Our discounted cash flow calculator allows users to quickly and easily adjust different variables
to get an intrinsic value for the company. We find the best way to learn is be doing, so we start by doing a complete walkthrough through an entire
discounted cash flow analysis, starting at estimating revenue growth rates, all the way down until we get the intrinsic value.
We also provide definitions of each variable (and how they relate to our calculator), as well as
the different formulas we use to get the intrinsic value based on your input.
It is important to remember that a DCF calculaion should be based on your story for the company. Some people may have a
different story then you. This is not financial/investment advice, and is meant for educational purposes.
In this example we go through a complete discounted cash flow calculation for Apple. We show you where to get the data needed and why we choose certain numbers. The numbers you choose should reflect the story that YOU believe the company will have going forward. This example may not be up to date at the time of you reading, and is not meant as financial advice. It is simply an example to help show you how to use the calculator.
In order to get revenue growth rates, we recommend looking at a variety of different methods to get a better idea. In this example we will look at analyst predictions, historical trends, and Apple's annual reports.
Revenue growth in year
one is generally much easier to predict, and often times companies will provide their own guidance for the next year.
According to YahooFinance, Analysts currently predict 4.3% revenue growth for the current year, and 4.4% for next year. 2021 Y/Y growth was 33.26%. This was
largely due to the release of 2 new iPhone models in the fiscal year. We expect revenue growth to be much lower than last year,
revenue growth from iPhone will likely be negative, but we expect revenue from services to grow at 20%+.
We are going to use 5% for Year one.
Depending on where your company is in their business cycle, they might have explosive growth during these years, or slowing growth for more mature companies.
I expect Apple to have slower growth for the next 2 years, then a spike due to newer iPhone models (every 3 years revenue from iPhone's spikes). I also expect their revenue from
services will continue to increase at an average of 15-20% per year over the next 5 years.
Analysts predict 4.4% growth for next year, but 15.43% growth per annum for the next 5 years.
We are going to use 6% growth for years 2-5.
For revenue growth in perpetuity we will keep it as the default, which is the current 10 year US risk free rate. This prevents us from using
an impossible growth rate, and also allows valuation consistency. We get this from
the current 10 year US treasury yield. In our calculator, this is updated daily for us automatically, but if you are valuing a company in another currency other then
USD, you should change it to reflect the countries risk free rate. If you think the risk free rate will be higher in the future, you
may change this number, but your cost of capital should also reflect this change. You must be consistent throughout the valuation.
As of the time of this writing, the 10 year risk free rate was 1.68%. That is what we will use for our revenue growth in perpetuity.
Operating margins can be estimated by looking at the average/trend over the past 5 years, the industry average, and ongoing competition. You should also look into the annual reports to determine what is causing those trends, if they will continue, and anything else that might affect it going forward. Here are a few examples of things that can affect operating margin;
The marginal tax rate is used here as we make the assumption that after 10 years, the effective tax rate will be equal to marginal tax rate.
In this case, Apple pays taxes in many countries around the world. Most of the taxes they pay are in the United States, where their is a flat
21% federal corporate tax rate. With state taxes it is closer to 25%. At the time of this writing there is talk of raising it to 28%.
For this example, we will be using 25%.
Sales to capital is an efficiency ratio, used to determine how much revenue is generated per dollar of invested capital.
For sales to capital, it's a good idea to look at the company average/trend over the past 5 years, as well as the industry average.
We will get the industry average from Aswath Damodaran's data, which is provided on the same page as our calculator.
Industry Average: 1.81
5 Year Average: 2.35
TTM: 2.92
Trending up over the last 5 years, as Apple has improved efficiency
We will use 2.9 for Year one, 3 for years 2-5, and 3.3 for years 6-10.
The cost of capital is the primary method for measuring and adjusting for risk in the expected
cash flows. It can also be described as the risk-adjusted discount rate.
This is probably the most difficult step, and although important, it is not as crucial as your growth estimates.
Although there are a lot of services out there that offer weighted average cost of capital for companies, they all use different formulas.
Many of them use a market premium that is quite high. We are going to use an implied equity risk premium.
Aswath Damodaran also provides sector averages for cost of capital, which we provide on the DCF page.
We will be calculating it as per Aswath Damodaran's teachings, which is calculated as per the picture below. For year 10, we will use
his recommendation for typical mature companies in stable growth, which is risk free rate + 4.5%. Don't forget this should reflect
any changes you made to revenue growth in perpetuity earlier.
The risk free rate should be the countries 10 year t-bond rate, minus default risk. We assume the US has no default risk, so in
this example, since we are valuing in US dollars, our risk free rate is 1.68%. If you want to use a more normalized risk free rate,
you can, but you must reflect that in your growth as well. You must be consistent throughout the valuation.
We are going to use an implied equity risk premium of 4.53%, which is provided by Aswath Damodaran at https://pages.stern.nyu.edu/~adamodar/
Finally it will calculate our intrinsic value for us. In this case it comes back with an intrinsic value of $125.88
The final step is to check the final numbers to make sure they make sense, and then do a sensitivty analysis to see how different inputs affect the intrinsic value. To do this you will check the terminal year revenues and overall value against other companies in the sector, to make sure they are reasonable. You can then slighlty change revenue growth, operating margins, or other variables to see the affect it has on intrinsic value, in case you're story doesn't quite play out how you originally thought.
Revenue is the money generated from normal business operations, calculated as the average sales price times the number of units sold. It is the top line (or gross income) figure from which costs are subtracted to determine net income.
Revenue growth is the percentage change between revenue in a given time period. In the context of our calculator, we have revenue growth year 1, years 2-5, and revenue growth in perpuitity, which we will talk about in the next section. Revenue growth can be chosen based on a variety of factors, such as analyst predictions, company trends, new products the company may have in the future, ect.
The risk-free rate of return is the theoretical rate of return of an investment with zero risk. The risk-free rate represents the interest an investor would expect from an absolutely risk-free investment over a specified period of time. The so-called "real" risk-free rate can be calculated by subtracting the current inflation rate from the yield of the Treasury bond matching your investment duration.
The operating margin measures how much profit a company makes on a dollar of sales after paying for variable costs of production, such as wages and raw materials, but before paying interest or tax. It is calculated by dividing a company’s operating income by its net sales. Higher ratios are generally better, illustrating the company is efficient in its operations and is good at turning sales into profits.
Operating income is the amount left after subtracting operating expenses from revenue. It does not subtract interest expenses or taxes. It is often also referred to as Earnings Before Interest and Taxes (EBIT).
The sales to capital ratio, also known as the capital turnover ratio or sales to working capital ratio, is an efficiency ratio. The sales to capital ratio tell us how efficiently a company can turn one dollar of capital into one dollar of revenue.
Free cash flow to firm is the amount of cash left over after taking into account operating expenses, taxes, and reinvestment needs.
For valuation purposes, cost of capital can be thought of as the hurdle rate, or the opportunity cost. It is used to discount our valuation back to present value.
Cost of debt is the rate at which a company can borrow long-term today. If a company has long-term bonds outstanding or has recently borrowed from a bank long term,
you can use the interest rate on those.
The equity risk premium is the premium above the risk free rate that an investor requires to make an
investment worth the added risk.
Often times analysts use historic equity risk premiums, by taking the historic average annual return in the stock market
and subtracting the historic average annual return from t-bonds.
The issue with this is that your answer will depend on various factors, such as; how far back in history you go, whether you use T-bill or T-bond rates,
whether you use a geometric or arithmetic averages, ect.
For that reason we use implied equity risk premium for our calculation.
The implied equity risk premium is a forward looking equity risk premium.
To calculate the implied equity risk premium, you take the expected return on stocks and subtract the 10 year t-bond rate.
Aswath Damodaran also calculates this on a monthly basis, and posts the results on his website at https://pages.stern.nyu.edu/~adamodar/
The risk free rate must have no default risk and no reinvestment risk. For US dollars we use the 10 year treasury bond rate, as we assume the US has no default risk. The reason we use the 10 year instead of another time frame, is that we generally estimate cashflows for a long time into the future, and the 10 year is updated often.
