How To Calculate The Required Rate Of Return

Investopedia

The required rate of return (RRR) is a component in many of the metrics and calculations used in corporate finance and equity valuation. It goes beyond just identifying the return of the investment, and factors in risk as one of the key considerations to determining potential return. The required rate of return also sets the minimum return an investor should accept, given all other options available and the capital structure of the firm. To calculate the required rate, 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 (the risk-free rate of return), and the volatility of the stock or the overall cost of funding the project. Here we examine this metric in detail and show you how to use it to calculate the potential returns of your investments.

Discounting Models
One particularly 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 cash flow will use slightly different rates with the same intention - finding the net present value.

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

Equity, debt and corporate expansion decisions are made by placing a value on the periodic cash received and measuring it against the cash paid. The goal is to receive more than what you paid. In corporate finance, the focus is on the cost of funding projects compared to the return; in equities, the focus is on the return given compared to the risk taken on.Equity and Debt
In equities the required rate of return is used in various calculations. For example the dividend discount model uses the RRR to discount the periodic payments and calculate the value of the stock. Finding the required rate of return can be done by using the capital asset pricing model (CAPM).

The CAPM will require that you find certain inputs:

  • 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 current yield to maturity of a 10 year T-bill - let’s say it’s 4%.

Then, take the expected market risk premium for this stock. This can have a wide range of estimates. For example, it could range between 3% to 9%, based on factors such as business risk, liquidity risk, financial risk. Or, you can simply derive it from historical yearly market returns. Let’s use 6%, rather than any of the extreme values. Often, the market return will be estimated by a brokerage, and you can just subtract the risk-free rate.

Last of all, get 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:

Return of Stock = α + βstock Rmarket

Where:
  • βstock is the beta coefficient for the stock, meaning it is the covariance between the stock and the market divided by the variance of the market. We will assume 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 trading on it - and even some stocks not on the index, but related to businesses that are.
  • α is a constant that measures excess return for given level of risk

Now we put together these three numbers using the capital asset pricing model:

E(R) = RFR + βstock (Rmarket – RFR)

E(R) = 0.04 + 1.25 (6)

E(R) = 11.5%

Where:

  • E(R) = the required rate of return, or expected return
  • RFR = the risk free rate
  • βstock = beta of the stock
  • Rmarket = return of the market as a whole
  • (Rmarket – RFR) = the market risk premium, or the return above the risk-free rate to accommodate additional unsystematic risk

Dividend Discount Approach
An investor could also use the dividend discount model, also known as the Gordon growth model. By finding the current stock price, the dividend payment and an estimate of the growth rate for dividends, you can rearrange the formula into:

k=(D/S)+g

Where:

  • k = required rate of return
  • D = dividend payment (expected to be paid next year)
  • S = current stock value (if using the cost of newly issued common stock you will need to minus the flotation costs)
  • g = growth rate of the dividend

Again, it is important to note that there needs to be some assumptions, particularly the continued growth of the dividend at a constant rate.

Required Rate of Return in Corporate Finance
Investment decisions are not limited to stocks; every time money is risked for something like expansion or a marketing campaign an analyst can look at the minimum return these expenditures demand. If the current project will give a lower return than other potential projects, then it will not be done. Other factors do go into these decisions, such as risk, time horizon and available resources, among others, but the required rate of return is the basis for deciding between multiple investments. When looking at an investment decision in corporate finance, the overall required rate of return will be the weighted average cost of capital (WACC). Capital Structure
The WACC is the cost of financing new projects based on how a company is structured. If a company is 100% debt then it would be easy: just find the interest on the issued debt and adjust for taxes (because interest is tax deductible). In reality, a corporation is much more complex. Finding the true cost of capital requires a calculation based on a combination of sources. Some would even argue that, under certain assumptions, the capital structure is irrelevant, as outlined in the Modigliani-Miller theorem.

To calculate the WACC simply take the weight of the source of financing and multiply it by the corresponding cost. There is one exception: you should multiply the debt portion by one minus the tax rate. Then sum the totals. The equation looks something like this:

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 debt
  • kd = cost of debt financing
  • t = tax rate
  • Wp = weight of preferred shares
  • kps = cost of preferred shares
  • Wce = weight of common equity
  • kce = cost of common equity

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

The Bottom Line
The required rate of return is a difficult metric to pinpoint due to the various estimates and preferences from one decision maker to the next. The risk return preferences, inflation expectations and the firm’s capital structure all play a role in determining the required rate. Any one of the many 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 become dramatically more predictable.

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