## What Is Required Rate of Return – RRR?

The required rate of return (RRR) is the minimum amount of profit (return) an investor will receive for assuming the risk of investing in a stock or another type of security. RRR also can be used to calculate how profitable a project might be relative to the cost of funding the project. RRR signals the level of risk that's involved in committing to a given investment or project. The greater the return, the greater the level of risk. A lesser return generally means that there is less risk. RRR is commonly used in corporate finance and when valuing equities (stocks). You may use RRR to calculate your potential return on investment (ROI).

When looking at an RRR, it is important to remember that it does not factor in inflation. Also, keep in mind that the required rate of return can vary among investors depending on their tolerance for risk.

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## What RRR Considers

To calculate the required rate of return, you must look at factors such as the return of the market as a whole, the rate you could get if you took on no risk (risk-free rate of return), and the volatility of a stock (or overall cost of funding a project).

The required rate of return is a difficult metric to pinpoint because individuals who perform the analysis will have different estimates and preferences. The risk-return preferences, inflation expectations, and a firm's capital structure all play a role in determining the required rate. Each of these, among other factors, can have major effects on an asset's intrinsic value. As with many things, practice makes perfect. As you refine your preferences and dial in estimates, your investment decisions will become dramatically more predictable.

## Discounting Models

One important use of the required rate of return is in discounting most types of cash flow models and some relative-value techniques. Discounting different types of the cash flow will use slightly different rates with the same intention—to find the net present value (NPV).

Common uses of the required rate of return include:

• Calculating the present value of dividend income for the purpose of evaluating stock prices
• Calculating the present value of free cash flow to equity
• Calculating the present value of operating free cash flow

Analysts make equity, debt, and corporate expansion decisions by placing a value on the periodic cash received and measuring it against the cash paid. The goal is to receive more than you paid. Corporate finance focuses on how much profit you make (the return) compared to how much you paid to fund a project. Equity investing focuses on the return compared to the amount of risk you took in making the investment.

## Equity and Debt

Equity investing uses the required rate of return in various calculations. For example, the dividend discount model uses the RRR to discount the periodic payments and calculate the value of the stock. You may find the required rate of return by using the capital asset pricing model (CAPM).

The CAPM requires that you find certain inputs including:

• The risk-free rate (RFR)
• The stock's beta
• The expected market return

Start with an estimate of the risk-free rate. You could use the yield to maturity (YTM) of a 10-year Treasury bill—let's say it's 4%. Next, take the expected market risk premium for the stock, which can have a wide range of estimates.

For example, it could range between 3% and 9%, based on factors such as business risk, liquidity risk, and financial risk. Or, you can derive it from historical yearly market returns. For illustrative purposes, we'll use 6% rather than any of the extreme values. Often, the market return will be estimated by a brokerage firm, and you can subtract the risk-free rate.

Or, you can use the beta of the stock. The beta for a stock can be found on most investment websites.

To calculate beta manually, use the following regression model:

﻿\begin{aligned} &\text{Stock Return} = \alpha + \beta_\text{stock} \text{R}_\text{market} \\ &\textbf{where:} \\ &\beta_\text{stock} = \text{Beta coefficient for the stock} \\ &\text{R}_\text{market} = \text{Return expected from the market} \\ &\alpha = \text{Constant measuring excess return for a}\\ &\text{given level of risk} \\ \end{aligned}﻿

βstock is the beta coefficient for the stock. This means it is the covariance between the stock and the market, divided by the variance of the market. We will assume that the beta is 1.25.

Rmarket is the return expected from the market. For example, the return of the S&P 500 can be used for all stocks that trade, and even some stocks not on the index, but related to businesses that are.

Now, we put together these three numbers using the CAPM:

﻿\begin{aligned} &\text{E(R)} = \text{RFR} + \beta_\text{stock} \times ( \text{R}_\text{market} - \text{RFR} ) \\ &\quad \quad = 0.04 + 1.25 \times ( .06 - .04 ) \\ &\quad \quad = 6.5\% \\ &\textbf{where:} \\ &\text{E(R)} = \text{Required rate of return, or expected return} \\ &\text{RFR} = \text{Risk-free rate} \\ &\beta_\text{stock} = \text{Beta coefficient for the stock} \\ &\text{R}_\text{market} = \text{Return expected from the market} \\ &( \text{R}_\text{market} - \text{RFR} ) = \text{Market risk premium, or return above} \\ &\text{the risk-free rate to accommodate additional} \\ &\text{unsystematic risk} \\ \end{aligned}﻿

## Dividend Discount Approach

Another approach is the dividend-discount model, also known as the Gordon growth model (GGM). This model determines a stock's intrinsic value based on dividend growth at a constant rate. By finding the current stock price, the dividend payment, and an estimate of the growth rate for dividends, you can rearrange the formula into:

﻿\begin{aligned} &\text{Stock Value} = \frac { D_1 }{ k - g } \\ &\textbf{where:} \\ &D_1 = \text{Expected annual dividend per share} \\ &k = \text{Investor's discount rate, or required rate of return} \\ &g = \text{Growth rate of dividend} \\ \end{aligned}﻿

Importantly, there need to be some assumptions, in particular the continued growth of the dividend at a constant rate. So, this calculation only works with companies that have stable dividend-per-share growth rates.

## RRR in Corporate Finance

Investment decisions are not limited to stocks. In corporate finance, whenever a company invests in an expansion or marketing campaign, an analyst can look at the minimum return these expenditures demand relative to the degree of risk the firm expended. If a current project provides a lower return than other potential projects, the project will not go forward. Many factors—including risk, time frame, and available resources—go into deciding whether to forge ahead with a project. Typically though, the required rate of return is the pivotal factor when deciding between multiple investments.

In corporate finance, when looking at an investment decision, the overall required rate of return will be the weighted average cost of capital (WACC).

## Capital Structure

### Weighted Average Cost of Capital

The weighted average cost of capital (WACC) is the cost of financing new projects based on how a company is structured. If a company is 100% debt financed, then you would use the interest on the issued debt and adjust for taxes—as interest is tax deductible—to determine the cost. In reality, a corporation is much more complex.

### The True Cost of Capital

Finding the true cost of capital requires a calculation based on a number of sources. Some would even argue that, under certain assumptions, the capital structure is irrelevant, as outlined in the Modigliani-Miller theorem. According to this theory, a firm's market value is calculated using its earning power and the risk of its underlying assets. It also assumes that the firm is separate from the way it finances investments or distributes dividends.

To calculate WACC, take the weight of the financing source and multiply it by the corresponding cost. However, there is one exception: Multiply the debt portion by one minus the tax rate, then add the totals. The equation is:

﻿\begin{aligned} &\text{WACC} = W_d [ k_d ( 1 - t ) ] + W_{ps} (k_{ps}) + W_{ce} ( k_{ce} ) \\ &\textbf{where:} \\ &\text{WACC} = \text{Weighted average cost of capital} \\ &\text{(firm-wide required rate of return)} \\ &W_d = \text{Weight of debt} \\ &k_d = \text{Cost of debt financing} \\ &t = \text{Tax rate} \\ &W_{ps} = \text{Weight of preferred shares} \\ &k_{ps} = \text{Cost of preferred shares} \\ &W_{ce} = \text{Weight of common equity} \\ &k_{ce} = \text{Cost of common equity} \\ \end{aligned}﻿

When dealing with corporate decisions to expand or take on new projects, the required rate of return is used as a benchmark of minimum acceptable return, given the cost and returns of other available investment opportunities.