# Required Rate of Return (RRR): Formula & Calculation

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• 0:00 Required Rate of Return (RRR)
• 0:34 Using the RRR in Stock…
• 1:39 The Capital Assets…
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Lesson Transcript
Instructor: James Walsh

M.B.A. Veteran Business and Economics teacher at a number of community colleges and in the for profit sector.

Both investors and businesses have a required rate of return (RRR) for potential investments and projects. We will use examples and formulas to calculate an RRR for both.

## Required Rate of Return (RRR)

The required rate of return (RRR) on an investment is the minimum annual return that is necessary to induce people to invest in it. In other words, if an investment returns 3% and the investor's RRR is 10%, he or she is unlikely to put money into that investment.

The RRR is used to evaluate investments by individuals in financial assets, like stocks. It is also used by businesses to evaluate whether new projects are a good use of their money.

## Using the RRR in Stock Investments

Let's follow Drew as he evaluates the RRR when considering new investments. Drew invests his savings in stocks and government securities. He works hard at picking the right one, since his kid's education and his and Mrs. Drew's retirement are on the line. He has a different RRR for each stock he looks at, since they have different levels of risk. Let's see how he would evaluate two stock investments:

An established company like Big Green Corp has established products that sell, so it is low risk. The stock price doesn't go up and down too much, and Drew will accept a lower return since it's more of a sure thing. On the other hand, Edge Technology makes parts for self-driving vehicles. It is a new company that has little sales yet and the stock price goes up and down like a roller coaster, since there is big risk that Edge could be huge in ten years or bankrupt if self-driving vehicles don't catch on.

Drew has a higher RRR for Edge Technology because of that risk but how much higher should it be than for Big Green. For that, he will turn to the capital assets pricing model.

## The Capital Assets Pricing Model

The capital assets pricing model (CAPM) has many uses in finance. One of them is to determine the RRR for investments with different levels of risk. Here is the formula, but don't worry, it is much easier to work with than it looks:

To use it, you need three variables:

Rf: risk free rate

A U.S. government security is considered to be risk free, since the U.S. has never defaulted on its debts, despite all of the threats from blustering politicians.

Rm: return on the market

Usually a broader index like the S&P 500 captures something close to the average return on all stocks.

Beta: measure of risk

A safe stock like Big Green has low price volatility, low risk, and a low beta. A risky stock like Edge has prices that jump around a lot, so it has a high beta. A beta of 1.0 is the market average.

Drew looks up the numbers. He will use the return on a ten-year U.S. treasury bill for the risk free rate; it is 3%. The return on the market was 10% in the most recent year. The beta for Big Green is 0.75 since it is less volatile than the market. The beta for Edge is 3.0, since it is very volatile. Now Drew is ready to calculate the RRR for both.

For Big Green, it is:

3+ 0.75 (10 - 3) = 8.25%

For Edge Technology, it is:

3 + 3.0 (10 - 3) = 24%

It is easy to see from those numbers how the RRR is much greater for risky investments.

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