*Welcome to our Value Investing 101 series. In this post, I’ll explain how to calculate a discount rate for your DCF analysis. If you don’t know what that sentence means, be sure to first check out How to Calculate Intrinsic Value.*

As I mentioned in **Value Investing 101: The Time Value of Money**, interest rates are determined by a combination of:

- The asset’s risk
- The asset’s liquidity
- The asset’s maturity
- The expected inflation rate
- The “risk-free rate”

It’s easy to see how – academically – these five determinants can drive interest rates, but how can we actually determine the interest rate (that is, *discount rate*) we use in our Discounted Cash Flow analysis?

A business school professor would tell you to use the Weighted Average Cost of Capital, or **WACC**.

## Weighted Average Cost of Capital (WACC)

A company finances its assets by using either debt or equity. The WACC is the cost of the company’s debt (interest payments) and the cost of the company’s equity (shareholders’ required return), both of which are weighted proportionately to the company’s overall capital structure. Therefore, a company’s WACC is the overall required return that a firm must achieve to satisfy both its debt holders and its shareholders.

As an example:

Suppose that lenders require a 10% return on the money they have lent to a firm, and suppose that shareholders require a minimum of a 20% return on their investments in order to retain their holdings in the firm.

On average, then, projects funded from the company’s pool of money will have to return 15% to satisfy debt and equity holders. The 15% is the WACC.

If the only money in the pool was $50 in debt holders’ contributions and $50 in shareholders’ investments, and the company invested $100 in a project, to meet the lenders’ and shareholders’ return expectations, the project would need to generate returns of $5 each year for the lenders and $10 a year for the company’s shareholders. This would require a total return of $15 a year, or a 15% WACC.

The actual calculation for WACC is:

WACC = (E/V) x Re + (D/V) x Rd x (1 – T)

*Where:*

Re = Cost of equity

= Expected return of the asset as determined by the **Capital Asset Pricing Model (CAPM)**

= risk-free rate + beta of the security x (expected market return – risk-free rate)

Rd = Cost of debt (i.e. interest rate on the debt)

E = Market value of the firm’s equity

D = Market value of the firm’s debt

V = E + D = Total market value of the firm’s financing (equity and debt)

E/V = % of financing that is equity

D/V = % of financing that is debt

T = Corporate tax rate

You can skip the algebra and use one of these online calculators **here **and **here** if you want.

If WACC seems very complicated to you, don’t worry because (a) it is and (b) it has several key flaws, so you don’t have to use it (Warren Buffett doesn’t).

What flaws?

### 1. More debt results in a lower WACC… which means a less risky investment?

Let’s say you had a company with a 10% cost of equity and a 10% cost of debt. Because of the (1 – T) tax shield, the WACC would not be 10%… it would be lower than 10%. This means that the more debt a company has, the lower its cost of capital will be due to this tax shield, which ultimately results in a higher valuation for the company’s stock (remember: a lower discount rate results in a higher valuation).

According to WACC, more debt means a less risky investment and therefore a higher valuation.

This clearly doesn’t make sense. If I showed you two companies that are equal in every aspect except that Company A has $0 debt and Company B has $50 million of debt, you would say that Company A is less risky. WACC says the opposite.

### 2. WACC uses beta, a measure of volatility, to determine a stock’s risk

In order to calculate the cost of equity in WACC, you use the **Capital Asset Pricing Model (CAPM)**. The CAPM says that the expected return on a stock (the firm’s cost of equity) is equal to the risk-free rate plus the equity market premium adjusted for the riskiness of that individual stock. This individual riskiness adjustment is done by multiplying the equity market premium by what is called “the stock’s beta.”

Beta is supposed to measure risk by comparing a stock’s volatility to the entire market. The volatility of the S&P 500 is usually used as the base and is given a beta of one. Any stock with a beta above one is said to be more volatile and therefore more risky than the market, and a stock with a beta of less than one is less volatile and therefore less risky than the market.

But as Warren Buffett notes in his **2014 Berkshire Hathaway Shareholder Letter**, risk is not equal to volatility:

“Stock prices will always be far more volatile than cash-equivalent holdings. Over the long term, however, currency-denominated instruments are riskier investments – far riskier investments – than widely-diversified stock portfolios that are bought over time and that are owned in a manner invoking only token fees and commissions.

That lesson has not customarily been taught in business schools, where volatility is almost universally used as a proxy for risk. Though this pedagogic assumption makes for easy teaching, it is dead wrong: Volatility is far from synonymous with risk. Popular formulas that equate the two terms lead students, investors and CEOs astray.”

Now take as an example Stock A and Stock B. Stock A returns 25.0% in Year 1 and 40.0% in Year 2. Stock B returns -0.5% in Year 1 and 1.0% in Year 2. The stock market returns 10.0% in Year 1 and 12.0% in Year 2. Stock A’s beta would actually be much higher than 1 and Stock B’s beta would be much lower than 1, implying that Stock A is more risky than Stock B.

Not only does the beta result in a wrong conclusion about the riskiness of Stock A and Stock B, it also bases that conclusion on past price data, which says very little about the future value of a stock. As Buffett says: “If past history was all there was to the game, the richest people would be librarians.”

**Simply put, risk is not volatility. Risk is the probability of losing your investment.**

## So What Discount Rate Should We Use Instead of WACC?

There is a lot of debate about what discount rate Buffett uses, and the man himself has given conflicting information on the matter over the years. But I think this exchange from the 2003 shareholder meeting sheds the most light on the issue:

**Buffett:*** Charlie and I don’t know our cost of capital. It’s taught at business schools, but we’re skeptical. We just look to do the most intelligent thing we can with the capital that we have. We measure everything against our alternatives. I’ve never seen a cost of capital calculation that made sense to me. Have you Charlie?*

**Munger:*** Never. If you take the best text in economics by Mankiw, he says intelligent people make decisions based on opportunity costs — in other words, it’s your alternatives that matter. That’s how we make all of our decisions. The rest of the world has gone off on some kick — there’s even a cost of equity capital. A perfectly amazing mental malfunction.*

**Buffett:*** 10% is the figure we quit on – we don’t want to buy equities when the real return we expect is less than 10%, whether interest rates are 6% or 1%. It’s arbitrary. 10% is not that great after tax.*

**Munger:*** We’re guessing at our future opportunity cost. Warren is guessing that he’ll have the opportunity to put capital out at high rates of return, so he’s not willing to put it out at less than 10% now. But if we knew interest rates would stay at 1% we’d change. Our hurdles reflect our estimate of future opportunity costs.*

For Warren Buffett and Charlie Munger, everything is a function of opportunity cost – which is the return of your next best investment option. Buffett says this is *at least* 10%, which is “not that great after tax.”

What is your opportunity cost?

Well, everyone has the opportunity to buy a low cost index fund that tracks the entire stock market, so everyone’s opportunity cost should be the return of the S&P 500.

The S&P 500 has had a 9.6% annualized return for the **past 50 years**. However, if you are an active investor then you will have to sell your investments every once and a while. The maximum long-term capital gains for most people fluctuates between 10 – 15%. Therefore, you need a 15% pre-tax return in order to beat the stock market after taxes.

As stated in one of my favorite investment books ever, ** Buffettology**, Warren Buffett himself is generally unwilling to accept less than a 15% return on his money in any investment.

## Conclusion

So, your discount rate – according to Buffett’s and Munger’s principles – should be 15%. However, this is different for each investor. If you are content with 9.6% returns over the long run, then you should simply invest in an index fund and call it a day. But if you are interested in compounding your money more than 15% annually, then a 15% discount rate should be your target.

*Do you agree? Disagree? How do you determine a discount rate to use? Let’s hear it in the comments below.*

### Berkshire Hathaway Letters to Shareholders

###### by Warren Buffett

*This book compiles the full, un-edited versions of 50 years of Warren Buffett’s letters to the shareholders of Berkshire Hathaway. In addition to providing an astounding case study on Berkshire’s success, Buffett shows an incredible willingness to share his methods and act as a teacher to his many students.*

This is always an interesting subject. Thanks for sharing.

My opinion (and I could be completely wrong here) is that valuing a business is a matter of convention. It is not like an exact science. An exact science provides both formulas and ways to measure or compute the variables to be used in the formulas. In valuing a business, all we got is a formula (for the discounted cash flows for example) but no indication on how the variables in the formula (including the cost of capital) should be computed. Consequently, we are left with the choice of what should be used as the cost of capital.

Therefore, if the aim of the exercise is to compute an absolute intrinsic value for the shares of a company, expecting that the market will eventually track this value, better to use the convention that is mostly used by the market participants – currently the CAPM. For that reason, I use the CAPM WACC in valuing businesses.

I believe one should be careful in using an expected annual rate of return as cost of capital. It seems to me we are not comparing apples with apples here. Only an IRR computation can make both identical and will implicitly imposes constraints on growth rate and earnings yield that are not apparent at first.