Paper presented at FIA’s Professional Master’s Program – Business Management

Subject: Company Valuation – Class 8

Master’s Degree student Ronaldo Corrêa Martins in co-authorship with Prof. Dr. Rodolfo Leandro de Faria – PHD in Administration by FEA-USP and Professor at FIA – Fundação Instituto de Administração

How to invest? Where to invest? Should I buy shares of which company? What is the value of a company? Which value of a company should be considered in the acquisition or merger of companies?

These are frequently asked questions in the market, by investors as well as regular people, not financial experts.

Are the answers simple?

No. They are not simple. We know that many question the profits made by some investors, imagining that they are “lucky”.

On the contrary, many methods of valuing organizations are used by investors and experts in acquisitions and mergers for investment decision-making.

Among the main methods of company valuation, the most used by the market are the following:

- Valuation by Equity Value;
- Valuation by Market Value;
- Multiple Valuation;
- Valuation by Discounted Cash Flow.

Each one of them has its own particularities and importance for each phase of the company, of the negotiation or transaction that is intended.

As it turns out, the Discounted Cash Flow (DCF) method is the most widely used in company valuations for investment decisions.

However, as part of the company valuation methods, besides the Discounted Cash Flow – DCF, it is fundamental to evaluate and use the Growth Rate method, one of the most important methodologies to define the value of an organizational entity.

According to Damodaram (2014), the adoption of the **Growth Rate** must take into account:

- The historical growth of the organization to predict future cash flows
- The organization’s growth estimates
- Tying investment growth to the organizations’ funding policies

Another key element of the Growth Rate is terminal growth, better known as perpetuity, which acts as a barrier, a standard deviation, for measuring the growth and value of the business. A key element in the use of terminal growth is the investment assumptions of organizations.

The fundamental purpose of the Growth Rate is to establish the future cash flow, considering the expected life of the investment. The demonstration below gives a dimension of the elements considered in the use of the Growth Rate.

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- Historical cash flow to predict future cash
- Terminal growth = perpetuity
- Tying investment growth to financing policies
- Organization growth estimates
- Growth rate

Therefore, unlike the Discounted Cash Fund – FDC, which seeks to bring to present value the cash flow for a given period – it ranges from 5 to 10 years, therefore limited (Olivo, 2021), the Growth Rate aims at determining the future cash flow at present value for an undetermined future period. To this end, this methodology must consider a series of endogenous and exogenous factors as variables in its mathematical formulation, as shown in the graphs below.

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- Exogenous factors
- Endogenous factors
- Expected life of investment
- Future cash flow

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EVALUATION OF DISCOUNTED CASH FLOW

COMPANY’S HISTORY

Extraordinary Growth Period | Detailed Forecast of Cash Flow | Terminal Value |

– Company’s size – Growth rate in effect – Return on excess – Magnitude and sustainability of competitive advantages | – Historical data with reserves – Estimate periods – Excess return – Magnitude and sustainability | – Settlement value – Multiple approach – Stable growth |

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EXTERNAL GROWTH ESTIMATES

Management Estimates | Analysts’ Estimates | Fundamental Growth |

– Simplifies estimates – Guilty expansion | – Access to information – Competition analysis – Access to restricted information – Profit quality forecasts | – Profit growth – Return on stockholders’ equity – Medium and marginal returns – Growth in operating profit |

Desire list x realistic forecasts Binding to awards lower the expectations | Confidentiality (regulated by SEC) |

Besides these, other factors that must be considered concern certain “barriers” to the growth of the enterprise, and are related to:

- Factors for the high growth of organizations
- Company’s size
- Growth rate in effect and return on excesses
- Magnitude and sustainability of competitive advantages

Such factors are linked to the phases of the Growth Rate – two phases: the first that considers:

- Period of extraordinary growth = cash flows for this period
- Historical data should be viewed with reservations
- Periods of estimates
- Negative profits

In addition, the second, which considers growth by stable rates – indefinitely – after the termnal year, having the following elements:

- Length of the period of extraordinary growth
- Estimating cash flows during the period of high growth
- Calculating terminal value = path of cash flows in the terminal year

For a better conceptual understanding of what we have presented above, the following are the fundamentals used by Damodaram (2014):

__1 – Scenario of stable return on capital __

**Reinvestment Rate**

- Measures how much a company is sowing to generate overall growth;
- More recent financial statements of the company are suitable for evaluation;
- Maturity of the business tends to reduce the reinvestment rate.

**Return on capital**

- Based on companies’ return on existing investments;
- Any company that earns a return on capital greater than its cost of capital is generating an excess return;
- These returns can be a competitive advantage or barriers to entry for competitors;
- High returns over long periods demonstrate that the company holds a permanent competitive advantage.

__2 – Positive scenario and change in return on capital__

- When the return on capital changes, the expected growth rate will have a second element:

Return on Capital

Growth Rate

__Examples:__

- Companies with poor return on capital that improve operating efficiency and margins;
- Companies with very high return on capital from their active investments with new competitors in the business

__3 – Scenario of negative return on capital__

**Revenue Growth**

- Rate will decrease as revenue increases;
- Compounded rates of growth in revenue over time may seem low;
- Dollar revenue tracking;
- Growth assumptions in revenues and operating margins should be internally consistent;
- Subjective judgments (competition, the company’s ability to handle growth in revenue, and its marketing skills).

**Operating margin forecasts**

- High growth companies, early in their life cycle, have low revenues and negative operating margins;
- If revenue growth converts low revenues into high revenues, but operating margins remain negative → there is no company value, and they will not survive;
- Main input of high growth is expected operating margin → when it becomes mature.

__4 – Scenario of negative return on capital__

**Sales/capital ratio**

- Relating revenue growth to reinvestment needs, one analyzes the revenue that each dollar of invested capital generates.
- This ratio (sales/capital) allows to estimate the additional investment to generate the growth in projected revenues.
- This can happen through internal projects or working capital.

**Link of return on capital**

- The biggest risk is using the sales/capital ratio, aiming at generating views of reinvestments. It may underestimate or overestimate such needs;
- To estimate the return on capital, use operating profit after taxes and divide by invested capital;
- Companies that lose money today, the return on capital will be negative at first, but improve as margins improve.

__5 – TERMINAL VALUE OR PERPETUITY__

Damodaran (2014), points out that it is not feasible to estimate cash flows forever by calculating a terminal value of the company as of a certain point in time.

This terminal value for business valuation purposes is usually calculated assuming a going concern.

By considering a stable growth rate, it is possible to calculate the terminal value by a perpetuity growth model.

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- Terminal value
- Settlement value
- Multiple approach
- Stable growth

**TERMINAL VALUE – SETTLEMENT VALUE**

It is assumed that the company will **cease operations** at a certain time in the future and sell the assets for the highest bid.

The estimate of the settlement value can be obtained in two ways:

- (i) Accounting value of assets adjusted for any inflation in the period;
- (ii) Value based on the profit generating power of the assets.

The estimated value of debt in the terminal year needs to be subtracted from the settlement value to arrive at the settlement procedures for equity investors.

** ****TERMINAL VALUE – multiple approach**

- Going concern basis at the time of the terminal value estimate;
- Value is estimated by a multiple to profits or revenues in that year;
- Simple method, but of influence on the relevant final value;
- The source can be criticized;
- When multiples are estimated by comparable processes, it results in a risky combination of relative and discounted cash flow valuation.
- A cash flow valuation should provide an estimate of intrinsic, not relative, value.
- The most consistent way to estimate terminal value in a discounted cash flow model is through liquidation value or a stable growth model.

**TERMINAL VALUE – stable growth model**

** **Changes in the stable growth rate (SGR) can alter the terminal value in a significant way.

The effect is greater as the growth rate approaches the discount rate.

The fact that a SGR is sustained forever places restrictions on what they can achieve.

__Constant growth rate < overall growth rate of the economy.__

Adjusting SGR to be lower than or equal to the growth rate of the economy is the most conscientious move and ensures that the growth rate is lower than the discount rate.

**Risk-free rate is part of the discount rate and the growth rate of the economy.**

In the long run, real risk-free rate will converge to the economy’s real growth rate and the nominal risk rate will be closer to the economy’s nominal growth rate.

The basic rule is that the stable growth rate should not exceed the risk-free rate used in the valuation.

**Stable Growth Restrictions**

It is necessary to evaluate **3 matters** to judge what the **limits of the stable growth rate (SGR)** are:

*Is the company Local or Multinational?*

Internal: the growth rate in the domestic economy is the limiting value.

External: the growth rate of the global economy will be the limiting value.

*Valuation in nominal or real terms?*

If the valuation is nominal, the SGR should be a nominal growth rate, it should include an inflation forecast.

If the valuation is real, the SGR should be restricted to a lower level.

*iii. Currency used for estimating cash flows and discount rates *

The limits of the SGR vary depending on the currency used.

Using a high inflation currency to estimate cash flows and discount rates will make the SGR high, as inflation is added to real growth.

If a low inflation currency is used the limits will be lower.

**STABLE GROWTH ASSUMPTIONS**

** **For every discounted cash flow valuation, there are two basic assumptions

** ****First**: characteristics that will be in stable growth in terms of return on investment, cost of equity and cost of capital.

** ****Second**: how the company under valuation will make the transition from high growth to stable growth.

*Characteristics of stable growth *

Companies are lower risk, use more debt, have lower (or zero) excess returns, and reinvest less than high-growth companies.

** ***Adjustment of each of these variables*

**i) Risk of stocks**

High growth companies are exposed to market risk, betas > 1.5 or even 2.

As the market matures, less exposure and betas near 1.

More volatile businesses → beta of 1.2. USA betas between 0.8 and 1.2, range for stable period betas.

For commodity companies with betas < 1, the beta can be kept at current levels.

If there are growth estimates, the beta should be adjusted upwards, close to 1, but requires diversification into other businesses.

**ii) Project Returns**

Tends to have high returns on capital and equity and earn excess returns.

In the process of steady growth, it is more difficult to sustain excess returns. Return on capital equal to the cost of capital.

Assuming that returns on equity and capital will approximate industry averages will produce more reasonable estimates of value for many companies.

**iii) Debt ratios and cost of debt **

They use less debt than those of stable growth. With maturity the debt capacity increases.

When valuing equity, changing the debt ratio will change both the cost of equity and the expected cash flows.

The practical question is what debt ratio and cost of debt use in stable growth?

The financial leverage of larger, more mature firms in the segment should be examined.

Use the industry average leverage ratio and cost of debt for the company in stable growth.

**iv) Reinvestment and retention ratios**

Reinvestment is lower than that of high-growth companies.

Capture the effects on reinvestment of slower growth.

Ensure that the company reinvests enough to sustain the stable growth rate in the terminal phase.

: Expected growth rate in earnings per share is a function of the retention ratio and return on equity.__i) Dividend discount model__: Focuses on increasing net income.__ii) Free cash flow to equity (FCFE) model__

SGR is a function of the reinvestment rate in equity and the return on equity.

* iii) Free cash flow to the firm (FCFF) model*: Expected growth in operating profit as a function of return on capital and reinvestment rate.

The reinvestment rate used to generate the free cash flow at the first of stable growth.

Linking the reinvestment rate and retention ratio to the stable growth rate also makes the valuation less susceptible to assumptions about stable growth.

**The transition to stable growth **

When deciding that the company will be in stable growth at some point in the future, it should be analyzed how it will change as it approaches that growth.

For this there are **three scenarios**:

- i) Maintain high growth rate for a period and then abruptly convert to stable growth,
**two-stage model**.

Applied to companies with moderate growth rates, transfer will not be drastic;

- ii) Maintain high growth rate for a period and then through transition phases (characteristics gradually changed),
**three-stage model**.

Applied at high rates of increase in operating profit, allows adjustments in growth rate, risk characteristic, return on capital, and reinvestment rates;

iii) The characteristics change each year, from the initial period to the stable growth phase, **n-stage model**.

Applied to young companies or those with negative margins.

**ESTIMATE APPROACH – EXPECTED VALUE**

** **The cash flow → estimated in different scenarios from optimistic to pessimistic, and the conclusions are based on a range of values.

Steps to be followed:

- i)
**Scenario identification**– best case and worst case scenarios, and in more sophisticated analyses is created from macroeconomic or competitive factors. - ii)
**Cash flow estimate and valuation under each scenario**– follows a verification process of the first stage. The expected cash flows are estimated under each scenario. The values are different under each scenario analyzed.

iii) **Estimate of the probability of each scenario** – each scenario has a probability. Without this information the decision maker is impaired in evaluating the value estimates.

- iv)
**Presentation of the result**– can be presented in two ways:

Calculate an expected value among the scenarios – estimated by the probability of occurrence.

Report a range of values as the lowest value or the highest value for all scenarios represented at the end of the list.

**ESTIMATE APPROACH – SIMULATIONS**

** **The simulations increase flexibility in the way uncertainties are handled.

Value distribution is estimated for each parameter in the valuation (growth, market share, operating margin, beta, etc.). It extracts a result from each distribution – a single cash flow and value.

It is possible to get a distribution that will reflect the basic uncertainty when estimating the inputs to the valuation.

There are **two restrictions** to good simulations:

- i) informational: estimating value distributions for each input to the valuation is difficult;
- ii) Computational constraint.

There are **three potential problems**:

- i) Inputs incorrectly specified as to type and parameters;
- ii) Misconception – cash flows from simulation are risk-adjusted because they count on the probability of poor outcomes;

iii) Scenario analysis and simulation share and double the risk count.

First calculating an expected value through the risk-adjusted discount rates and then considers the probability that the value will be lower.

Olivo (2021) demonstrates in detail the assumptions and methodologies to calculate the value of perpetuity, and its relevance in its Growth Rate methodology.

**CONCLUSIONS – What are the Concepts and assumptions for assessing the value of organizations, using the Growth Rate method**

- Forecasting future cash flow is the key to valuing businesses
- Past growth rates do not generate reliable forecasts
- Manager and analysts’ growth estimates are partial
- For a consistent valuation the expected growth should be tied to the company’s investment policies
- To keep terminal values restricted and reasonable:

Growth rate adopted ≤ Growth rate of the economy

Reinvestment rate **consistent** with the growth rate

Finally, and borrowing the considerations of Ignacio Velez-Pareja (2011) in his work, “*we find restrictions on the value of a parameter used in defining the cost of capital for perpetuities and terminal values: the growth rate of free cash flow. When defining the growth rate for the free cash flow, the usual warning is to set it below the growth of the economy or industry, because in the long run the company would be larger than the economy or industry. This approach can be considered somewhat standard in the sense that they generally take the growth of NOPLAT (mathematically) and/or check that it is in accordance with the statement above. However, in this article we propose to find other objective limits derived from the formulation for the cost of capital in perpetuity and the traditional formula for terminal value in a world where the discount rate for the fiscal economy is Kd, the cost of debt. These limits provide additional criteria for determining the value of g. The limits are calculated in terms of the real growth rate. We use an example to show the effects of violating these limits. The calculation of these limits is very important in the valuation because usually the terminal value is a significant portion of the leveraged value of the company.”*

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- CONCLUSIONS – GROWTH RATE
- Fundamental factors
- Terminal period
- Perpetuity
- Subsidiary factors
- Reinvestment rate
- Return on capital
- Return on capital should be higher than capital cost
- Equity should be higher than equity cost

**CONCLUSIONS – GROWTH RATE**

FLOW OF DISCOUNTED CASH FLOWS

Its main purpose is to bring the company’s value from the future to the present, based on the future projections, taking into account the barriers and the internal and external valuation factors, mainly the terminal period and the business perpetuity.

Growth rate is the flow of discounted flows, having as a barrier or a true standard deviation, perpetuity, for determining the value of the business, to be the object of investment or transaction.

**Bibliography **

Olivo, Rodolfo L. F.; Breve História das Finanças e as suas lições práticas para investidores, Almedina,2021, pages 295, 301-304.

A Damodaran – Investment Valuation, 2002 – pages.stern.nyu.edu

Ignacio Velez-Pareja SSRN Electronic Journal (2011) Proper Determination of the Growth Rate for Growing Perpetuities: The Growth Rate for the Terminal Value