# An Intrinsic Calculation For Vitru Limited (NASDAQ:VTRU) Suggests It's 39% Undervalued

In this article we are going to estimate the intrinsic value of Vitru Limited (NASDAQ:VTRU) by projecting its future cash flows and then discounting them to today's value. We will use the Discounted Cash Flow (DCF) model on this occasion. There's really not all that much to it, even though it might appear quite complex.

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.

Check out our latest analysis for Vitru

## The Model

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, and so the sum of these future cash flows is then discounted to today's value:

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

 2023 2024 2025 2026 2027 2028 2029 2030 2031 2032 Levered FCF (R\$, Millions) R\$326.0m R\$463.5m R\$700.0m R\$769.0m R\$819.0m R\$857.3m R\$890.7m R\$920.5m R\$947.8m R\$973.4m Growth Rate Estimate Source Analyst x2 Analyst x2 Analyst x1 Analyst x1 Analyst x1 Est @ 4.68% Est @ 3.90% Est @ 3.35% Est @ 2.96% Est @ 2.70% Present Value (R\$, Millions) Discounted @ 13% R\$288 R\$361 R\$481 R\$467 R\$439 R\$405 R\$372 R\$339 R\$308 R\$279

("Est" = FCF growth rate estimated by Simply Wall St)
Present Value of 10-year Cash Flow (PVCF) = R\$3.7b

After calculating the present value of future cash flows in the initial 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 5-year average of the 10-year government bond yield (2.1%) 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 13%.

Terminal Value (TV)= FCF2032 × (1 + g) ÷ (r – g) = R\$973m× (1 + 2.1%) ÷ (13%– 2.1%) = R\$8.9b

Present Value of Terminal Value (PVTV)= TV / (1 + r)10= R\$8.9b÷ ( 1 + 13%)10= R\$2.5b

The total value, or equity value, is then the sum of the present value of the future cash flows, which in this case is R\$6.3b. In the final step we divide the equity value by the number of shares outstanding. Compared to the current share price of US\$22.0, the company appears quite good value at a 39% 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.

## The 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 Vitru 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 13%, which is based on a levered beta of 1.009. 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.

### SWOT Analysis for Vitru

Strength

• Earnings growth over the past year exceeded the industry.

Weakness

• Interest payments on debt are not well covered.

• Shareholders have been diluted in the past year.

Opportunity

• Annual earnings are forecast to grow faster than the American market.

• Trading below our estimate of fair value by more than 20%.

Threat

• Debt is not well covered by operating cash flow.

## Moving On:

Whilst important, the DCF calculation shouldn't be the only metric you look at when researching a company. DCF models are not the be-all and end-all of investment valuation. Preferably you'd apply different cases and assumptions and see how they would impact the company's valuation. For instance, if the terminal value growth rate is adjusted slightly, it can dramatically alter the overall result. Can we work out why the company is trading at a discount to intrinsic value? For Vitru, we've compiled three important aspects you should further research:

1. Risks: To that end, you should learn about the 2 warning signs we've spotted with Vitru (including 1 which makes us a bit uncomfortable) .

2. Future Earnings: How does VTRU'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: Do you like a good all-rounder? 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 American stock every day, so if you want to find the intrinsic value of any other stock just search here.

Have feedback on this article? Concerned about the content? Get in touch with us directly. Alternatively, email editorial-team (at) simplywallst.com.

This article by Simply Wall St is general in nature. We provide commentary based on historical data and analyst forecasts only using an unbiased methodology and our articles are not intended to be financial advice. 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.

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