Required rate of return: formula, meaning, and examples

Isabel Peña Alfaro is a guest contributor. The views expressed are hers and do not necessarily reflect the views of Rho.

What is the required rate of return (RRR)?

The RRR, also known as the hurdle rate, is the minimum return an investor expects to receive on an investment based on the investment’s level of risk. In other words, the RRR is an investor’s compensation for taking on risk. 

What does the required rate of return tell me?

The RRR provides valuable insights into the risk profile and potential profitability of an investment opportunity. 

What makes an investment enticing? 

In most cases, the expected return of an investment should be greater than the RRR for an investment to be considered attractive. An expected return lower than the RRR would be too risky or unprofitable. 

Following the same logic, a high RRR, for instance one in which the expected return would likely not  surpass,  indicates that the investment carries significant risk, and investors will demand a higher return to compensate. So, in contrast, a low RRR suggests that the investment is relatively low-risk, and investors are generally willing to accept a lower return.

For instance, a net present value calculation uses the RRR as the key discount rate to find the present value of future cash flows and get an idea for the return or an average return on investment.

Required rate of return (RRR) vs. rate of return (ROR)

The RRR is the minimum acceptable return an investor expects from an investment, and it acts as a benchmark. 

The rate of return (ROR), on the other hand, is the actual gain or loss incurred over a specified period. It measures the profitability of investment after it has been made. The ROR can be calculated by dividing the total income from the investment (including capital gains and any other income) by the initial investment cost.

Internal rate of return (IRR) vs. required rate of return (RRR)

The Internal Rate of Return (IRR) is a way to measure how profitable an investment is.

The IRR is a calculated value based on the investment's projected cash flows. It is the interest rate at which the money you expect to make from the investment (future cash flows) matches the amount of money you put into the investment (the initial cost), making the net gain or loss zero. 

Essentially, the IRR tells you the annual growth rate of your investment. If the IRR is higher than the return you could get from other investments, it means this investment is a good choice.

Now, the relationship between the IRR and the RRR is important because it helps investors, including those in real estate, determine whether a potential investment is worth it. If the IRR exceeds the RRR, the investment is potentially profitable; similarly, if the IRR is lower than the RRR, the investment is not appealing. 

Required rate of return (RRR) vs. expected rate of return (ERR)

The expected rate of return (ERR) is an estimate of the actual return that an investor anticipates earning from an investment over a specific time period, based on various assumptions and analysis. The ERR accounts for factors including financial risk, growth rates, and market conditions. 

Before we compare RRR to ERR (in our previous subsection), let’s review the difference between the IRR and the ERR. The IRR assumes reinvestment of cash flows at the IRR rate itself, while the ERR assumes reinvestment at a different specified rate (e.g., cost of capital).

So, what’s the difference between the RRR and the ERR? While the RRR is a predetermined minimum rate or threshold that an investment should meet or exceed to be considered acceptable, the ERR is a forward-looking estimate of the investment's potential returns. Investors typically compare the ERR to the RRR to determine whether an investment opportunity is worth pursuing or not.

Required rate of return (RRR) vs. cost of capital

The cost of capital refers to the expected returns a company should pay to its investors and/or creditors for raising funds. It is the minimum return a company's existing and potential capital providers demand for investing in the company's securities or projects.

The cost of capital is calculated from the company's perspective, taking into account its capital structure and the costs of different sources of financing (debt, equity, etc.). 

While the RRR is set by investors, the cost of capital is determined by the company based on market conditions and its financing mix. 

Required rate of return formula: three ways to calculate

There are three ways to calculate the RRR,  with the Capital Asset Pricing Model (CAPM) formula, the Weighted Average Cost of Capital (WACC) formula, and the Dividend Discount Model (DDM) formula.

Let’s dive into each of these formulas.

Capital Asset Pricing Model (CAPM) formula

The CAPM calculates the required rate of return for an asset based on its risk relative to the overall market. It considers the risk-free rate, the asset's beta (a measure of volatility relative to the market), and the return of a market. 

While the CAPM has limitations due to its assumptions, it remains an important and widely-used model for market risk premium, risk-adjusted asset pricing, and portfolio management.

RRR = r_f + ß(r_m – r_f) 

• RRR: The required rate of return
• r_f: Risk-free rate; the yield on a government bond matching the investment horizon.
• ß: Beta coefficient of an investment; it measures volatility or systematic risk.
• r_m: Return of a market; the expected return of the portfolio over the risk-free rate.

Considerations: 

1. Assumes investors are rational and risk-averse, seeking to maximize returns for a given level of risk.
2. Assumes markets are efficient and all investors have the same expectations about risk and returns.
3. Beta is used as the sole measure of risk, capturing only systematic (non-diversifiable) risk.

Best for: 

1. Estimating the cost of equity, which is important for valuations and financial modeling.
2. Evaluating whether an investment is attractively priced relative to its risk level.
3. Making asset allocation decisions by identifying undervalued assets with higher expected returns than predicted by CAPM.
4. Providing a benchmark rate of return to evaluate the performance of portfolio managers.

Weighted Average Cost of Capital (WACC) formula

The WACC is a calculation that determines a company's overall cost of capital by taking into account the capital structure (debt and equity). It provides a comprehensive view of the company's cost of financing and is used in various financial analyses and valuations. Its calculation requires careful consideration of the company's capital structure, risk profile, and market conditions.

RRR = w_Dr_D(1 – t) + w_er_e

• w_D: Weight of debt; represents the weight or proportion of debt in the company's capital structure. It is calculated by dividing the market value of debt by the total market value of capital (debt + equity).
• r_D: Cost of debt; this is the interest rate the company pays on its outstanding debt obligations, such as bonds and loans.
• t: Corporate tax rate; the term “(1-t)” accounts for the tax-deductibility of interest payments on debt.
• w_e: Weight of equity; the weight or proportion of equity in the company's capital structure. It is calculated by dividing the market value of equity by the total market value of capital.
• r_e: Cost of equity; the expected rate of return that equity investors demand for investing in the company. It is typically calculated using the Capital Asset Pricing Model (CAPM).

Considerations: 

1. The formula weighs the costs of equity and debt by their respective market rate value proportions in the company's capital structure.
2. The marginal corporate tax rate is commonly used, as it reflects the tax savings from interest deductibility.
3. The market values of equity and debt should be used, not book values, to reflect the current costs and market perceptions.

Best for: 

1. Used as the discount rate to calculate the present value of future cash flows in Discounted Cash Flow (DCF) valuation models.
2. As a hurdle rate to evaluate the potential profitability of new projects or investments. If the expected return exceeds the WACC, the project may be accepted.
3. To determine the optimal capital structure by assessing the overall cost of capital for different debt-equity mixes.
4. To compare a company's return on invested capital (ROIC) to assess whether it is creating or destroying value. Often used by corporate finance teams.

Dividend Discount Model (DDM) formula 

The dividend discount model (DDM) is  used to value a company's stock by discounting its expected future dividends to their present value. It is a widely used valuation method for income-oriented investors and analysts covering mature, dividend-paying companies; however, it should be used in conjunction with other valuation techniques. 

One specific case of the DDM is called the Gordon Growth Model, which assumes that dividends grow at a constant rate in perpetuity. 

RRR =  (Expected dividend payment / Share Price) + Forecasted dividend growth rate

• Expected dividend payment: Dividend amount per share that the company is expected to pay out in the next period.
• Share price: Current market stock price.
• Forecasted dividend growth rate: Estimated annual rate at which the company’s dividends are expected to grow.

Considerations: 

1. The model relies on accurate forecasts of future dividend payments, which can be challenging, especially for companies with irregular or no dividend history.
2. The DDM values a stock into perpetuity, which may not be suitable for companies with finite life cycles or those expected to be acquired/liquidated.
3. The DDM cannot be applied to companies that do not pay dividends, such as high-growth firms that reinvest earnings.
4. The DDM assumes that a stock's intrinsic value is equal to the sum of all its future dividend payments, discounted back to their present value using an appropriate required rate of return on investment.  An inappropriate discount rate can significantly impact the valuation.

Best for: 

1. Valuing established companies with a consistent dividend payment history and relatively stable growth prospects.
2. Comparing the calculated intrinsic value to the current market price to identify potential buying or selling opportunities.
3. For investors focused on dividend-paying stocks and income-oriented investment opportunities and strategies.

Example of RRR using the Capital Asset Pricing Model (CAPM) formula

Let’s look at an example of how to use CAPM to calculate the RRR. 

As a reminder, the CAPM is the following formula: RRR = r_f + ß(r_m – r_f). 

Let’s use Excel or Google Sheets for our calculations, which makes it easy to analyze the sensitivity of RRR to changes in the inputs like beta, market return, or risk-free rate of return.

First, we’re going to look at our assumed values:

• Risk-free rate (R_f) based on the yield of a 10-year U.S. Treasury Bond = 3%.
• Market return (R_m) based on the historical average annual return of the S&P 500 index = 10%.
• ß = 1.2. This value can be calculated in Excel using the '=SLOPE()' function on historical stock and market returns.

Now, let’s plug those values into our formula.

RRR = r_f + ß(r_m – r_f)

RRR = 3% + 1.2 x (10%-3%)

This gives an RRR of 11.4%. 

What does that mean? It means that if you were evaluating whether to invest, the CAPM suggests you should require an expected return of at least 11.4% to compensate for the risk relative to the overall market.

Example of RRR using the Weighted Average Cost of Capital (WACC) formula

Let’s do another example, but this time we’ll use WACC. 

As a reminder, the WACC formula is RRR = w_Dr_D(1 – t) + w_er_e. Again, we’ll use Excel or Google Sheets for our calculations so we can easily do sensitivity analyses by changing input values such as costs of debt/equity, weights, and tax rate. 

First, the assumed values:

• Market value of equity (e) = $200 million
• Market value of debt (D) = $100 million
• Cost of equity (r_e) = 12% (calculated using CAPM)
• Cost of debt (r_D) = 6%
• Corporate tax rate (t) = 25%

We’ll use Google Sheets for the following five steps. 

1. Calculate the total market value of capital:
   $200 M + $100 M
   = $300 million
2. Calculate weight of equity (w_e):
   =$200 M / $300 M
   = 0.667 or 66.7%
3. Calculate weight of debt (w_d):
   =$100 M / $300 M
   = 0.333 or 33.3%
4. Use the WACC formula to calculate RRR:

RRR = (33.3% * 6%) * (1 - 25%) + (66.7% * 12%)

RRR = 9.5%

Example of RRR using the Dividend Discount Model (DDM) formula

Here’s one  more example, this time using DDM. 

As a reminder, the DDM formula is RRR =  (Expected dividend payment / Share Price) + Forecasted dividend growth rate. 

This calculation in Google Sheets is straightforward and allows for easy sensitivity analysis by changing the input values, such as dividend payment, share price, or growth rate. 

Assume the following:

• Expected dividend payment  = $2 per share
• Share price = $40
• Forecasted dividend growth rate = 5%

Now, use Excel to calculate the formula as follows:

1. Calculate the dividend yield

$2 / $40 = 0.05 or 5%

2. Add the forecasted dividend growth rate

0.05 + 5% = 0.10 or 10%

Therefore, the Dividend Discount Model gives an  RRR for this stock of 10%. This means that an investor would require a minimum return of 10% to consider investing in a stock with an expected dividend payment of $2 per share, a current share price of $40, and a forecasted dividend growth rate of 5%.

Limitations of the required rate of return

Though the RRR is an important tool for investors, it’s not infallible. 

The following limitations highlight the importance of using the RRR as a guideline rather than a definitive measure:

• Subjectivity in assessing risk. Though it attempts to quantify risk, each investor has a different perception of higher risk and the risk related to a particular investment, leading to multiple RRR calculations for the same investment opportunity. 

• May not accurately reflect the specific return requirements of individual investors. The RRR assumes that all investors will have the same risk tolerance, personal circumstances, and investment goals, and fails to account for individual preferences. 

• Limited in focus to quantitative factors such as risk levels and expected returns. While these are very important, qualitative factors — such as management quality, competitive advantages, and industry trends — can also significantly impact an investment’s potential risks and returns. 

FAQs about the required rate of return formula

What is a reasonable required rate of return?

A reasonable required rate of return (RRR) typically ranges from 7% to 15%, depending on the risk profile of the investment. For example, a reasonable RRR for low-risk investments such as government bonds can be  around 7-10%, while a reasonable RRR for high-risk investments such as small-cap stocks might be around 12-15%. 

Can the required rate of return be negative?

While it is possible for the RRR to be negative, it is almost never seen in investments. Since the RRR represents the minimum return expected by an investor, a negative value would imply the investor is willing to accept a guaranteed loss, which is highly unlikely. 

Can the required rate of return change over time?

As market conditions, risk factors, and investor preferences evolve, so does the RRR. For example, if a company has greater risk due to increased competition or economic uncertainty, investors may demand a higher RRR to compensate. 

Can a company use multiple calculations to find the required rate of return?

Yes, a company can use multiple calculations to find the RRR. Examples include the capital asset pricing model (CAPM), dividend discount model (DDM), and weighted average cost of capital (WACC), all of which might provide different RRR values based on their inputs and assumptions. Companies often analyze the RRR from various perspectives to account for different risk factors, financing sources, and growth projections before making investment decisions. 

What's the most important part of the required rate of return formula?

The most important part of the RRR formula is the risk premium, which accounts for the additional return an investor demands to compensate for the risk associated with a particular investment opportunity. The risk premium reflects factors such as the investment's volatility, market risk, and company-specific risks, making it a crucial determinant of the overall RRR calculation.

Conclusion: Be more efficient with Rho 

To sum it up, the RRR represents the minimum acceptable return an investor demands for undertaking a particular investment opportunity based on its risk level. 

It serves as a benchmark against which the potential returns of an investment are evaluated and calculated using various methods, each with their own assumptions and applications. By carefully evaluating the RRR alongside these factors, investors can make more informed decisions and better align their investment strategies with their risk tolerance and return expectations.

Looking to enhance your capital efficiency and improve your RRR? Rho offers a frictionless business banking platform, from idea to IPO. Learn more about us here.

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