# Discounted Cash Flow: What Discount Rate To Use?

by: Bargain Bin

There are many methods to estimate the value of a company, but one of the most fundamental and frequently used is Discounted Cash Flow (DCF) analysis. The general idea behind the method is this: the value of a company is the sum of all future cash flows that the company will generate discounted back to today. Since a dollar one year from now is worth less than a dollar today, future cash flows are discounted by a discount rate. The formula to calculate the value of future cash flows is:

...where Ci is the cash flow in year i, N is the total number of years the cash flows will be generated (typically taken out to infinity), and r is the discount rate. There are two things you need to perform this calculation:

1) The cash flows for all future years. Obviously, this is a guess, but it can be based on previous performance. These should be conservative estimates and are difficult to make for a company that has a short operating history or erratic cash flows.

2) The discount rate. This is the rate at which you discount future cash flows.

The discount rate is by how much you discount a cash flow in the future. For example, the value of \$1000 one year from now discounted at 10% is \$909.09. Discounted at 15% the value is \$869.57. Paying \$869.57 today for \$1000 one year from now gives you a 15% return on your investment. The discount rate is essentially your required annual return on investment.

How Much Would You Pay?

Imagine I offer you a contract. The contract says that every year I will pay you \$1,000 for a one time payment today. How much is such a contract worth? The answer is, it depends. It depends on what type of return you require. Let's use the above formula to calculate the value of this contract for various discount rates. If you demand a 5% return on your investment, the value of this contract is \$20,000. If you demand a 10% return, the value of the contract is \$10,000. Here's a table for different discount rates:

 Required Annual Return (Discount Rate) Value of Contract 3% \$33,333 4% \$25,000 5% \$20,000 6% \$16,666 7% \$14,286 8% \$12,500 9% \$11,111 10% \$10,000 11% \$9,091 12% \$8,333 13% \$7,692 14% \$7,143 15% \$6,667 16% \$6,250 17% \$5,882 18% \$5,556 19% \$5,263 20% \$5,000

This contract does not have a set value. There is no "correct" discount rate. The value depends on the minimum rate of return that you require. For someone who only needs a 3% rate of return, the contract is worth \$33,333. For someone who needs a 20% rate of return, the contract is only worth \$5,000.

Margin of Safety

So does this mean that if I require a 12% return on my investment and I'm offered this contract for \$8,333 that I should buy it? Probably not. The reason is, of course, the risk of me not paying you. If there were zero risk, then you should buy the contract for \$8,333. But there is never really zero risk. So you adjust for this risk by applying a Margin of Safety. The Margin of Safety is the discount to the fair value that you require to compensate you for the risk of the investment. Let's say that you think that there is a 50% chance of me skipping town the moment you pay me for this contract. If you apply a 50% margin of safety to the fair value, you arrive at a price of about \$4,166. You should only buy the contract if the cost is lower than this price. If you were to buy 100 of these contracts from different people for \$4,166 each, each having a 50% chance of returning nothing, your annual return would be:

which is exactly what you require. The Margin of Safety allows you to be wrong part of the time and still reach your required rate of return. Many people will adjust the discount rate to account for risk (like people who use WACC - see below), but I think it's fairly clear that doing so doesn't make any sense. Risk is accounted for in the Margin of Safety. A cash flow is a cash flow. It doesn't matter where it comes from. The value is the same.

One Step Further

Let's take my analogy one step further. Suppose that there are so many contracts being bought and sold that a "contract market" is formed where people can buy and sell these contracts. The market price of each contract will move up and down each day. Sometimes a contract will cost \$7,000 one day and \$12,000 a week later. But nothing has changed. The value of a contract given a person's required rate of return is still the same. Someone requiring a 10% rate of return may buy this contract for \$7,000 but not for \$12,000. The fluctuations of the market price have nothing to do with the value of the contract. More importantly, the fluctuations of the market price have nothing to do with the risk of the contract. The larger Margin of Safety one can buy a contract for the lower the risk.

The stock market is essentially the same thing as this "contract market" I've described. When you buy a share of stock you are buying a small piece of the underlying company's cash flow. You will not receive all of this cash flow directly, unlike the contract. Most will be reinvested into the company in order to increase next year's cash flow or to pay down debt, thus creating value for you, the share holder. But the value of the company for you is still just the future value of cash flows discounted at your required rate of return (minus any debt and plus any cash on the balance sheet - you're buying that too).

Quick Summary:

1) The discount rate in a DCF calculation is your required rate of return on the investment. This is different for different people. There is no "correct" discount rate.

2) Risk is accounted for in the Margin of Safety, NOT the discount rate.

One last thing...

WACC

Many DCF calculations you will see use the WACC, or the Weighted Average Cost of Capital, as the discount rate. The WACC is defined as follows:

Where E is the market value of equity, D is the market value of debt, RE is the cost of equity, RD is the cost of debt, and t is the tax rate. The cost of debt is simply the interest rate the company pays on its outstanding debt. The cost of equity is more complicated. The Capital Asset Pricing Model (CAPM) has a simple equation for cost of equity:

Where Rf is the risk free rate (typically a 10-year US bond), RP is the so called risk premium, and beta is a measure of the correlation of the stock's returns with the returns of the market as a whole. I have a few problems with this.

1) In this equation beta is supposed to be a measure of risk. So according to CAPM the past performance of the stock determines the discount rate and, according to the people who use the WACC, the risk. In other words, the movement of the stock price determine how much a company's future cash flows are worth. I felt dirty just typing that.

2) People who use WACC claim that "you can't just pick any discount rate". These people do essentially the same thing with the risk premium. Different people will come up with different values.

3) Imagine two companies that are identical except that one company's capital structure is all equity and the other's is half debt, half equity. Typically the cost of debt is lower than the cost of equity, so WACC implies that the company with MORE debt is LESS risky and the cash flows generated are worth more. This is clearly ridiculous.

4) CAPM is based on assumptions that are clearly false in general. A great overview of the shortcomings of CAPM can be read here. And more on why WACC doesn't make any sense as a discount rate can be found here.

Conclusion

When doing a DCF calculation the discount rate that you should use is your required rate of return, not WACC or whatever other nonsense people say. You do NOT adjust for risk by changing the discount rate. You adjust for risk by applying an ample margin of safety. I'll leave you with a quote from Warren Buffet:

The riskiness of an investment is not measured by beta (a Wall Street term encompassing volatility and often used in measuring risk) but rather by the probability -- the reasoned probability -- of that investment causing its owner a loss of purchasing power over his contemplated holding period. Assets can fluctuate greatly in price and not be risky as long as they are reasonably certain to deliver increased purchasing power over their holding period.

Disclosure: I have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours.