*By Samuel Lee*

*This article incorporates elements of an article published in the January 2013 issue of Morningstar ETFInvestor. Download a complimentary copy here.*

The main tasks of the active value investor are to estimate intrinsic value, buy assets trading at sizable discounts to their estimates, and sell or avoid those trading at premiums. The assumption is that asset prices can't help but gravitate to their fair values over time. However, history shows that prices can become untethered from fair value for years at a time and move in self-fulfilling cycles of fear and greed. A full account of investing needs to acknowledge and manage these short-term movements, but the beating heart of investing should always be fair value.

Many popular books on investing don't even touch upon the details of estimating intrinsic value as well as the conceptual apparatus justifying its use. I find that odd, as intrinsic value is perhaps the most important idea in all of finance. As Charlie Munger likes to say, not understanding basic quantitative investing concepts is like being "a one-legged man in an ass-kicking contest."

Being an active investor without understanding intrinsic value is a terrible mistake. But being a passive investor doesn't get you off the hook, either. Every once in a while, markets go nuts, and a passive investor with a strong grasp of fundamental investing concepts like intrinsic value can take advantage of the madness or at least avoid participating in it. A good example is when Treasury Inflation-Protected Securities sold off in late 2008 -- even normally passive investors such as Larry Swedroe identified in real time the incredible risk-reward payoff TIPS offered.

This article is the first part of a two-part series on intrinsic value, discount rates and expected returns, and how they relate to each other, as well as some practical advice on applying these ideas.

**Time, Money and Risk**

Before we get into intrinsic value and all that good stuff, let's talk about the relationship between money and time. When someone borrows money, he is pulling future earnings to the present. In a real sense, he is taking money from his future self and giving it to his present self. Likewise, when he lends money, he is taking money from his current self and giving it to his future self. The interest rate on borrowing or lending is the conversion rate at which money can be exchanged through time.

Interest rates differ, depending on the creditworthiness of the borrower. Suppose your uncle -- call him Sam -- wants to borrow $100 from you for 10 years, promising to repay $131 at the end, for an annualized interest rate of 2.7%. If he's anything like the typical uncle hitting up a nephew for cash to be paid back a decade hence, your wallet should be shut tight like a vise. You could, after all, lend to the other Uncle Sam -- the one with the printing presses and nukes -- for the same rate today and not run any credit risk. Lending to the less creditworthy uncle only makes sense if the interest rate he offers is high enough to be competitive with yields on similarly risky investments available to you.

Let's step back for a second. First of all, why can the U.S. government borrow money at the lowest rates possible? Because investors widely consider U.S. Treasuries to be "risk-free." The U.S. government has taxing power over a huge economy, a lot of accumulated good will, and control over its own currency. Furthermore, investors have been clamoring for safe assets since 2008 and are willing to tolerate low yields. Of course, Treasuries are not actually risk-free. Aside from negligible default risk, they bear reinvestment risk, the possibility that interest rates will unexpectedly rise, and inflation risk, the possibility that unexpected inflation eats away at the value of future nominal-dollar payments. Both risks usually show up as an upward-sloping yield curve: The longer a Treasury's maturity, the higher its interest rate.

The Treasury rate can be thought of as the "pure" exchange rate of nominal dollars through time, stripped of any credit risk. It is hugely important because all conversions of money through time — all borrowing and lending, and therefore all investing — must take into consideration the risk-free rate. It would make no sense for any investor to lend at a lower rate, so the market tends to price most assets such that they offer a higher yield than the risk-free rate. The difference between this higher expected yield and the equivalent-duration Treasury yield is called the "risk premium."

Naturally, the market assigns different risk premiums for different assets. In general, the riskier an asset, the higher its risk premium, another way of saying you can't get more return without more risk. But what is a "fair" risk premium for a given asset? Many investors rely on history. The U.S. stock market has returned about 4%-5% more than Treasuries. Other stock markets have returned about 3%-4% more than local "risk-free" bonds.

The "right" risk premium is a matter of preference. Investors tolerant of volatility and long and steep drawdowns may be fine investing in stocks when they offer only a 1% premium to Treasuries. Other investors may be allergic to risk, demanding very wide risk premiums to own stocks. The market's risk premium is determined by the buying and selling activity of many investors with different preferences. Assuming the historical risk premium is fair, is a bet that average risk appetite gravitates to the historical norm.

In short, an asset's interest rate, yield, or expected return takes into account the risk-free rate and a risk premium.

**Intrinsic Value**

We're now ready to tackle the notion of "intrinsic value" or "fair value." It can be defined as the value of all of an asset's future cash flows, adjusted for their riskiness and timing. A more precise definition is net present value: the sum of the present value of all future cash flows. Let's break this statement down.

A cash flow is a payment, either incoming or outgoing.

Present value is what a future cash flow is worth today. One dollar today is worth more than a dollar tomorrow on account of opportunity cost and risk. The annual rate at which future dollars are "shrunk" or "discounted" to today's dollars is called, fittingly, the discount rate or the required rate of return. For example, if the discount rate is 10%, $100 one year from now is only worth around $91 today ($100/(1+0.1)). The discount rate is a combination of the risk-free rate and a risk premium, but for now I'll lump them together.

More generally, a future cash flow is discounted to the present by multiplying by a "discount factor," which compounds the annual discount rate from the present until the future cash flow. The discount factor d is computed by the following equation:

d = 1/(1+r)^{n},

where r is the annual discount rate and n is the number of years from the present until the cash flow. The discount factor is the exchange rate between future and present dollars. Multiplying a future cash flow by the appropriate discount factor yields the present value:

PV = x/(1+r)^{n},

where PV is the present value, x is the future cash flow, r is the discount rate, and n is the number of years.

Let's consider an example. Uncle Warren writes an IOU for $1,000 maturing 30 years from now. The 30-year Treasury rate is 3.5%. Uncle Warren is filthy rich and considered highly creditworthy, so you assign him a credit risk premium of 1%. The discount rate is equal to the Treasury rate plus the risk premium, so our required rate of return is 4.5%. How much are we willing to pay today for Uncle Warren's IOU? Plugging into the above formula, we get:

PV = $1,000/(1+0.045)^{30} = $267.

A couple of things to note here. As time passes, the PV of the bond slowly converges to its face value. Second, the PV of the bond can change because discount rates change. This can happen either because the risk-free rate changes or the credit risk premium changes. On the market level, most price changes are driven by changing discount rates, not changing expectations of cash flows.

Calculating fair value is a matter of identifying the future cash flows of an asset and then applying the correct "exchange rates" to discount them to the present. Of course, many assets make series of payments. Calculating such an asset's present value is simply a matter of discounting each payment to the present, then summing all the present values.

So what does it mean for an asset to be over- or undervalued relative to fair value? If its price is below fair value, it either means that the market has assigned too high of a risk premium to the asset's future cash flows or the market's estimates of the asset's cash flows are too low (or both). If the current price is above fair value, it means either the market has assigned too low of a risk premium or its estimates of future cash flows are too high.

The central message of this primer is that all assets have a yield or expected return owing to future cash flows and that these future cash flows can be converted into dollars today. The rate at which future dollars are converted to present dollars must take into account the risk-free rate and a risk premium.

In the second and final part of this series, I'll discuss how to turn the intrinsic value framework into a practical way to estimate the future cash flows a variety of asset classes.

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