Calculating The Fair Value Of Bouygues SA (EPA:EN)

Today we will run through one way of estimating the intrinsic value of Bouygues SA (EPA:EN) 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.

Companies can be valued in a lot of ways, so we would point out that a DCF is not perfect for every situation. Anyone interested in learning a bit more about intrinsic value should have a read of the Simply Wall St analysis model.

View our latest analysis for Bouygues

What's the estimated valuation?

We're using the 2-stage growth model, which simply means we take in account two stages of company's growth. In the initial period the company may have a higher growth rate and the second stage is usually assumed to have a stable growth rate. To start off with, we need to estimate 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.

A DCF is all about the idea that a dollar in the future is less valuable than a dollar today, so we discount the value of these future cash flows to their estimated value in today's dollars:

10-year free cash flow (FCF) estimate

	2020	2021	2022	2023	2024	2025	2026	2027	2028	2029
Levered FCF (€, Millions)	€836.0m	€913.6m	€1.07b	€1.03b	€1.01b	€994.9m	€987.5m	€984.0m	€983.2m	€984.4m
Growth Rate Estimate Source	Analyst x6	Analyst x5	Analyst x2	Est @ -3.28%	Est @ -2.12%	Est @ -1.32%	Est @ -0.75%	Est @ -0.35%	Est @ -0.08%	Est @ 0.12%
Present Value (€, Millions) Discounted @ 9.4%	€764	€763	€813	€718	€642	€579	€525	€478	€437	€400

("Est" = FCF growth rate estimated by Simply Wall St)
Present Value of 10-year Cash Flow (PVCF) = €6.1b

After calculating the present value of future cash flows in the intial 10-year period, we need to calculate the Terminal Value, which accounts for all future cash flows beyond the first stage. 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 (0.6%) 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 9.4%.

Terminal Value (TV)= FCF₂₀₂₉ × (1 + g) ÷ (r – g) = €984m× (1 + 0.6%) ÷ 9.4%– 0.6%) = €11b

Present Value of Terminal Value (PVTV)= TV / (1 + r)¹⁰= €11b÷ ( 1 + 9.4%)¹⁰= €4.5b

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 €11b. In the final step we divide the equity value by the number of shares outstanding. Compared to the current share price of €27.7, the company appears about fair value at a 1.1% discount to where the stock price trades currently. Remember though, that this is just an approximate valuation, and like any complex formula - garbage in, garbage out.

Important assumptions

The calculation above is very dependent on two assumptions. The first is the discount rate and the other is the cash flows. You don't have to agree with these inputs, I recommend redoing the calculations yourself and playing with them. 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 Bouygues 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 9.4%, which is based on a levered beta of 1.281. 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.

Next Steps:

Valuation is only one side of the coin in terms of building your investment thesis, and 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 Bouygues, We've put together three further aspects you should look at:

1. Risks: Consider for instance, the ever-present spectre of investment risk. We've identified 3 warning signs with Bouygues , and understanding them should be part of your investment process.
2. Future Earnings: How does EN'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.
3. Other Solid Businesses: Low debt, high returns on equity and good past performance are fundamental to a strong business. Why not explore our interactive list of stocks with solid business fundamentals to see if there are other companies you may not have considered!

PS. Simply Wall St updates its DCF calculation for every FR stock every day, so if you want to find the intrinsic value of any other stock just search here.

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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. We aim to bring you long-term focused analysis driven by fundamental data. Note that our analysis may not factor in the latest price-sensitive company announcements or qualitative material. Simply Wall St has no position in any stocks mentioned. Thank you for reading.