Making the Discount Rate Formula Simple – Explain it Like I’m a 7th Grader

To me, one of the hardest parts of understanding a DCF valuation was the discount rate. It didn’t help that the formula was complex. I’d like to make the discount rate simple, using simple words.

Maybe if you can understand the basic concept of the discount rate, it will help with calculating one for yourself, whether for a Discounted Cash Flow (DCF) model or for a Dividend Discount Model.

In my attempt to make the discount rate formula simple, we’ll go over the following:

  • What’s the point of a discount rate?
  • The main components of a discount rate
  • The two major types of discount rates

Let’s start with the discount rate concept itself. Using three birds.

What’s the point of a discount rate?

Warren Buffett has a fantastic way of helping us visualize the concepts of the discount rate formula and its role in a DCF valuation.

He says using a discount rate and a DCF is like the parable, “a bird in the hand is worth two in the bush”.

Think of a bird in the hand as your cash today.

As part of making an investment, you are letting go of cash in your hand, for more cash in the future.

How willing are you to let go of the cash in your hand?

It depends on several things.

1—If you are guaranteed to double your cash tomorrow, that’s probably a great deal. But if there’s a 50-50 chance you lose all of your cash, maybe not so much.

Two birds in the bush is great (double cash tomorrow), but it depends on how risky those birds in the bush are. You don’t want your chances to make a bird in the hand exchanged for zero birds in the bush.

2—The next part of letting go of your cash; what are your options?

If there are two birds in the bush over here, but three birds in the bush over there, then giving up cash for the bush with two birds is no good.

But if there are two birds in our bush and the other bush only has one bird, our bush is looking pretty good.

How much you want to let go of cash in the hand depends on how much cash you can get in the bushes around you. A simple discount rate formula will help us include that factor.

3—Inflation is the last factor in this.

Stepping away from the bush and into cash in our hands; say we had $100. Getting $200 next year for our investment could be a great option. Spending $100 on a pair of jeans today would not be a good trade if we could wait until next year and have $200, and 2 pairs of jeans next year.

But that assumes no inflation. Say inflation makes the $100 jeans cost $250 next year. Then, not buying the jeans today in order to get $200 next year would not be a good investment for us, because we would be $50 short of buying just one pair of jeans next year.

Taking those three factors is what the Discounted Cash Flow (DCF) formula tries to do in its simplest form.

  1. How risky is the investment?
  2. What are your other investment options?
  3. How does inflation impact your returns?

The Main Components of a Discount Rate

Now that we have the three factors of a DCF the next part is easy. The discount rate simply considers the first two factors.

That is—opportunity cost (our other options), and risk.

In general, everything to do with money has risk. There is risk if you:

  • Hold cash, as inflation makes it worth less
  • Let someone borrow money, as they could not pay you back
  • Buy a piece of a business, as that business could go bankrupt

The key about investing and managing money is “discounting” these risks.

Letting the government borrow money is seen as the lowest risk investment because it’s rare for governments to go bankrupt. To do this is called buying a Government Bond.

Right now the U.S. government sells (“issues”) the lowest risk bonds. They are seen as the safest right now because so many people in the world use U.S. dollars, so that’s why they’re considered the lowest risk.

You could also let big companies borrow from you, these are called Corporate Bonds.

And then you could invest in a piece of a business, which is what buying stocks essentially is. Stocks are generally riskier than bonds because the returns are unpredictable compared to bonds.

To account for the higher risk of stocks, we use the “equity risk premium” in a discount rate formula.

Component #1: Riskiness of Cash Flows

Equity risk premium: We use this to set an acceptable rate of return for the riskiness of stocks. It is similar to the concept of a “hurdle rate”. The equity risk premium is generally accepted at around 4%-6%; I’ve seen most estimates for DCFs at around 5%.

It is generally combined with a stock’s “beta” to find our acceptable risk-adjusted rate of return.

The “beta” is supposed to account for the riskiness of a stock. Generally a stock with more volatility is seen as higher risk, and so has a higher beta. Beta could vary widely in theory, but most of time you’ll probably see betas between 0.75 – 1.5+.

We combine the beta with the equity risk premium to get the “risk premium”.

Risk premium: This will take the riskiness of stocks in general, combined with the riskiness of the particular stock we are examining, in order to make a final acceptable return for our risk.

This metric is taken by simply multiplying together the equity risk premium and the beta.

The higher the number, the higher the discount rate. That means the more return we are requiring to make up for the fact that this is a riskier option for our cash in the hand.

Important note: If a beta is too far away from the typical 0.75-1.5 range, it will skew your risk premium greatly, which skews your discount rate formula greatly.

That’s where it’s important NOT to get lost in the numbers and to instead really understand what the formula means, and what it’s trying to do.

A discount rate is simply trying to allow us to compare investments on an apples-to-apples basis.

Higher discount rates mean I don’t value a company’s cash flows as highly because they are riskier. And it’s vice versa, lower discount rates means a certain company’s cash flows are more valuable to me.

That’s the bottom line.

If you are putting lower discount rates in your DCF, that means you perceive that investment as lower risk. Period.

So be careful at setting these discount rates too low.

Component #2: Opportunity Cost

To account for the fact you could also invest in low risk government bonds, instead of the stock you are evaluating, we also have what’s called the “risk-free rate” in the discount rate formula.

For a final simple discount rate (on equity) component, you just add the risk-free rate to the risk premium we calculated earlier. Done.

The risk-free rate is the rate that we could earn if we buy a U.S. government bond instead.

Note that this risk-free rate changes pretty much everyday. The higher the government bond yields, the higher your discount rate will be, and vice versa.

This is why discount rates have been so low during the late 2010’s/ early 2020’s, because interest rates have been so low (which makes U.S. Government bond yields low).

Lower discount rates pushes a DCF intrinsic value higher, which is a big reason why we’ve seen such historically high Price to Earnings (P/E) ratios in the stock market lately. Earnings are generally tied to Free Cash Flows (FCF); FCF is what we are discounting for a DCF.

The bottom line: Discount Rates and Valuation

Discount rates and intrinsic value are tied against each other like a seesaw; the higher the discount rate the lower the valuation, and vice versa.

Go back to the bird in the hand against the two in the bush.

A high discount rate says that the birds in the bush are too risky or there are better options out there. So, we better get a good price for our cash in hand.

A low discount rate says that the birds in tomorrow’s bush are pretty low risk, or there simply aren’t many other options there. We will more easily part with our cash in hand—in other words pay higher valuations for the stock investment.

The Two Major Types of Discount Rates

When you start getting into actually using discount rates in a DCF model, you might be confused that most DCFs don’t actually use those two simple components that I explained above.

Instead, you often hear using a “WACC” (weighted average cost of capital), which is split into the three components of “Cost of Equity”, “Cost of Debt”, and “Cost of Preferred”.

What I explained with the discount rate estimating Riskiness and Opportunity Cost is really just a Cost of Equity.

It did NOT consider how much debt a company has.

In the real world, companies have debt and those with heavier debt loads are more risky. To account for that, investors should use “levered beta” versus “unlevered beta”. That’s more hairy, and you can read a great breakdown here.

Before you fully dive into the greeks however, let’s finish our discussion on types of discount rates so you have the entire picture and don’t miss the forest for the trees.

The two major types of discount rates are:

  1. Cost of Equity
  2. WACC

To determine which discount rate to use, you have to determine which kind of a DCF model you are going to use. There are two major types of DCFs:

  1. Levered Free Cash Flow to Equity (FCFE)
  2. Unlevered Free Cash Flow to Firm (FCFF)

Simply put, FCFE uses a Cost of Equity. FCFF uses a WACC.

With that mouthful, the simplest way to think of the two types of FCF, Equity and Firm, is to think of the two types of “owners” of a company’s cash flows.

There are two major ways a company will tend to raise cash.

One—they will borrow it.
Two—they will issues shares (equity), typically through an IPO.

When a company borrows cash, they make a debt agreement where the lender gets a guaranteed flow of future cash. Just like with a credit card bill, a lender will expect future cash payments from the borrowing company.

The lender always gets “first claim” to a company’s cash flows, because of the debt agreement.

Whatever is left after paying back what is due for debt becomes free cash for owners.

In the stock market, the owners are equity shareholders. They get the rest of the claim to the cash flows; this is why cash flows after debt (interest payments) is called Free Cash Flow to Equity.

You can use either FCFE or FCFF, which means you can use the Cost of Equity as the discount rate, or the WACC.

But you have to make sure you use the Cost of Equity discount rate for FCFE DCFs and the WACC discount rate for FCFF DCFs, you CAN NOT mix the two.

Final Thoughts

At the end of the day, a simple discount rate formula just tries to measure the attractiveness of those two birds in the bush (in the future) versus your cash in the hand today.

Once you understand and learn the Cost of Equity and how that can be a discount rate, it becomes much easier to then understand the WACC, since the Cost of Equity is one part of the WACC.

I hope you take each step of a DCF with one piece at a time, and don’t try to learn it all at once. Even the Free Cash Flow part of a DCF can get confusing and overwhelming, especially if you’re trying to understand the discount rate part at the same time.

If I could sum it all up for you, it’d be these two concepts:

  1. The discount rate compares risk, other options, and projected future return
  2. The higher the discount rate, the lower the intrinsic value of today’s cash flows

Best of luck and feel free to ask any questions in the comments, and I’ll do my best to answer them when I can.

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