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### Step by step through the calculation

I use what is known as a 2-stage model, which simply means we have two different periods of varying growth rates for the company’s cash flows. Generally the first stage is higher growth, and the second stage is a more stable growth phase. To begin with we have to get estimates of the next five years of cash flows. For this I used the consensus of the analysts covering the stock, as you can see below. The sum of these cash flows is then discounted to today’s value.

#### 5-year cash flow estimate

 2018 2019 2020 2021 2022 Levered FCF (€, Millions) €110.02 €144.02 €158.25 €173.20 €181.50 Source Analyst x1 Analyst x2 Analyst x2 Analyst x1 Analyst x1 Present Value Discounted @ 13.08% €97.29 €112.63 €109.44 €105.93 €98.16

Present Value of 5-year Cash Flow (PVCF)= €523

We now need to calculate the Terminal Value, which accounts for all the future cash flows after the five years. For a number of reasons a very conservative growth rate is used that cannot exceed that of the GDP. In this case I have used the 10-year government bond rate (0.7%). In the same way as with the 5-year ‘growth’ period, we discount this to today’s value at a cost of equity of 13.1%.

Terminal Value (TV) = FCF2022 × (1 + g) ÷ (r – g) = €182 × (1 + 0.7%) ÷ (13.1% – 0.7%) = €1,478

Present Value of Terminal Value (PVTV) = TV / (1 + r)5 = €1,478 / ( 1 + 13.1%)5 = €799

The total value, or equity value, is then the sum of the present value of the cash flows, which in this case is €1,323. In the final step we divide the equity value by the number of shares outstanding. If the stock is an depositary receipt (represents a specified number of shares in a foreign corporation) or ADR then we use the equivalent number. This results in an intrinsic value of €15.11, which, compared to the current share price of €16.85, we see that Arcadis is fair value, maybe slightly overvalued at the time of writing.

### 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 my inputs, I recommend redoing the calculations yourself and playing with them. Because we are looking at Arcadis as potential shareholders, the cost of equity is used as the discount rate, rather than the cost of capital (or weighed average cost of capital, WACC) which accounts for debt. In this calculation I’ve used 13.1%, which is based on a levered beta of 1.332. This is derived from the Bottom-Up Beta method based on comparable companies, with an imposed limit between 0.8 and 2.0, which is a reasonable range for a stable business.

### Next Steps:

Although the valuation of a company is important, it shouldn’t be the only metric you look at when researching a company. For ARCAD, I’ve compiled three relevant aspects you should further examine:

1. Financial Health: Does ARCAD 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 ARCAD’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 ARCAD? Explore our interactive list of high quality stocks to get an idea of what else is out there you may be missing!

PS. The Simply Wall St app conducts a discounted cash flow for every stock on the ENXTAM every 6 hours. If you want to find the calculation for other stocks just search here. 