The foundation of modern finance is the idea – called the time value of money – that a dollar today is worth more than a dollar tomorrow. There are good reasons that this concept should be true, and we talk about those in the IOI 102 Course on Valuation.

This is a very important rule for value investors, because the fundamental law of value investing is that the value of a firm is value of the cash flows the firm can generate over its economic life. Because some of the cash flows a firm will generate will be in the future, a value investor must somehow “translate” those flows into “present value” terms.

There is a very well-established way of doing this using a simple mathematical formula, the key term of which is called the “discount rate.”

But while there are bookshelves filled with erudite discussions of discount rates and how to apply the time value of money to investing using “discounted cash flow” (DCF) analyses, there is a tremendous amount of misunderstanding, mythology, and logical contradictions surrounding the question of how to do so.

This article sets out to bust those myths and replace confusion with elegant simplicity.

#### Discount Rate Difficulties

Discount rates are conceptually tied to the risk of not receiving some future payment. The discount rate for a loan is called its interest rate, and we all understand the principle of tying risk to interest rates. For example, a loan collateralized by a hard asset that can be sold if the loan is not repaid (e.g., a mortgage) will carry a lower interest rate than an uncollateralized loan of the same amount to the same borrower.

An interest rate on a loan is explicit, but the discount rate on a share of a company’s equity is not. People have tried to tie the concept of risk to an equity discount rate (also called “cost of equity”). But this leads to its own issues, which we discuss more below. In the end, equity analysts end up usually having some subjective control over what discount rate they use to analyze the future cash flows of a given company.

The fact that equity discount rates are, to a large extent arbitrary, causes some pretty big problems for people trying to value firms using DCF analysis – namely, the valuation is very sensitive to small changes in the discount rate. One of the most esteemed value investors in the world – Bruce Greenwald, the director of Columbia University’s Value Investing program – believes using DCF analysis is “folly” because of this issue (see the figure below).

Indeed, I have seen professional analysts using DCF models twist themselves into knots trying to justify setting the discount rate to be lower on a stock they “like” (since the lower discount rate will give them a higher fair value estimate for the stock) and higher on a stock on which they are bearish.(The above observation about analysts’ choice of discount rates highlights the kinds of “structural issues” that we discuss in the IOI 101 course on Behavioral Biases and Structural Factors in Investing. In my experience, most analysts have some *intuition* about what a stock is worth, then try to twist their models to give them the “fair value” or “target price” that their intuition tells them is right. A scientist would be black-listed for doing something similar!)

It turns out that the “academically-approved” method for selecting discount rates is ridiculous as well – a point brought up in a conversation between Warren Buffett and his partner, Charlie Munger:

Buffett: I’ve never seen a cost of capital calculation that made sense to me. Have you Charlie?

Munger: Never.

[*N.B.* Cost of capital is just the weighted average of the cost of equity – the discount rate – and the cost of debt – the interest rate – borne by the firm. Interest rate is very easy to observe, so it’s clear that Buffett is talking about problems with the cost of equity in the above quote.]

Academics’ starting point for calculating discount rate is to assume that markets are efficient (i.e., that there are no over- or under-valued stocks) and to equate stock price movement to “risk.” The task of equating stock price movement to risk is accomplished using a regression formula called the Capital Asset Pricing Model (CAPM). In this model, risk is a statistical measure (named “beta”) of the historical stock price movement of a stock versus an appropriate stock index.

Most investment professionals trained by academics – virtually all of us, in other words – forget that the base assumption about discount rate contradicts the reason they were hired in the first place. Namely, equity analysts are trying to find mispriced stocks using a theoretical model (CAPM) that says stocks are never mispriced!

Legions of analysts will dutifully churn through spreadsheets of historical prices, applying the approved mathematical formula to find beta (or simply pull beta from a Bloomberg terminal), without even a second thought that the method they are using to value companies directly contradicts their professional *raison d’être*. Some analysts compound this problem by comparing the faulty number generated by this contradictory analysis with another mythical, nonsense number named “Return on Invested Capital.”

Does this mean that DCF analyses should not be used to estimate the value of an investment? IOI says No! [1]

#### A Better Discount Rate

In our 100 Series classes, we talk about the proof that our modern economy is based on the concept of discount rate. Indeed, the reason you are able to read this article on a computer that you can hold in your hand or (if old-fashioned like me) fold up and put in your briefcase is because the process of discounted cash flows works. It’s also the reason, of course, why you get paid (not much these days) for loaning money to a bank in the form of a deposit account. Virtually none of the advances in our civilization over the past few thousand years would have been enjoyed if the concept of the time value of money was substantially incorrect.

So, as investors, let’s figure out a way to harness a provably accurate idea to find investments that will allow us to benefit! We have three rules of thumb about discount rates that allow us to feel confident that we are accurately assessing the value of companies through a DCF analysis:

- There is no way to choose a discount rate that will compensate an investor for “risk.”
- The proper discount rate is the rate you can expect to earn on your second best investing idea.
- By default, “the second best investing idea” is always an investment in a broad index.

Regarding the first rule, just think about any one of countless unexpected events that a discount rate is completely unsuited to assessing: Union Carbide’s Bhopal disaster, Johnson & Johnson’s Tylenol murder case, Cantor Fitzgerald and the 911 attacks. In our opinion, these kinds of issues can only be handled by thinking about possible valuation scenarios, not by tweaking a discount rate to try to cover events that may or may not materialize.

The second rule comes from Buffett and Munger’s comments in the same conversation quoted above. It’s a sensible idea that provides a “hurdle rate” (though Buffett and Munger hate that term) to assess a new investment.

The third rule comes from the voluminous amounts of statistical evidence that it is extremely difficult to actively select stocks that will consistently beat an index portfolio over time. Investing geniuses may exist (though the population is certainly much, much smaller than the number of professional money managers), but the vast majority of investors should not kid ourselves about our chances of beating the market. An index portfolio should be considered a “strong second” in considering any investment opportunity.

What we are left with is a “common yardstick” by which we can weigh the value of any firm as long as we are diligent about focusing on the handful of factors that drive the cash flow creation process.

An understanding about how economies, companies, and stock markets grow over time, and a few simple principles are enough to stand an intelligent investor in good stead! Certainly, we think our approach is better than arbitrary choices influenced by personal and professional biases or than esoteric mathematical formulae that have consistently failed to accurately explain important observations in the real world.

Notes:

[1] Greenwald would say “Yes – discount rates should not be used.” Instead, he recommends using multiples analysis. The funny thing is that multiples are actually just a shorthand way of expressing the discounted cash flow equation that has what I consider to be a critical shortcoming – it completely obfuscates the discount rate being used and the analyst’s assumptions for future growth!

[2] Figure 1 has been changed to correct for a calculation error in the 12% discount line. Many thanks to SA reader SingaporeFred for the catch!