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Calculating Required Rate of Return (RRR)

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When an individual or company embarks on an investment, they estimate the project’s benefit or profit. The Required Rate of Return (RRR) represents the minimum amount an investor expects to receive given a level of risk and helps determine their Return on Investment (ROI).

Key Takeaways

  • The Required Rate of Return is the minimum amount an investor seeks when they embark on an investment or project.
  • The RRR helps determine Return on Investment (ROI).
  • Equity investing utilizes the Capital Asset Pricing Model (CAPM) to find the RRR.

Using Required Rate of Return

The required rate of return (RRR) is the minimum amount an investor will receive for assuming the risk of investing and helps determine the return on investment (ROI). It shows how profitable a project might be relative to the cost of funding that project. The greater the return, the greater the level of risk.

The required rate of return depends on an investor’s tolerance for risk. Investors rely on the market’s risk-free rate of return, the volatility of a stock, or the overall cost of funding a project. Inflation expectations and a firm’s capital structure also affect an asset’s intrinsic value.

Common uses of the RRR include calculating the present value of dividend income to evaluate stock prices, calculating the present value of free cash flow to equity, and calculating the present value of operating free cash flow.

Warning

Required Rate of Return (RRR) calculations do not account for inflation.

Capital Asset Pricing Model (CAPM)

Investors can find the required rate of return by using the capital asset pricing model (CAPM). The CAPM requires the following inputs:

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

The yield to maturity (YTM) of a 10-year Treasury bill can estimate the risk-free rate. Let’s assume 4%.

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. Let’s assume 1.25. Investors may use the beta of the stock found on most investment websites or calculate the beta manually by using the following regression model:

Stock Return=α+βstockRmarketwhere:βstock=Beta coefficient for the stockRmarket=Return expected from the marketα=Constant measuring excess return for agiven level of riskbegin{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}

​Stock Return=α+βstock​Rmarket​where:βstock​=Beta coefficient for the stockRmarket​=Return expected from the marketα=Constant measuring excess return for agiven level of risk​

Rmarket is the return expected from the market. For example, the return of the S&P 500 can be used for all stocks. It could range between 3% and 9%, based on business risk, liquidity risk, financial risk, or historical yearly market returns. Let’s assume 6%.

To find the RRR using the CAPM:

E(R)=RFR+βstock×(Rmarket−RFR)=0.04+1.25×(.06−.04)=6.5%where:E(R)=Required rate of return, or expected returnRFR=Risk-free rateβstock=Beta coefficient for the stockRmarket=Return expected from the market(Rmarket−RFR)=Market risk premium, or return abovethe risk-free rate to accommodate additionalunsystematic riskbegin{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}

​E(R)=RFR+βstock​×(Rmarket​−RFR)=0.04+1.25×(.06−.04)=6.5%where:E(R)=Required rate of return, or expected returnRFR=Risk-free rateβstock​=Beta coefficient for the stockRmarket​=Return expected from the market(Rmarket​−RFR)=Market risk premium, or return abovethe risk-free rate to accommodate additionalunsystematic risk​

Dividend Discount Model

Discounting different types of cash flow will find the net present value (NPV). The dividend discount model, known as the Gordon Growth Model (GGM), uses the RRR to discount the periodic payments and calculate the value of the stock.

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, investors can rearrange the formula into:

Stock Value=D1k−gwhere:D1=Expected annual dividend per sharek=Investor’s discount rate, or required rate of returng=Growth rate of dividendbegin{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}

​Stock Value=k−gD1​​where:D1​=Expected annual dividend per sharek=Investor’s discount rate, or required rate of returng=Growth rate of dividend​

The Gordon Growth Model works best for companies with stable dividend-per-share growth rates.

Weighted Average Cost of Capital (WACC)

Investment decisions are found in corporate finance. When a company invests in an expansion or marketing campaign, an analyst looks at the minimum return these expenditures demand relative to the degree of risk. The required rate of return is often a pivotal factor when deciding between multiple investments.

The RRR is calculated using the Weighted Average Cost of Capital (WACC). The WACC is the cost of financing new projects based on how a company is structured. If a company is 100% debt financed, it uses the interest on the issued debt and adjusts for taxes, as interest is tax deductible, to determine the cost. Finding the true cost of capital requires a calculation based on certain assumptions 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 how it finances investments or distributes dividends. To calculate WACC, the weight of the financing source is multiplied by the corresponding cost. Multiply the debt portion by one minus the tax rate, then add the totals. The equation is:

WACC=Wd[kd(1−t)]+Wps(kps)+Wce(kce)where:WACC=Weighted average cost of capital(firm-wide required rate of return)Wd=Weight of debtkd=Cost of debt financingt=Tax rateWps=Weight of preferred shareskps=Cost of preferred sharesWce=Weight of common equitykce=Cost of common equitybegin{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}

​WACC=Wd​[kd​(1−t)]+Wps​(kps​)+Wce​(kce​)where:WACC=Weighted average cost of capital(firm-wide required rate of return)Wd​=Weight of debtkd​=Cost of debt financingt=Tax rateWps​=Weight of preferred shareskps​=Cost of preferred sharesWce​=Weight of common equitykce​=Cost of common equity​

Is WACC the Same as RRR?

In corporate finance, the overall required rate of return will be the weighted average cost of capital (WACC).

What Is the Difference Between Return on Investment and Rate of Return?

Return on investment is a ratio that measures a company’s profitability and equals net income divided by total cost. By comparison, the rate of return measures an investment’s performance over a given period.

What Is Opportunity Cost?

The loss of value from not choosing one option is the opportunity cost. It is often examined when considering the required rate of return (RRR).

The Bottom Line

The required rate of return (RRR) is used as a benchmark of minimum acceptable return, given the cost and returns of other available opportunities. Various models such as the CAPM or WACC help individuals and corporations determine the RRR for an investment or project.

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