What You’ll Learn
- The difference between an investors discount rate analysis and corp finance discount rates
- How to choose a discount rate
- How to apply discount rates as a stock investor
- Rules of Thumb for deciding on discount rates
Discount Rate Analysis
What type of person are you?
- DIY investor looking to determine what price you should pay for a stock.
- Corporate finance professional doing mergers, buyouts, or MBA students taking valuation classes.
This discussion of discount rates is dedicated to #1 – The everyday investor focusing on valuing public stocks to determine a good entry and exit point of the stock.
The details and discussion that goes into corp finance discount rates is a different beast. As a small investor, you have more leeway, and by following simple rules of thumbs, you can apply DCF stock valuations to get a good and surprisingly accurate fair value range.
In the corp finance world, the intricacies involved with calculating discount rates include matching the correct cash flow types, risk-free rates, tax rates, betas, market risk premium, country risk premium, and so on.
Typically, here’s an example of the types of inputs and calculations you will have to do for Weighted Average Cost of Capital (WACC) and corporate discount rate calculations.
As an individual investor, how much of this information is important?
And how much does all this data affect the fair value of a company?
Making adjustments to the unlevered beta or risk-free rate will definitely change the final valuation, but that’s only important if your goal is to pinpoint it to the nearest cent.
In the stock market, such accuracy is not needed and it will only lead to biases and overconfidence.
Using Discount Rates like an Everyday Investor
Before getting into the meat of the content on discount rates, here’s a look at Siri’s (SIRI) fair value using a discount rate of 7% and 9%.
To keep it simple, I’m only going to adjust the discount rate to see the effect of discount rate changes.
With a 9% discount rate, FCF of 1.5B and all other inputs being equal, the fair value for SIRI comes out to $5.40 per share.
Change the discount rate to 7% and the fair value is now $6.63 per share. Also, consider that discount rates in general operate within a tight range.
I’ve never seen a DCF model using a 30% discount rate. Conversely, I’ve never seen a DCF using a 2% discount rate. For a 2% discount rate, you might as well buy guaranteed government bonds.
When it comes to actually usable discount rates, expect it to be within a 6-12% range. The problem is that analysts spend too much of their time finessing and massaging basis points.
What’s the difference between having 7% and 7.34%?
- 7% discount rate = $6.63
- 7.34% discount rate = $6.40
If your buy/sell decision depends on a difference of $0.23, there’s something wrong.
For my part, I did the calculations lazily for SIRI in 30 seconds. It’s a simple way to get the ball rolling for further analysis and refining.
The fair value difference between a 7% and 9% discount rate is $1.23. For SIRI, I can start my initial assumption of fair value to be in the range of $5.40 to $6.63 and then continue to fine-tune it from there.
We don’t believe in single fair values around here.
Before I keep going, though, I want to let you know about my favorite stock ratios, which are super helpful for analyzing a stock’s fundamentals. Click the image to have them sent directly to your inbox.
Anyway, this is the important point I want to make in this discount rate discussion. I am referring to discount rates relevant to investors.
There are plenty of books and material for MBA students out there to learn about discount rates, weighted average cost of capital (WACC), CAPM models and so on, but not enough practical and usable content for value investors who don’t need all the details.
Cost of Capital Definition
I use the term cost of capital and discount rate interchangeably as a public equities investor.
Investopedia explains the difference as:
The cost of capital refers to the actual cost of financing business activity through either debt or equity capital. The discount rate is the interest rate used to determine the present value of future cash flows in standard discounted cash flow analysis. Many companies calculate their weighted average cost of capital and use it as their discount rate when budgeting for a new project. This figure is crucial in generating a fair value for the company’s equity.
However, this definition boxes it in too much.
Prof Aswath Damodaran provides one of the best approaches to wrapping your head around the terms.
Defining the Cost of Capital
There are three different ways to frame the cost of capital and each has its use. Much of the confusion about measuring and using the cost of capital stems from mixing up the different definitions:
- For businesses, the cost of capital is a cost of raising financing: The first is to read the cost of capital literally as the cost of raising funding to run a business and thus build up to it by estimating the costs of raising different types of financing and the proportions used of each. This is what we do when we estimate a cost of equity, based on a beta, betas or some other risk proxy, a cost of debt, based upon what the business can borrow money at and adjusting for any tax advantages that might accrue from borrowing.
- For businesses, the cost of capital is an opportunity cost for investing in projects: The cost of capital is also an opportunity cost, i.e., the rate of return that the business can expect to make on other investments, of equivalent risk. The logic is simple. If you are considering investing in a new asset or security, you have to earn more than you could make by investing the money elsewhere. There are two subparts to this statement. The first is that it is the choices that you have today that should determine this opportunity cost, not choices that you might have had in the past. The second is that it has to be on investments of equivalent risk. Thus, the cost of capital should be higher for riskier investments than safe ones.
- For investors, the discount rate is an opportunity cost of capital to value a business: Investors looking at buying into a business have many different options, but if you invest one business, you can’t invest that same money in another. So the discount rate reflects the hurdle rate for an investment to be worth it to you vs. another company.
Following on point number 3, the discount rate for value investors is your desired rate of return to be compensated for the risk.
The part that trips up many people is this:
“While discount rates obviously matter in DCF valuation, they don’t matter as much as most analysts think they do.”Aswath Damodaran
Because if you actively think about how you use discount rates day-to-day, you will find that you use them like a yardstick for your rate of return.
After all, even if businesses use WACC as a way of raising financing or calculating it as an opportunity cost, the cost of capital has to be measured against something.
That something is a rate of return.
Nobody and no business lends or invests money without weighing what the returns will be or comparing it against some other form of investment return. Banks lend money to people at different interest rates depending on the financial risk profile. I invest in the stock market willing to take on more risk than a savings account or a guaranteed treasury bond, for a rate of return exceeding both.
The value of any stock, bond or business today is determined by the cash inflows and outflows – discounted at an appropriate interest rate – that can be expected to occur during the remaining life of the asset.Warren Buffett
The interest rate that Buffett mentions here resembles the desired rate of return.
This is a lot of talk on discount rates, so let’s make it more practical.
Calculate the Future Value
To see how discount rates work, calculate the future value of a company by predicting its future cash generation and then adding the total sum of the cash generated throughout the life of the business.
This requires you to calculate a growth rate and then apply it to the company’s free cash flow.
To illustrate, let’s assume a company’s fiscal filing revealed $100 in free cash this year. With a growth rate of 10%, the company will be able to generate $110 in free cash next year and $121 the year after and so on for the next 10 years. The total sum of the free cash for the next 10 years comes out to $1,753.
The Present Value of a Company
But the sum of $1,753 over 10 years is not worth $1,753 today.
If you had the choice of receiving a total sum of $1,753 spread out over 10 years or $1,753 in one lump sum today, which would you choose?
The single up-front payment, of course.
Before I explain why, let me show you:
|Year||Cash Flow||Discount Factor||Present Value|
Getting $1,753 paid out over 10 years is worth the same as having $1,000 today (assuming your personal discount rate is 10%).
Does that make sense? Another way to put it is, if I give you $1000 today, I expect to be paid $110 in one year, $121 in two years, and so on for 10 years, to meet my internal required rate of return of 10%.
The Time Value of Money
That’s because of the time value of money. You know intuitively that a dollar today is worth more than a dollar a year from now.
Part of that is due to inflation: you’d need about $1.02 in a year for it to just have the same purchasing power (2% inflation rate).
But nobody wants to just have the same amount of money next year — you want to earn a return on it! If you invested in the stock market, you could turn that $1 into $1.10 or $1.30. A dollar next year is no good to you, because you’ve lost out on a year of deploying it to make additional returns. This is the opportunity cost of your capital.
The last reason a dollar in the future is worth less than one today is because a dollar in your hand now is guaranteed, but a future payment always has some uncertainty. Instead of turning your $1 into $1.30 in the stock market, it could turn into $0.80 in a bad year. That risk also needs to be built into your required hurdle rate of return.
The point is, you need to discount the future cash flows of the businesses you’re investing in, because money in the future is worth less than money today. And the discount rate you choose should be based on the rate of return you require for your investment, which is usually a function of both the uncertainty of the investment and what else you can invest in.
Calculating the Discount Factor
In case you’re wondering how to calculate the discount factor in the above table, well, it’s closely related to calculating the growth rate at period t.
To calculate what $100 will turn into in 5 years of compounded 10% growth, the formula is:
So, to figure out the discount factor that will show that the present value of $161 in 5 years is $100 today, you do:
Or, more generally:
Where r is the discount rate and p is the number of periods.
If you want to calculate your own discounted cash flows, you’ll need this. But you don’t actually need this for figuring out what your personal investor discount rate should be.
Choosing a Discount Rate
As an everyday investor, you do not need to use complex inputs and models. I admit my method is far from perfect. But it gets better each year as I continue to refine my approach.
Prof Damodaran provides awesome tips and has written a great piece on being consistent.
1. Unit Consistency: a DCF first principle is that your cash flows have to be defined in the same terms and unit as your discount rate.
2. Input Consistency: The value of a company is a function of three key components: its expected cash flows, the expected growth in these cash flows, and the uncertainty you feel about whether these cash flows will be delivered. A discounted cash flow valuation requires assumptions about all three variables but for it to be defensible, the assumptions that you make about these variables have to be consistent with each other.
3. Narrative consistency: a good valuation connects narrative to numbers. A good DCF valuation has to follow the same principles and the numbers have to be consistent with the story that you are telling about a company’s future and the story that you are telling has to be plausible, given the macroeconomic environment you are predicting, the market or markets that the company operates in and the competition it faces.
Not as simple as it looks, but not as hard as it seems.
Here are some rules of thumb to help choose a discount rate that should apply to the majority of investors.
- Most likely you will use FCF as the cash flow. It is the most common value you’ll come across and one that is easy for value investors.
- FCF is post-tax and not adjusted for inflation (real, not nominal value).
- Therefore, the discount rate should also be considered post-tax.
- E.g., if you like to use 10% returns in your calculations, you are likely thinking about a 10% pre-tax return. If you do desire a 10% return post-tax, then your pre-tax discount rate is likely 11.5 to 13%. But again, if your pre-tax desired rate of return is 10%, then your post-tax discount rate should be 7 to 8.5%.
In terms of what the discount rate should be, that’s up to you.
There is no hard and fast rule for choosing a discount rate. As we’ve discussed, there is a common range of discount rates, but the final choice is based on your expectations and narrative.
If you choose to use a high discount rate such as 12% or 15% to discount the future cash, it just means you are willing to pay less today for the future cash.
But an important point to understand is that
“You can’t compensate for risk by using a high discount rate.”
If 15% was used to discount $1,753, you would only be willing to pay $1,524 in today’s money for $1,753.
On the other hand, using a 9% discount rate would give a value of $1,608 for the $1,753.
You can see how using a high discount rate will give a lower valuation than a low discount rate like the example with SIRI from earlier.
But Buffett Used The 10 Year Treasury Rate!
Here’s an important side trip in this discussion.
When Warren Buffett first started to build a position in Coca-Cola in 1987, he used the treasury rate as a yardstick.
Check out these 10 year Treasury rates.
- 1980: 10.8%
- 1981: 12.57%
- 1982: 14.59%
- 1983: 10.46%
- 1984: 11.67%
- 1985: 11.38%
- 1986: 9.19%
- 1987: 7.08%
- 1988: 8.67%
- 1989: 9.09%
- 1990: 8.21%
When he started accumulating Coca-Cola, the rate was 7%, but only 2 years removed from double digits.
I wouldn’t be surprised if he was thinking that interest rates would rise again. So using a discount rate of 11%+ to start buying Coca-Cola made total sense.
You can see how choosing and thinking through a narrative is important in choosing a discount rate.
Buffett’s choice to discount by the treasury rate was his minimum required return. He also used the treasury rate as a measuring stick for all businesses, rather than assigning a different rate for different businesses.
“In order to calculate intrinsic value, you take those cash flows that you expect to be generated and you discount them back to their present value – in our case, at the long-term Treasury rate. And that discount rate doesn’t pay you as high a rate as it needs to. But you can use the resulting present value figure that you get by discounting your cash flows back at the long-term Treasury rate as a common yardstick just to have a standard of measurement across all businesses.”
So What Is A Good Discount Rate?
I like to use a post-tax discount rate of 7-12%.
Like Buffett, I have a minimum return rate that I want and that happens to be between 7-12% in today’s world of low interest rates and dependent on the type of company.
In the example above using SIRI, I used 7% and 9% to show the difference it can make. As SIRI is a company with strong cash flows, strong ownership and a business model that can churn out money, a high discount rate doesn’t make sense.
That’s my narrative.
If we thought we were getting a stream of cash over the thirty years that we felt extremely certain about, we’d use a discount rate that would be somewhat less than if it were one where we expected surprises or where we thought there were a greater possibility of surprises. – Buffett & Munger Shareholder Meeting
If the company was a biotech with no revenue streams and only a single drug in phase 2 or 3 trials, the discount rate would be significantly higher.
Now it seems like the longer this gets, the more I’m confusing you… But I’ll add another piece of information anyways.
Don’t use different discount rates for different businesses…it doesn’t really matter what rate you use as long as you are being intellectually honest and conservative about future cash flows.Buffett & Munger Shareholder Meeting
Don’t Forget Margin Of Safety
Whatever rate you choose, never forget to apply a margin of safety to the final intrinsic value because no one can accurately predict the future. But note that a high discount rate may warrant a lower margin of safety — but that is up to the investor.
10 years ago, I regularly used a 12-15% discount rate with a 25% or 50% margin of safety.
Today, it’s in the 7-12% range with a 25% margin of safety. I would love to get back to the days when you could buy $1 for $0.50, but reality bites.
As an individual investor, I’m not being pressured by peers and other analysts to conform to their models and inputs.
I have freedom to choose my discount rates based on my narrative and by keeping it consistent with my investment goals and strategy.
Please be careful that you do not match your discount rate to the valuation you want to see. But rather, you should approach the valuation and discount rate process as a way to poke and prod to discover the fair value range of a stock.
I run across people who use our Old School Value DCF model and enter numbers to match what they want to see. The outcome isn’t good of course.
Don’t justify the purchase of a company just because it fits the numbers. Don’t fool yourself into believing that a cheap company will yield good returns because you’ve used some cool numbers.
- This discussion is for individual value investors. Not for corp finance, MBA or CFA study.
- Discount rates WILL affect your valuation
- Discount rates are usually range bound. You won’t use a 3% or 30% discount rate. Usually within 6-12%.
- For investors, the cost of capital is a discount rate to value a business.
- Discounts rates for investors are required rates of returns
- Be consistent in how you choose your discount rate
- Don’t forget margin of safety. A high discount rate is not a margin of safety.