In this article we are going to estimate the intrinsic value of PagSeguro Digital Ltd. (NYSE:PAGS) by taking the expected future cash flows and discounting them to their present value. I will be using 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.

Check out our latest analysis for PagSeguro Digital

### What's the estimated valuation?

We are going to use a two-stage DCF model, which, as the name states, takes into account two stages of growth. The first stage is generally a higher growth period which levels off heading towards the terminal value, captured in the second 'steady growth' period. 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.

Generally we assume that a dollar today is more valuable than a dollar in the future, and so the sum of these future cash flows is then discounted to today's value:

#### 10-year free cash flow (FCF) estimate

2020 | 2021 | 2022 | 2023 | 2024 | 2025 | 2026 | 2027 | 2028 | 2029 | |

Levered FCF (R$, Millions) | R$1.76b | R$2.35b | R$2.81b | R$3.20b | R$3.52b | R$3.80b | R$4.02b | R$4.21b | R$4.37b | R$4.51b |

Growth Rate Estimate Source | Analyst x2 | Analyst x2 | Est @ 19.15% | Est @ 13.93% | Est @ 10.27% | Est @ 7.71% | Est @ 5.92% | Est @ 4.67% | Est @ 3.79% | Est @ 3.17% |

Present Value (R$, Millions) Discounted @ 11% | R$1.6k | R$1.9k | R$2.1k | R$2.1k | R$2.1k | R$2.1k | R$2.0k | R$1.9k | R$1.8k | R$1.6k |

*("Est" = FCF growth rate estimated by Simply Wall St)***Present Value of 10-year Cash Flow (PVCF)** = R$19b

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 (1.7%) 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 11%.

**Terminal Value (TV)**= FCF_{2029} Ã— (1 + g) Ã· (r â€“ g) = R$4.5bÃ— (1 + 1.7%) Ã· 11%â€“ 1.7%) = R$52b

**Present Value of Terminal Value (PVTV)**= TV / (1 + r)^{10}= R$52bÃ· ( 1 + 11%)^{10}= R$19b

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 R$38b. In the final step we divide the equity value by the number of shares outstanding. Compared to the current share price of US$28.8, the company appears around fair value at the time of writing. Remember though, that this is just an approximate valuation, and like any complex formula - garbage in, garbage out.

### The assumptions

The calculation above is very dependent on two assumptions. The first is the discount rate and the other is the 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 PagSeguro Digital 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 11%, which is based on a levered beta of 0.960. 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:

Although the valuation of a company is important, it 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 PagSeguro Digital, I've compiled three pertinent factors you should look at:

**Future Earnings**: How does PAGS'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 PAGS? 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 valuation for every stock on the NYSE every day. If you want to find the calculation for other stocks 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.*