareholder should be higher because you are running a higher risk than a lender (i.e., the lender has a charge over the company’s assets, but shareholders don’t)

There is a distinction between “valuing the equity” of the firm using ROE (as I’ve seen you do in Sharechat many times with your Buffet spreadsheets) and “valuing the firm”. You could “value the firm” using a very similar procedure to that of Buffet, with the exception that instead of using ROE as a discount rate, you would use the WACC. Of course, the cashflows are also different – in the case of “valuing equity” (like you do), you can use as cashflows: net income x payout ratio (discounted at ROE). In the case of “valuing the firm”, you use as cashflows: EBIT x (1-tax rate) – Depreciation – changes in working capital, all discounted at WACC). As you would expect, the difference between these two calculations (Value of Firm minus Value of Equity) would give you the Value of Debt.

What I am trying to say here is that the purchase of shares does not imply the transfer of the obligations to repay debt. The only implication of debt on the share price you pay is given by the fact that a company with debt is riskier than a company without it, and that risk is reflected in the ROE through beta, which in turn impacts the share price.

The “share of the pie” (as you say) you are buying when purchasing shares is a share of the “equity pie”. As you correctly pointed out in your example, a 10% share of the “equity pie” is NOT 10% of the “company pie” – it is only 5% of the “company pie” in a 50:50 leveraged company. The other 45% percent in “owned” by other shareholders, and the other 50% is “owned” by lenders. The rights and responsibilities that you have as owner of 5% of the company pie do NOT include the responsibility for meeting debt obligations. The firm holds that responsibility. If it cannot pay debt, then it may raise more equity (thus diluting you).

Your example of listing a house is flawed (assuming I understand what you mean correctly) because it is not the asset that is listed (that is, $1M) – it is the equity that is listed ($100k). No one will pay $1M because that’s not what it is being offered.

What it is being offered is NOT the mortgaged portion but the 10% equity in the house. If after listing such 10%, the rental income doesn’t cover interest and principal expenses, the lender will reposses the house, will sell it to recover $900k and the shareholders will get whatever surplus is achieved through a mortagee sale over $900k.

At no stage the shareholders are LEGALLY OBLIGED to put their hands in their pockets to fund the shortfall of principal and interest payments.

Also, in your example, please let’s not confuse the notion of limited liability of company shareholders, by which shareholders are not liable for the company’s debt with the notion of the owner of a house who has personally guaranteed the repayment of debt.

I suspect that the use of different terminology makes us appear to disagree. However, the only thing for certain is that by using net earnings or dividends discounted at ROE, then you get the value of the equity (from which you can derive a fair share price). But you are definitely NOT getting the value of the firm, or the value of ALL assets.

[Snoopy]

Snoopy – In your example of purchasing shares in a leveraged company ($50M equity, $50M debt), 10% of equity means, as you say, “owning” $5M of the company’s equity. In other words, you “own” $5M worth of assets. So far, so good.

However, owning $5M of assets or equity does not imply that you (as a shareholder) are responsible for paying the debt. Neither does the bank have any recourse on you as a shareholder for unpaid debt. The only entity that is responsible for debt repayment is “the firm” – that is a principle of limited liability. The only big caveat is when shareholders have provided a personal guarantee to a lender; this is common in small entrepreneurial companies. With this particular exception, you as a shareholder have no responsibility to repay the debt.

I agree with what you say above. However, as an investor I am more interested in a company that is a going concern. Not a company that is on the cusp of being 'wound up' by a bank.

Collectively as shareholders (and leaving a side the case of the shareholder with a personal guarantee to the lender) in a company we have no *obligation* to put in further capital or indeed pay the bank back any of its capital or interest on that capital. This is as you say in accordance with the principle of limited liability. However, consider what would happen if we shareholders of a business that was a 'good going concern' *chose* to make a collective decision not to pay our interest bill for a month.

We as shareholders would certainly be within our *legal rights* not to pay the bank their interest. But the bank would be very unhappy if we did that. So unhappy in fact that they would probably have caveats that entitled then to seize control of the company (which includes our precious shareholders equity) and force the company to pay them . So although we don't have to pay the bank, by law, it is *mutually beneficial* for both parties for we shareholders to do so. After all, we want to have an ongoing relatiuonship with our bank - do we not? And the bank do not want to step in and have the hassle of running what was our business just so they can get their own money back.

However, company debt impacts a shareholder in various ways:

1) Company earnings are reduced by interest and principal repayments to lenders (cashflows to lenders) thus reducing dividends (that is, cashflows to shareholders). This is so because lenders rank at a higher priority than shareholders

That is one way of looking at things. But companies do not go into debt for the express purpose of incurring costs and reducing dividends to shareholders. Rather they borrow to make a bigger better company that will be larger in scale than if reliant on shareholders equity alone and in "dollar terms" will *increase* return to shareholders.

2) ROE is a strict function of the “equity beta” (the company risk premium), which in turn is dependent on the level of debt. The more debt a firm takes on, the higher the beta will be of the equity in that business. Debt creates a fixed cost, interest expenses, that increases exposure to market risk.

ROE is dependent on company and market sector performance, which you might express as the 'company risk premium'. It is *also* dependent on the level of company debt which I would regard as a separate and independent variable.

The “share of the pie” (as you say) you are buying when purchasing shares is a share of the “equity pie”. As you correctly pointed out in your example, a 10% share of the “equity pie” is NOT 10% of the “company pie” – it is only 5% of the “company pie” in a 50:50 leveraged company. The other 45% percent in “owned” by other shareholders, and the other 50% is “owned” by lenders.

50% of 50:50 leveraged company is “owned” by lenders? You might want to clarify what you mean there.

If we take Telecom as a (real) example the FY2007 annual report shows total equity and liabilities of $8,276m (page 31). This includes total long term debt of $2,404m. Most of this long term debt ($1,921m) is in Euro Medium Term Notes (page 50, note 23). I am sure you would agree that

$1,921m/$8,276m= 23.2%

is a very substantial part of the company. Yet if you go to the list of 20 largest shareholders (page 98) you will not a single European based shareholder on that top 20 shareholding list. If the Euro Medium Term Note people "own" 23.2% of Telecom how is this possible?

The rights and responsibilities that you have as owner of 5% of the company pie do NOT include the responsibility for meeting debt obligations. The firm holds that responsibility. If it cannot pay debt, then it may raise more equity (thus diluting you).

Yes, or the firm may choose to raise new capital through a general rights issue in which case your equity is not diluted.

Your example of listing a house is flawed (assuming I understand what you mean correctly)

It was an example that was meant to make things clearer. But I think you are right it was a poor analogy. I'll stick to the subject at hand.

SNOOPY