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Financial Accounting: Help and Review18 chapters | 235 lessons

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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.

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.

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 (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.

Tracie is the chief financial officer for Big Green Corp. Big Green needs to make more on it's new projects than the money they raise to fund them, so their RRR for new projects = cost of funds or capital. Projects that will make more than Big Green's costs of funds will get the green light, since they will be profitable for the company. Every month, Tracie calculates the **weighted average cost of capital (WACC)**, and puts it in a memo for the top executives and project managers. It is the cost of capital for the company, where each category of capital, including both debt and equity, is proportionally weighted. It is also the RRR for new projects.

Here is the formula she uses:

**WACC = Wd(Kd(1 - t)) + We(Ke)**

Corporations raise funds either by borrowing it or by selling shares of new stock to investors. Here are what all of these variables mean:

d: is what they borrow; in other words, debt

e: is what they raise from stock, known as equity

K: stands for cost

t: stands for the tax rate

Kd: is the cost of debt; it is the interest rate paid on the debt, and it is multiplied by (1-t) to reduce it, since the interest paid is tax deductible.

Ke: is the cost of equity

Wd: stands for the weight of debt

We: the weight of the equity

The rates for each are weighted for their percentages of the total. For example, since Big Green has $6 million in debt and $4 million in equity, it's total capital is $10 million.

The weight of the debt = 6/10, or 0.6

The weight of the equity (We) = 4/10, or 0.4

Tracie gets the costs of Big Greens debt from the company treasurer, which turns out to be 8%, while the cost of equity is 4%. So, now it's time to put all of the numbers into the formula.

If the tax rate = 30%, or 0.3, the calculation looks like this:

WACC = 0.6 (0.08 (1 - 0.3) + 0.4 (0.04)

WACC = 0.6 (0.056) + 0.016

= 0.0336 + 0.016

= 0.0496

or rounded 0.05 = 5%

The project managers know now that any new project idea of theirs that doesn't make more than 5% return for the company will be rejected.

The **required rate of return (RRR)** on an investment is the minimum annual return that is necessary to induce people to invest in it. Investors use an RRR that is based on the risk of the investment. That is calculated using the **capital assets pricing model (CAPM)**, which determines the RRR for investments with different levels of risk, where beta is a measure of the investment's risk. The formula is:

Rf: risk free rate

Rm: return on the market

Beta: measure of the investment risk

Businesses use an RRR that is based on their cost of funds. New projects must return more than the costs of the money needed to fund them. The cost of funds is calculated using the **weighted average cost of capital (WACC)** formula. It is:

**WACC = Wd(Kd(1 - t)) + We(Ke)**

This formula weighs the cost of debt (Kd) and cost of equity (Ke) by the percentage of total capitalization for each piece (W).

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