Stock Investing 101 – Required Rate of Return

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The 5 Components of an Investor’s Required Rate of Return

Understanding How Rational Investors Value Cash Flows

In financial theory, the rate of return at which an investment trades is the sum of five different components. Over time, asset prices tend to reflect the impact of these components fairly well. For those of you who want to learn to value stocks or understand why bonds trade at certain prices, this is an important part of the foundation.

The Real Risk-Free Interest Rate

This is the rate to which all other investments are compared. It is the rate of return an investor can earn without any risk in a world with no inflation. Most people reference the three-month U.S. Treasury bill as offering the risk-free rate.

An Inflation Premium

This is the rate that is added to an investment to adjust it for the market’s expectation of future inflation. For example, the inflation premium required for a one-year corporate bond might be a lot lower than a 30-year corporate bond by the same company because investors think that inflation will be low in the short term, but pick up in the future as a result of the trade and budget deficits of years past.

A Liquidity Premium

Some investments don’t trade very often, and that presents a risk to the investor. Thinly traded investments such as stocks and bonds in a family-controlled company require a liquidity premium. That is, investors are not going to pay the full value of the asset if there is a very real possibility that they will not be able to dump the stock or bond in a short period of time because buyers are scarce. This is expected to compensate them for that potential loss. The size of the liquidity premium is dependent upon an investor’s perception of how active a particular market is.

Default Risk Premium

Do investors believe a company will default on its obligation or go bankrupt? Often, when signs of trouble appear, a company’s shares or bonds will collapse as a result of investors demanding a default risk premium.

If someone were to acquire assets that were trading at a huge discount as a result of a default risk premium that was too large, they could make a great deal of money.

Many asset management companies actually bought shares of Enron’s corporate debt during the now-famous meltdown of the energy-trading giant. In essence, they bought $1 of debt for only a few pennies. If they can get more than they paid in the event of a liquidation or reorganization, it can make them very, very rich.

K-Mart is another example. Prior to the retailer’s bankruptcy, distressed debt investors bought an enormous portion of its debt. When the company was reorganized in bankruptcy court, the debt holders were given equity in the new company. Lampert then used his new controlling block of K-Mart stock with its improved balance sheet to start investing in other assets.

Maturity Premium

The further in the future the maturity of a company’s bonds, the greater the price will fluctuate when interest rates change. That’s because of the maturity premium. Here’s a very simplified version to illustrate the concept: Imagine you own a $10,000 bond with a 7% yield when it is issued that will mature in 30 years. Each year, you will receive $700 in interest. Thirty years in the future, you will get your original $10,000 back. Now, if you were going to sell your bond the next day, you would likely get around the same amount (minus, perhaps, a liquidity premium as we already discussed).

Consider if interest rates rise to 9%. No investor is going to accept your bond, which is yielding only 7% when they could easily go to the open market and buy a new bond that yields 9%. So, they will only pay a lower price than your bond is worth – not the full $10,000—so that the yield is 9% (say, maybe $7,775.) This is why bonds with longer maturities are subject to a much greater risk of capital gains or losses. Had interest rates fallen, the bondholder would have been able to sell his or her position for much more. If rates fell to 5 percent, then he could have sold for $14,000.

Required Rate of Return

The required rate of return, defined as the minimum return the investor will accept for a particular investment, is a pivotal concept to evaluating any investment. It is supposed to compensate the investor for the riskiness of the investment. If the expected return of an investment does not meet or exceed the required rate of return, the investor will not invest. The required rate of return is also called the hurdle rate of return.

Required Rate of Return Explanation

Required rate of return, explained simply, is the key to understanding any investment. This essentially requires determining the investor’s cost of capital. The investment will be attractive as long as the expected returns on the project or investment exceed the cost of capital. The cost of capital can be the cost of debt, the cost of equity, or a combination of both.

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If the investor is a company considering the required rate of return on a corporate project, then calculating the cost of debt is simple. It is the interest rates on the company’s debt obligations. If the company has numerous differing debt obligations, then use the weighted average of those interest rates to find the cost of debt.

Calculating the cost of equity can be done using the capital asset pricing model (CAPM). Estimate this by finding the cost of equity of projects or investments with similar risk. Like with the cost of debt, if the company has more than one source of equity – such as common stock and preferred stock – then the cost of equity will be a weighted average of the different return rates.

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Required Rate of Return Formula

The core required rate of return formula is:

Required rate of return = Risk-Free rate + Risk Coefficient(Expected Return – Risk-Free rate)

Required Rate of Return Calculation

The calculations appear more complicated than they actually are. Using the formula above. See how we calculated it below:

Required rate of Return = .07 + 1.2($100,000 – .07) = $119,999.99

Risk-Free rate = 7%
Risk Coefficient = 1.2
Expected Return = $100,000

Weighted Average Cost of Capital (WACC)

Combining the cost of equity and the cost of debt in a weighted average will give you the company’s weighted average cost of capital, or WACC. Consider this rate to be the required rate of return, or the hurdle rate of return, that the proposed project’s return must exceed in order for the company to consider it a viable investment.

Required Rate of Return for Investments

In terms of investments, like stocks, bonds, and other financial instruments, the required rate of return refers to the necessary expected return on the investment needed by the investor in order for him to consider investing. This rate can be based on investments with similar risk, or it can be the rate of the investor’s next best alternative investment opportunity.

For example, if an investor has his money in a savings account earning 5% annual interest, and he is considering investing in a risk-free treasury bond, then he might say the return on assets for such an investment is 5%. The treasury bond must yield more than 5% per year for the investor to consider taking his money out of the savings account and investing it in the bond. In this case, the investor’s required rate of return would be 5%.

Required Rate of Return Example

For example, Joey works for himself as a professional stock investor. Because he is highly analytical, this work perfectly fits him. Joey prides himself on his ability to evaluate where the market is and where it will be.

Joey knows his next investment option is high-stakes and risky. He wants to know his required rate of return on equity for a stock he is thinking about investing in. Joey performs the calculation below to find his answer:

Required Rate of Return = .07 + 1.2($100,000 – .07) = $119,999.99

If:
Risk-Free rate = 7%
Risk Coefficient = 1.2
Expected Return = $100,000

Joey decides that his investment is not a good decision because his required rate of return is quite high. He resolves to find less risky decisions in order to protect the success he has already created. Without calculating his required rate of return on stock Joey could have ruined everything that he has created so far. Joey uses this experience to humble himself as he moves forward.

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Required Rate of Return

is the minimum return in percentage that an investor must receive due to time value of money and as compensation for investment risks.

There are multiple models to work out required rate of return on equity, preferred stock, debt and other investments.

The most basic framework is to estimate required rate of return based on the risk-free rate and add inflation premium, default premium, liquidity premium and maturity premium, whichever is applicable.

The formula for the general required rate of return can be written as:

Required Return = rf + IRP + DRP + LRP + MRP

Where,
rf is the real risk-free rate is the rate of return on Treasury inflation-protected securities.
IRP stands for inflation risk premium, the compensation for inflation risk;
DRP stands for default risk premium, the compensation for risk of investment loss due to default;
LRP stands for liquidity risk premium, the compensation for illiquidity and lack of marketability and
MRP stands for maturity risk premium, the compensation for higher interest rate risk and reinvestment risk that results from longer maturities.

Required Return on Equity (i.e. Common Stock)

The required return on equity is also called the cost of equity. There are three common models to estimate required return on common stock: the capital asset pricing model, the dividend discount model and the bond yield plus risk premium approach.

Capital Asset Pricing Model (CAPM) Formula

The capital asset pricing model estimates required rate of return using the following formula:

Required Return on Equity (CAPM)
= Risk Free Rate (rf) + Equity Risk Premium
= Risk Free Rate (rf) + Beta × Market Risk Premium
= Risk Free Rate (rf) + Beta × (Market Return (rm) − Risk Free Rate (rf))

Where rf is the nominal risk-free rate, beta coefficient is a measure of systematic risk and rm is the return on the broad market index such as S&P 500. Equity risk premium equals beta multiplied by market risk premium and market risk premium equals the difference between rm and rf.

Dividend Discount Model (DDM) Formula

The dividend discount model (DDM) estimates required return on equity using the following formula:

Required Return on Equity (DDM) = D0 × (1 + g) + g
P0

Where D0 is the current annual dividend per share, P0 is the current price of the stock and g is the growth rate of dividends. The growth rate equals the product of retention ratio and return on equity (ROE).

g = Retention Ratio × ROE

Bond Yield plus Risk Premium Approach Formula

The bond yield plus risk premium approach adds a certain equity risk premium (based on historical analysis) to the yield on a company’s publicly-traded bonds.

Required Return on Preferred Stock

Required return on preferred stock is also called cost of preferred stock and it equals the ratio of preferred dividends per share (D) to the current price of the preferred stock (P0):

Required Return on Preferred Stock = D
P0

Required Return on Debt

Required return on debt (also called cost of debt) can be estimated by calculating the yield to maturity of the bond or by using the bond-rating approach.

The yield to maturity is the internal rate of return of the bond i.e. the rate that equates the current price of the bond to its future cash flows based on the following equation:

Bond Price = c × F × 1 − (1 + r) -t + F
r (1 + r) t

Where, c is the periodic coupon rate which equals annual coupon rate divided by number of coupon payments per year, F is the face value i.e. principal amount, t is total number of coupon payments till maturity, and r is the periodic yield to maturity. Annual yield to maturity equals periodic yield to maturity multiplied by coupon payments per year.

Where the debt is not publicly traded, the required return on debt can be inferred from the yield to maturity of other marketable bonds which carry the same bond rating as the bond under consideration.

The build-up approach can also be used to estimate required return on debt. It involves adding inflation, default, liquidity and maturity premia to the real risk free rate.

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