Valuation Elements: Correct use of the Cost of Capital within the Discounted Cash Flow Analysis.

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Back in 1938 the book, The Theory of Investment Value by John Burr Williams was released, and it became an instant investment classic. Williams’s book was the first to provide a framework for valuing financial assets, through the use of discounted cash flow (DCF) analysis.

“In The Theory of Investment Value, written over 50 years ago, John Burr Williams set forth the equation for value, which we condense here:  The value of any stock, bond or business today is determined by the cash inflows and outflows – discounted at an appropriate interest rate – that can be expected to occur during the remaining life of the asset.  Note that the formula is the same for stocks as for bonds.  Even so, there is an important, and difficult to deal with, difference between the two:  A bond has a coupon and maturity date that define future cash flows; but in the case of equities, the investment analyst must himself estimate the future “coupons.”  Furthermore, the quality of management affects the bond coupon only rarely – chiefly when management is so inept or dishonest that payment of interest is suspended.  In contrast, the ability of management can dramatically affect the equity “coupons.”

– Warren Buffett, 1992 Berkshire Hathaway Annual Report (Bold italics mine)

The formula for discounted cash flow is simply this:




Do not substitute the company’s cash flows for the company’s dividends paid out to shareholders in the DFC formula, because it is the wrong application of the DCF equation, it is the equivalent of trying to start a wood fire using ice cubes instead of fire starter cubes, in both activities you are fooling yourself. Too many financial institutions, financial experts (according to the media) and universities continue to teach or advise people to participate in the activity.

Before we start to dig into the different elements that make up the DFC formula, we need to adjust the DFC formula slightly.

The CF2 & CF3 in the above DFC formula requires forecasting to determine what future cash flows to use. Charlie Munger has said the following about forecasting: “When you mix raisins with turds, they are still turds.” What Charlie is referring to is when you add unreliable data to reliable data with your equations, they become less accurate. If you read analyst recommendations you will notice that their three-year forecasts for say revenue or net profit always smoothly increase year on year, in complete contrast to the past. So, hence avoid doing it at all. So from now on, we will apply the modified DFC equation below.


The Average Cost of Capital elements

“I’ve never heard an intelligent cost of capital discussion”.

– Charlie Munger

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This is simply working out what the average interest rate paid by the company on its debts. Found in financial statement + notes. This is easy.


In accounting, equity is the difference between assets and liabilities (Equity = assets – liabilities), but in reality if you liquidated the business you wouldn’t on average actually receive the full amount if you were the sole owner of the equity, as you are liquidating the business for a reason, and if it was thriving (as a going concern) you wouldn’t liquidate it, so the circumstances matters a lot. The way to think of equity is in these terms; equity is the amount of invested shareholder funds plus retained capital.

“Our experience suggests that investors tend to overestimate liquidation values, as the reality of a dying business tends to hide nasty surprises for investors.”

-Mihaljevic, John. The Manual of Ideas.

The way to think of equity is in these terms; equity is the amount of invested shareholder funds plus retained capital.

New equation: Equity = Shareholder Invested Capital + Retained Capital – Debt.

Venture capitalists also encounter this particular problem.

When you purchase a share you are purchasing someone’s claim on equity, and a few questions to ask are: how much should you pay for that equity claim? What return on capital (ROC) and return on equity (ROE) is the business producing and is it sustainable? Is the ROE high enough to create capital?

Now in practice.



Return on Equity for 2016 was 24% (7,623/31,800 rounded).

Net cash return on operating activities equaled 24% (7,569/31,800 rounded).

Free cash flow = $6.2 million!

1800 Smiles paid out $5.0 million in dividends.

Zero debt.

Question. If you had a bank account with $10,000 and you were earning 24% in interest, would you withdraw at the end of the year the full earnings of $2,400? Or would you leave the money in the account to compound?

Below is a table outlining the vast differences between allowing your capital to compound or withdrawing the full amount of interest earned at the end of each year.

Year One Year Two Year Three Year Four Year Five Year Ten Total
Compounding Interest $2,400 $2,976 $3,690 $4,576 $5,674 $85,944 $95,944
Simple Interest $2,400 $2,400 $2,400 $2,400 $2,400 $2,400 $34,000
Difference $61,944


Now think of a companies equity in the same terms of the above back account. The same principles apply to business as they do to your bank account.

As you can see from the 1800 Smiles balance sheet and the figures I have presented, growth in equity slows as well as the earnings growth rate due to management deciding to pay out all free cash flow as dividends instead of reinvesting it in the business. This significantly affects the share price over the long term. Telstra is another prime example of stagnant earnings and equity growth due to management’s desire to please dividend seeking shareholders.

“The truism that over the long term an investor in a business will earn a return closely matching the return on capital of the business is only partly true. If the business dividends out all free cash flow, a long-term shareholder will earn a return equal to the free cash flow yield implied in the original purchase price. The return on capital earned by the business is irrelevant when the payout ratio is 100 percent. As the payout ratio declines, the economics of the business becomes increasingly important.”

-Mihaljevic, John. The Manual of Ideas: The Proven Framework for Finding the Best Value Investments

If 1800 Smiles didn’t pay a dividend in 2016, the retained earnings within equity would have grown to $23.9m and with equity totalling $ 39.4m. And if they maintained the 24% ROE and all else remaining equal, then in 2017 retain earning would have grown to $29.6m and with equity totalling $45.1m.

Please note that the above only applies if 1800 Smiles can consistently earn those high rates on equity.

Ok, let’s now apply the DFC equation.

DFC = CF / (1+R)

Free Cash Flow = $6.2m

R = ?

 “[Interest rates] act on financial valuations the way gravity acts on matter: The higher the rate, the greater the downward pull. That’s because the rates of return that investors need from any kind of investment are directly tied to the risk-free rate that they can earn from government securities. So if the government rate rises, the prices of all other investments must adjust downward, to a level that brings their expected rates of return into line. Conversely, if government interest rates fall, the move pushes the prices of all other investments upward.” 

–  Warren Buffett (Bold Italics mine)

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I heard from Bruce Greenwald, that he believed that Buffett applied a 7% + 30 year US Govt. Bond Rate as his discount rate which is also he’s’ required return.

I recommend you use a discount rate that is your required return. If you need help determining what ‘required return’ to adopt, check out the Wealth Accumulation after 25 Years Chart, in the guest post by Lyn Alden click here.

Let’s use the 1800 Smiles as an example. To simplify this example we’ll assume that no dividends are paid out. We’ll apply 10% & 15% required returns.

How much are you willing to pay per share for a piece of equity?

In 2016, 1800 Smiles earnt $7.6m on beginning equity of $34.4m, and ROE at 24%.

@10% Required Return.

DCF = (7.6 / 0.10) = $76 million in value

Per share = $3.20

@15% RR

DCF = (7.6 / 0.15) = $50 million in value

Per share = $2.14 (Over a dollars difference)

At the current price of $7 dollars per share, the market is valuing 1800 Smiles at $177.60m. The discount rate applied, by the market is 4.30%. I believe the market is rationally pricing the stock considering that the 15 year Australian Bond rate is 3.19%. The 1.11% probably represents the risk premium.

“We try to deal with things about which we are quite certain. You can’t compensate for risk by using a high discount rate.” Warren Buffett

As Buffett’s quote applies, don’t increase your required return if you assess the business to be risky.

Your goal is not to buy shares at your determined required return price or referred to as intrinsic value but use the margin of safety concept, buy below it, this adds protection for any mistakes you may have made during your analysis.

You should be using the DFC equation after you have filter the business through your checklist, eliminating, for example, businesses laden with debt, businesses who earn low returns on invested capital, capital intensive businesses and the business you don’t understand. By now you should understand why Buffett plus others are constantly saying that the price is what you pay and value is what you get.

Several benefits occur: As you are buying with a margin of safety, your return increases, plus you are not paying for next years growth today, which means as growth in earnings increase over the years so do your return increases. So, in a few short years, your return can pass the 50% mark excluding dividends paid.

Disadvantages: Few opportunities like these occur, requiring a lot of patience and courage, but if you follow Munger and Buffett, then you know that they both recommend using the 20 hole punch card concept.


The discount rate and required return are the same things. The goal is to be approximately right and use a margin of safety!

Remember, you cannot discount risk away by increasing your required return.

A real life example.

It is common on Wall St to assume at 10% WACC. Carl Icahn sent an open letter to Tim Cook CEO of Apple, asking for a small $150 billion share buyback, which included taking on a little debt to fund. Carl reasoned that Apple shares were undervalued, and with $133 billion in cash sitting there earning little to nothing, essentially the cash was actually eroding Apple value. At a 10% cost of capital, that small $133 billion was costing $13.3 billion dollars a year whereas a share buyback would have delivered more value back to the Apple shareholder.

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