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# Estimating The Fair Value Of VINCI SA (EPA:DG)

Does the December share price for VINCI SA (EPA:DG) reflect what it's really worth? Today, we will estimate the stock's intrinsic value by taking the expected future cash flows and discounting them to their present value. This is done using the Discounted Cash Flow (DCF) model. It may sound complicated, but actually it is quite simple!

Remember though, that there are many ways to estimate a company's value, and a DCF is just one method. 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.

View our latest analysis for VINCI

### Crunching the numbers

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 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 (â‚¬, Millions) â‚¬3.83b â‚¬4.05b â‚¬4.11b â‚¬4.16b â‚¬4.21b â‚¬4.25b â‚¬4.29b â‚¬4.33b â‚¬4.36b â‚¬4.40b Growth Rate Estimate Source Analyst x10 Analyst x8 Est @ 1.56% Est @ 1.31% Est @ 1.14% Est @ 1.02% Est @ 0.93% Est @ 0.87% Est @ 0.83% Est @ 0.8% Present Value (â‚¬, Millions) Discounted @ 9.5% â‚¬3.5k â‚¬3.4k â‚¬3.1k â‚¬2.9k â‚¬2.7k â‚¬2.5k â‚¬2.3k â‚¬2.1k â‚¬1.9k â‚¬1.8k

("Est" = FCF growth rate estimated by Simply Wall St)
Present Value of 10-year Cash Flow (PVCF) = â‚¬26b

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 (0.7%) 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 9.5%.

Terminal Value (TV)= FCF2029 Ã— (1 + g) Ã· (r â€“ g) = â‚¬4.4bÃ— (1 + 0.7%) Ã· 9.5%â€“ 0.7%) = â‚¬51b

Present Value of Terminal Value (PVTV)= TV / (1 + r)10= â‚¬51bÃ· ( 1 + 9.5%)10= â‚¬21b

The total value, or equity value, is then the sum of the present value of the future cash flows, which in this case is â‚¬47b. In the final step we divide the equity value by the number of shares outstanding. Compared to the current share price of â‚¬96.8, the company appears around fair value at the time of writing. 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.

### 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 VINCI 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 9.5%, which is based on a levered beta of 1.312. 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:

Whilst important, DCF calculation shouldnâ€™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 VINCI, I've compiled three essential aspects you should further examine:

1. Financial Health: Does DG 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.
2. Future Earnings: How does DG'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 High Quality Alternatives: Are there other high quality stocks you could be holding instead of DG? 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 FR stock every day, so if you want to find the intrinsic value of any other stock just search here.

If you spot an error that warrants correction, please contact the editor at editorial-team@simplywallst.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.

We aim to bring you long-term focused research analysis driven by fundamental data. Note that our analysis may not factor in the latest price-sensitive company announcements or qualitative material. Thank you for reading.