# How the DCF Equation Applies to High-Growth Company Valuations

###### Companies seeking to raise money in private capital markets need an understanding of how to create value based on cash flow. This report reviews an aspect of valuing such companies through the discounted cash flow (DCF) method, the primary method used for cash flow analysis across all asset classes.

When evaluating loss-making companies for extended periods, it is difficult to utilize the DCF for anything other than discounting forward looking profitability. In this article, J&A introduces an alternative approach*—*a modified DCF model*—*that analyzes a company’s investment worthiness by understanding its risk profile and the investor’s expected returns.

The DCF model is used as a way to approximate the value of an investment. A DCF valuation starts by forecasting the future cash flows that an investment is expected to generate and considers the expected future growth of the asset’s cash flows. The equation incorporates risk factors by adjusting the discount or interest rate. In practice, the cash flows (CF1) include cash inflows and outflows such as revenue, expenses (excluding non-cash items such as depreciation and amortization), taxes, and other financial metrics related to the investment being evaluated. The discount rate (*r*) is determined based on factors like the cost of capital, the required rate of return, or a suitable benchmark rate.

## Discount Rate Substituted for Interest Rate

For high-growth companies, one uses the cost of capital as a substitute for the discount rate. This number is simply the factor by which future cash flows are reduced to account for the time value of money and the risk profile of a project. Typically, riskier projects require a higher cost of capital to compensate investors for taking on more risks.

The cost of capital includes multiple components, such as the cost of debt (interest rate on borrowed money) and the cost of equity (required rate of return expected by equity investors).

The weighted average cost of capital (WACC) is a weighted average of a company’s cost of equity and cost of debt based on the money the company has already raised or the cost of raising capital at the moment in time.

## Required Return of Equity or Cost of Equity

The required return on equity, also referred to as the cost of equity, is the minimum rate of return that shareholders (equity investors) expect to earn on their investment.

For high-growth companies that prioritize reinvesting their earnings to fund expansion and growth, the following formula is used:

In this formula, *r _{f} *represents the risk-free rate of return on a risk-free investment, the

*beta*is the measure of the stock’s risk, and

*r*is the expected return above the risk-free rate for investing in the overall market.

_{m}## Abbreviated DCF Equation for High-Growth Companies

By using algebra, the DCF is actually:

The equation above is the correct proper, mathematically detailed equation to calculate a business’s discounted cash flow at a future period. Some of these variables matter more for high-growth companies than others. Variables that are less important can be removed to create a more concise picture of how the DCF behaves.

## Focusing on the Variables that Matter

Small, high-growth companies receive investments because investors are betting they will become large companies, so the possible outcomes of these companies should be measured in extremes.

The purpose of a DCF equation for a high-growth company is to evaluate the extremes of potential value based on realistic cash flow scenarios in the future. Said differently, “If the company generates $100 million of cash flow but has to lose $200 million per year for three years, what is the asset’s value?” The DCF equation allows a financial modeler to create cash flow scenarios based on a projected income statement and calculate a likely business value. The DCF model also allows decision-makers to determine how much cash needs to be generated to meet valuation targets. A company that wants to be worth $1 billion will have mathematical cumulative cash generation requirements, taking into account losses based on a determined interest rate, cost of equity, and cost of debt.

For high-growth companies, one can ignore many variables that a traditional DCF model requires, such as the tax rate. A variable like the tax rate is important when an investor considers deploying large sums of money for low percentage returns, such as investing $100 billion cash into a treasury bond. But the tax rate is meaningless when considering investing $10 million into a company worth $0, $10 million, $100 million, or $1 billion in the future.

In other cases, companies might:

Based on all this, the appropriate DCF equation for a high-growth, early stage company is:

The variables considered by investors and decision-makers for companies of this profile are *beta*, the market’s return, and the asset’s cash flow. We will now investigate *beta* and *r _{m}* in more detail.

This more thorough view of the DCF equation allows us to analyze the relationships between its variables more rigorously. Investors in high-growth companies know they take on a lot of risk with their investments. Investors in high-growth companies expect to be compensated through this risk-taking by getting an outsized return. For the DCF model, this return can only come in cash flow that warrants a greater valuation than what the investor is paying for the asset. Based on these assumptions, many parts of the DCF equation become irrelevant because they do not impact the final valuation number the investor seeks to compensate for this risk.

## Selecting *Beta* and *r*_{m} for High-Growth Companies

_{m}

There is no perfect answer to determining the right *beta* for a small, high-growth company. *Beta* is a statistical measurement derived from the volatility of the S&P Index. The S&P has a *beta* of 1. If a stock also has a *beta* of 1, then the stock will move the same amount as the S&P 500 Index. If the S&P goes up by 1%, a stock with a *beta* of 1 will also go up by 1%. If the S&P goes up by 200%, the stock with a *beta* of 1 will also go up by 200%.

*Beta* plays a role in assessing a stock’s risk and how it moves in the overall market. *Beta* creates the slope, and it grows (or destroys) the underlying asset’s value based on performance. A *beta* of 15 is extremely high and would suggest the stock is volatile and risky since it moves 15 times more than the overall market.

As *beta* grows, so does the volatility of the stock in relation to the S&P. If a stock has a *beta* of 7, then it will go up or down seven times as much as the S&P. Suppose the S&P goes up by 10%, the stock with a *beta* of 7 will go up by 70%. And if the S&P goes up by 15%, the stock with a *beta* of 7 will go up by 105%. Small changes in the *beta* lead to large changes, positive or negative, in the underlying stock price as it moves. A larger *beta* leads to a lower valuation. If an investment is extremely risky, an investor is likely to pay less for it because there is a greater probability that their investment will decline in value.

A perceived *beta* of 2 is different from 5 and is different from 100. Various qualitative factors, including pending litigation against a company, management changes, negative publicity, and industry sentiment can influence *beta*. These events introduce uncertainty and risk, which cause a stock’s *beta* to deviate from 1. Generally, a *beta* of 5 for NYSE listed equities is considered very high.

The market return (*r _{m}*) is easier to estimate and requires less data for statistical analysis. The

*r*can be calculated by multiplying possible investment outcomes by their probabilities and summing the results to reach a weighted expected return of the market. Venture capital (VC) funds have historical data on the return of different investments, which helps them estimate the expected return on their portfolio of investments.

_{m}Nevertheless, historical performance does not guarantee future results, as investment outcomes vary significantly. Ideally, it will provide a conservative estimate of *r _{m}* when compared with the asset managers’ future performance.

Assume an investment in a Series A company has a 25% chance to either go to 0, increase by 50%, double, or quadruple equally. Note that we will not assume negative returns in this scenario since negative returns are most relevant for derivative trading. 25%*0+25%*50%+25%*1+25%*4 = 1.375%, so the *r _{m}* of this scenario is 1.375%.

These numbers can be altered to create a different *r _{m}* based on the investor’s model. One important thing to note is that the

*r*will remain relatively static. It would be uncommon for any investment opportunity to have an

_{m}*r*of 4, 10, or 100; this suggests the returns are too good to be true. Some high-frequency trading algorithms can reach results of this magnitude, but they are not consistent.

_{m}The selections for *beta* and *r _{m}* simply reduce the expected value of the cash flow in a period. Both these variables appear in the denominator of the traditional DCF and the modified one in this report. As the denominator of a fraction grows larger, the ultimate value of that fraction becomes smaller, leading to a decline in the expected value of the asset.

A larger *beta* leading to a lower valuation is intuitive. When an investment carries high risk, investors tend to offer a lower price due to the likelihood of potential losses. However, a greater *r _{m}* also contributes to a lower asset value. How can this happen? Remember, the cost of equity in this equation refers to the return investors require for the risk they are assuming. So, while a higher

*r*seems like it should increase the asset’s value, this

_{m}*r*is used to calculate the required return of equity to the investor, consequently increasing the company’s cost of equity. This subtle psychological indication of this simple equation holds powerful implications for the issuer raising money. Founders and CEOs often assume that belonging to a high-growth industry increases their value. However, this equation clarifies that the asset’s value only increases based on its ability to generate future cash flow. Mathematically, according to the DCF, the higher the expected market return of the investor, the lower the asset’s valuation—a point of utmost importance.

_{m}Since different returns and their likelihoods derive *r _{m}*, the positive and negative scenarios should be considered together. And counter-intuitively to many business owners, when a market is driving a return of 4, 10, or 40 times, it only puts the pressure on the company to provide higher returns, therefore reducing the valuation in the mind of the investor.

## Key Takeaways for Business Owners

Most of this is very theoretical. The equations used by cash flow and public equity investors were not developed for early stage, high-growth companies. However, there are vital lessons for business owners to grasp regarding investors’ thought processes. Private equity investors have expertise from public markets and were trained on financial fundamentals that include these equations. These equations provide a framework for an alternative investment to any subject seeking one. Investors possess the gift to choose where to allocate their capital. When an investment opportunity presents itself in a promising space, but its offering details are so outside the range of what is reasonable regarding these basic equations, investors will find it very difficult to commit to such an investment. This is particularly the case when these investors manage funds on behalf of their limited partners and are bound by a fiduciary duty to those whose capital they manage.

Qualitatively, business owners need to consider how they compete with investment assets for investor funds and how the *beta* or expected market return (*r _{m}*) of those other assets aligns with opportunities presented in a specific investment offering.

Quantitatively, there are outbound limits for *beta* and expected market return (*r _{m}*) that business owners can consider when determining what set of scenarios makes their investment offering enter the realm of mathematical reasonableness.

For example, a *beta* cannot be 100. Generally, public-traded equities can have *betas* of up to 20. A small, high-growth business that doesn’t trade frequently, will decrease *beta* since the stock is less volatile. The *r _{m}* of an offering shouldn’t be greater than 1 because it will lead investors to demand a greater return and therefore increase the cost of equity and lower the valuation of the business. Mathematically, an

*r*of less than 1 will reduce

_{m}*beta*and its subsequent exponential change in the denominator of the DCF equation.