Today we will run through one way of estimating the intrinsic value of Arch Coal, Inc. (NYSE:ARCH) by taking the expected future cash flows and discounting them to today's value. I will use the Discounted Cash Flow (DCF) model. Don't get put off by the jargon, the math behind it is actually quite straightforward.
We generally believe that a company's value is the present value of all of the cash it will generate in the future. However, a DCF is just one valuation metric among many, and it is not without flaws. If you want to learn more about discounted cash flow, the rationale behind this calculation can be read in detail in the Simply Wall St analysis model.
Step by step through the calculation
We use what is known as a 2-stage model, which simply means we have two different periods of growth rates for the company's cash flows. Generally the first stage is higher growth, and the second stage is a lower growth phase. To begin with, we have to get estimates of the next ten years of cash flows. Where possible we use analyst estimates, but when these aren't available we extrapolate the previous free cash flow (FCF) from the last estimate or reported value. We assume companies with shrinking free cash flow will slow their rate of shrinkage, and that companies with growing free cash flow will see their growth rate slow, over this period. We do this to reflect that growth tends to slow more in the early years than it does in later years.
Generally we assume that a dollar today is more valuable than a dollar in the future, so we discount the value of these future cash flows to their estimated value in today's dollars:
10-year free cash flow (FCF) forecast
Levered FCF ($, Millions)
Growth Rate Estimate Source
Est @ -27.06%
Est @ -18.12%
Est @ -11.87%
Est @ -7.49%
Est @ -4.42%
Est @ -2.28%
Est @ -0.77%
Est @ 0.28%
Present Value ($, Millions) Discounted @ 9.1%
("Est" = FCF growth rate estimated by Simply Wall St)
Present Value of 10-year Cash Flow (PVCF) = US$730m
We now need to calculate the Terminal Value, which accounts for all the future cash flows after this ten year period. For a number of reasons a very conservative growth rate is used that cannot exceed that of a country's GDP growth. In this case we have used the 10-year government bond rate (2.7%) to estimate future growth. In the same way as with the 10-year 'growth' period, we discount future cash flows to today's value, using a cost of equity of 9.1%.
Terminal Value (TV)= FCF2019 × (1 + g) ÷ (r – g) = US$84m× (1 + 2.7%) ÷ 9.1%– 2.7%) = US$1.3b
Present Value of Terminal Value (PVTV)= TV / (1 + r)10= US$1.3b÷ ( 1 + 9.1%)10= US$559m
The total value is the sum of cash flows for the next ten years plus the discounted terminal value, which results in the Total Equity Value, which in this case is US$1.3b. To get the intrinsic value per share, we divide this by the total number of shares outstanding. Compared to the current share price of US$77.8, the company appears about fair value at a 9.3% discount to where the stock price trades currently. Valuations are imprecise instruments though, rather like a telescope - move a few degrees and end up in a different galaxy. Do keep this in mind.
Now the most important inputs to a discounted cash flow are the discount rate, and of course, the actual cash flows. Part of investing is coming up with your own evaluation of a company's future performance, so try the calculation yourself and check your own assumptions. The DCF also does not consider the possible cyclicality of an industry, or a company's future capital requirements, so it does not give a full picture of a company's potential performance. Given that we are looking at Arch Coal as potential shareholders, the cost of equity is used as the discount rate, rather than the cost of capital (or weighted average cost of capital, WACC) which accounts for debt. In this calculation we've used 9.1%, which is based on a levered beta of 1.074. Beta is a measure of a stock's volatility, compared to the market as a whole. We get our beta from the industry average beta of globally comparable companies, with an imposed limit between 0.8 and 2.0, which is a reasonable range for a stable business.
Although the valuation of a company is important, it shouldn’t be the only metric you look at when researching a company. The DCF model is not a perfect stock valuation tool. Rather it should be seen as a guide to "what assumptions need to be true for this stock to be under/overvalued?" If a company grows at a different rate, or if its cost of equity or risk free rate changes sharply, the output can look very different. For Arch Coal, I've compiled three pertinent factors you should further examine:
Financial Health: Does ARCH have a healthy balance sheet? Take a look at our free balance sheet analysis with six simple checks on key factors like leverage and risk.
Future Earnings: How does ARCH's growth rate compare to its peers and the wider market? Dig deeper into the analyst consensus number for the upcoming years by interacting with our free analyst growth expectation chart.
Other High Quality Alternatives: Are there other high quality stocks you could be holding instead of ARCH? Explore our interactive list of high quality stocks to get an idea of what else is out there you may be missing!
PS. Simply Wall St updates its DCF calculation for every US stock every day, so if you want to find the intrinsic value of any other stock just search here.
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If you spot an error that warrants correction, please contact the editor at email@example.com. This article by Simply Wall St is general in nature. It does not constitute a recommendation to buy or sell any stock, and does not take account of your objectives, or your financial situation. Simply Wall St has no position in the stocks mentioned. Thank you for reading.