When an individual or company embarks on an investment, they estimate the project's benefit or profit. The 澳洲幸运5官方开奖结果体彩网:Required Rate of Return (RRR) represents the minimum amount an investor expects to receive given a level of risk and helps determine their 澳洲幸运5官方开奖结果体彩网:Return on Investment (ROI).

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 澳洲幸运5官方开奖结果体彩网:relative to the cost of funding that project. The greaꦑter the return, the greater the level of risk.

The required rate of return depends on an investor's 澳洲幸运5官方开奖结果体彩网:tolerance for risk. Investors rely on the market's 澳洲幸运5官方开奖结果体彩网:risk-free rate of return, the volatility of a stock, or the overall cost of funding a project. Inflation expectations and a firm's 澳洲幸运5官方开奖结果体彩网:capital structure also affect an asset's 澳洲幸运5官方开奖结果体彩网: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 calcu🐈lating the present value of operating free cash flow.

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 澳洲幸运5官方开奖结果体彩网: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 澳洲幸运5官方开奖结果体彩网: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 澳洲幸运5官方开奖结果体彩网:regression model:

$\begin{aligned} &\text{Stock Return} = \alpha + \beta_\text{stock} \text{R}_\text{market} \\ &\textbf{where:} \\ &\beta_\text{stock} = \text{Beta coefficient for the stock} \\ &\text{R}_\text{market} = \text{Return expected from the market} \\ &\alpha = \text{Constant measuring excess return for a}\\ &\text{given level of risk} \\ \end{aligned}$​Stock Return=α+βstock​Rmarket​where:βstock​=Beta coefficient ꦯ;for the stockRmarket​=Return expected from the mark♈etα=Constan✨t measuring excess return for 🐠agiven level of risk​

R_market is the return expected from the market. For example, the return of the 澳洲幸运5官方开奖结果体彩网: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:

$\begin{aligned} &\text{E(R)} = \text{RFR} + \beta_\text{stock} \times ( \text{R}_\text{market} - \text{RFR} ) \\ &\quad \quad = 0.04 + 1.25 \times ( .06 - .04 ) \\ &\quad \quad = 6.5\% \\ &\textbf{where:} \\ &\text{E(R)} = \text{Required rate of return, or expected return} \\ &\text{RFR} = \text{Risk-free rate} \\ &\beta_\text{stock} = \text{Beta coefficient for the stock} \\ &\text{R}_\text{market} = \text{Return expected from the market} \\ &( \text{R}_\text{market} - \text{RFR} ) = \text{Market risk premium, or return above} \\ &\text{the risk-free rate to accommodate additional} \\ &\text{unsystematic risk} \\ \end{aligned}$​E(R)=RFR+βstock​×(Rmarket​−RFR)=0.04+1.25×(.06−.04)=6.5%where:E(R)=Required rate of 🦩retu🔯rn, or expected returnRFR=Risk-free rateβstock​=Beta coe♎fficient for the stockRmarket​=Return expꦛected f𝓡rom the market(Rmarket​−RFR)=Market risk premium, or return ab♊ovethe risk-free rate&nb💞sp;to accommoda✱te additionalunsystematic risk​

Dividend Discount Model

Discounting different types of cash flow will find the 澳洲幸运5官方开奖结果体彩网:net present value (NPV). The dividend discount model, known as the 澳洲幸运5官方开奖结果体彩网:Gordon Growth Model (GGM), uses the RRR to discoun�♍�t 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 澳洲幸运5官方开奖结果体彩网:dividends, investors can rearrange the formula into:

$\begin{aligned} &\text{Stock Value} = \frac { D_1 }{ k - g } \\ &\textbf{where:} \\ &D_1 = \text{Expected annual dividend per share} \\ &k = \text{Investor's discount rate, or required rate of return} \\ &g = \text{Growth rate of dividend} \\ \end{aligned}$​Stock Value=k−gD1​​where:D1​=Expected annual dividend&nb✱sp;per sharek=Investor’s discount ra🌃te,&n๊bsp;or required rate of returng=Growth rate of dividend​

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 rate꧑ o﷽f return is often a pivotal factor when deciding between multiple investments.

The RRR is calculated using the 澳洲幸运5官方开奖结果体彩🏅网: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 澳洲幸运5官方开奖结果体彩网:cost of capital requires a calculation based on certain assumptions outlined in the 澳洲幸运5官方开奖结果体彩网: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 i𓆉s:

$\begin{aligned} &\text{WACC} = W_d [ k_d ( 1 - t ) ] + W_{ps} (k_{ps}) + W_{ce} ( k_{ce} ) \\ &\textbf{where:} \\ &\text{WACC} = \text{Weighted average cost of capital} \\ &\text{(firm-wide required rate of return)} \\ &W_d = \text{Weight of debt} \\ &k_d = \text{Cost of debt financing} \\ &t = \text{Tax rate} \\ &W_{ps} = \text{Weight of preferred shares} \\ &k_{ps} = \text{Cost of preferred shares} \\ &W_{ce} = \text{Weight of common equity} \\ &k_{ce} = \text{Cost of common equity} \\ \end{aligned}$​WACC=Wd​[kd​(1−t)]+Wps​(kps​)+Wce​(kce​)where:WACC=Weighted&🏅🥀nbsp;average cost of capital(firm-wide required ratꦇe 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​

The Bottom Line

The required rate of return (RRR) is used as a benchmark of minimum acceptable return, given the cost and retu꧑rns of other available opportunities. Various models such as the CAPM or WACC help individuals and corporations determine the RRR for an investment or project.