Chapter 12 Notes: Determining the Cost of Capital

Chapter 12 - Determining Required Return on Assets

This chapter focuses on quantifying the required return on an asset based on its risk, building upon the understanding that higher risk necessitates higher expected returns (from Chapter 11).

Diversification and Risk

• Diversification Assumption: We assume investments are held in a well-diversified portfolio, eliminating specific risk, and focusing solely on market risk.

• Total Risk vs. Market Risk: Total risk is measured by standard deviation; market risk, for a diversified portfolio, is measured by beta.

• Beta Coefficient:

  • Market beta is one (\beta_{market} = 1).

  • Risk-free asset (Treasury bill) beta is zero (\beta_{risk-free} = 0), indicating no correlation with the market.

Understanding Beta

• Defensive Stocks: Stocks with a beta less than one (\beta < 1). If the market goes up by 1%, a stock with a beta of 0.8 is expected to rise by 0.8%, and vice versa.

• Negative Beta: Some assets may have a negative beta, implying an inverse relationship with market movements (when the market goes up, the stock price tends to go down, and vice versa).

Market Risk Premium

• Definition: The excess return required for investing in the market portfolio over the risk-free rate.

• Market Portfolio Proxy: The S&P 500 index is used as a proxy for the market portfolio, representing 500 large U.S. corporations.

S&P 500 Index Funds

• Market-Weighted Index: Investments are distributed among firms based on market capitalization (stock price multiplied by shares outstanding), with larger firms receiving a greater proportion of the investment.

• Magnificent Seven: Seven firms (Apple, Amazon, Netflix, Google, Meta, Tesla, Nvidia) constitute a significant portion (approximately 20-25%) of the S&P 500.

• Time in the market beats timing the market

Key Terminology and Formulas

• Market Portfolio: Represented by the S&P 500 index.

• Beta (β): Sensitivity of a stock's returns to changes in the market portfolio's returns.

• Market Risk Premium: Calculated as the return on the market (Rm) minus the risk-free rate (Rf): (Market Risk Premium = Rm - Rf)

• Return on the Market: the return on the S&P 500.

Determining Expected Return

To determine the expected return on an asset, we must understand its beta.

• A stock with a beta of one is as equally risky as the market portfolio.

• Aggressive Stocks: Stocks with betas greater than 1.

• Defensive Stocks: Stocks with betas less than 1. Examples are utility companies and food manufacturers.

Capital Asset Pricing Model (CAPM)

• Development: Developed in 1964, the CAPM quantifies the relationship between risk and expected return. William Sharp won a Nobel Prize in 1990 for his contribution to asset pricing.

• Significance: It was the first model to, in a sense, quantify naive approach to risk. Since CAPM, there have been more recent additions to the model.

• Application: Despite being theoretical, the CAPM is empirically tested to predict stock returns. The CAPM still does a really good job of predicting the stock's return.

Core Principles of CAPM

• Only market risk matters (undiversifiable risk).

• Specific risk (diversifiable risk) is not considered due to the assumption of a well-diversified portfolio.

Computing Expected Risk Premium

The expected risk premium on any asset is the market risk premium multiplied by the firm's beta

• The risk premium of an asset is the excess return for this asset above/beyond the risk free rate.

• Formula: \text{Risk Premium on Asset} = \text{Market Risk Premium} \times \text{Firm's Beta}

CAPM Equation and Security Market Line (SML)

• CAPM Equation: E(Ri) = Rf + \betai (E(Rm) - R_f)

  • Where:

    • E(R_i) = Expected return on asset i

    • R_f = Risk-free rate

    • \beta_i = Beta of asset i

    • E(R_m) = Expected return on the market

• Security Market Line Equation

• Based on the equation of a line: y = mx + b, but using stock terminology.

  • R_f is the y-intercept.

  • (E(Rm) - Rf) is the slope.

Important Considerations

It's important to understand the difference between market return and market risk premium

• The return on any asset always starts with the risk free rate.

• Make sure any unknowns can be solved for.

Example 1: Computing Expected Return and Risk Premium

Problem

The expected return on the stock market is 10%, and T-bills are yielding 3%. Stock X has a beta of 0.5. Find Stock X's expected return and risk premium.

Solution

• Right away, because the beta is less than one, its expected return is gonna be less than 10%.

• Expected Return: 3\% + (7\% \times 0.5) = 6.5\% , since the market risk premium is 10\% - 3\% = 7\%.

• Risk Premium for Stock X: 7\% \times .5 = 3.5\%.

• 6. 5% is guaranteed by the treasury bill rate, plus 3.5% to compensate for taking risk.

Security Market Line Visualization

• Returns on the Y axis and Risk can be found on the X axis.

• The Y intercept is the risk free rate.

• Stocks should plot on the security market line. This can only happen when there is no monopolies and there are lots of investors that have no private information.

• Stock Z lies above the security market line and has what is called alpha. Alpha is an abnormal return or extra return above and beyond what is predicted by the capital asset pricing model.

• Stock red sun lies below the security market line and can be referred to having a negative alpha.

Practical Applications

Assume:

• Risk free rate is 1%

• Market risk premium is 7%
  With these assumptions, we also plug in different firm's Beta Coefficients to get their Return.

A lot of S&P 500 firms were rated from this.

S& P 500 - Time in the Market

The longer you can keep your money in the stock market, the higher the probability that you will have a positive return.

• 1 Day - 53%

• 1 Month - 62%

• 1 Year - 74%

• 5 Years - 88%

• 10 Years - 95%

• 15 Years - 100%

Investing Today

You have to have a lot of patience, pay your bills and you have to pay yourself.

Example 2: Solving for Beta given Expected Return

Problem

Sprouts' common stock has an expected return of 14.48%. The expected return on the S&P 500 is 11.6%, and the U.S. T-bill rate is 3.42%. What is Sprout's beta?

Solution

Using the CAPM equation: 14.48\% = 3.42\% + \beta \times (11.6\% - 3.42\%)

Solving for beta, we get: \beta = 1.35

Testing the CAPM

• Aggressive Stocks are sometimes known as growth stocks (high beta stocks).

• Defensive Stocks are sometimes known as value stocks (low beta stocks).

Studies have found:

• Low Beta tend to be above the security market line.

• High Beta tend to be below the security market line. This is due to stocks being bid up so high that excess and expected return decreases.

The Takeaway is that to find opportunity, you have to something that other people do not.

Project Evaluation and Cost of Capital

• From the perspective of a corporation. General Electric. Applying cost of capital or required return.

• Another name for required return is cost of capital.
  Whenever we have a discount rate of which we use for projects to compute NPV we call that the opportunity cost of capital-required return.

• Required return, you see it in next couple of chapters, is also referred to as cost of capital. This is also something we saw back in chapter number six, chapter administration, we got introduced to it back in chapter number five.

• The discount rate that we shrink future cash flows back to the present will always be based on what we call our cost of capital or our required return. The book will use them interchangeably.

Project-Specific Required Returns

A firm's overall required return may differ from a specific project's required return.

Applying Appropriate Discount Rates

• When you're whenever you're trying something different, right, there's an unknown, the risk is gonna be greater. Right? There you probably gotta use a higher requirement to earn a higher cost of capital.

• General Electric is a is a good example there for brand new ventures.

• Coca Cola when opened up a new bottling plant should know the process from experience around the world.

Security Market Line - the projects expected return

• Expected return, required return and cost of capital pretty much mean the same thing.

Depend on the risk of the project and not on the risk of the company but what if the project has the same level of risk as the firm does? Then we can use the firms required return.
If the project is riskier than average then we have to adjust it, if the project is less risky that the average risk of the average project of the firm, we also can adjust it downward.

Company Cost of Capital

• Weighted average cost of capital if you're reading ahead.

• The opportunity cost is the company cost of capital of the firm as a whole.

• Lower risk projects should have lower discount rates since it is easy money.

• Higher risk projects should have higher discount rates since there is more risk involved.

Project and Firm Evaluation Example

Assumptions: It depends on the risk of the project and not on the risk of the company. Project has the same level of risk as the firm does! We can use the firm's required return.

There is a lot going on in Figure 12 right there.

Looking at Figure 12:

• Data is on the X axis.

• Expected return is on the Y axis.

• The is a firm with an expected return of 9.4%, which has a beta of .9.

• Project # 1: Beta of .4 and expected return of 7%.

• Project # 2: Beta of .8 and expected return of 8%.

• Project # 3: Beta of 1.2 and expected return of 13%.

• Project # 4: Beta of 1.4 an expected return of 11%.

What should be the best course of actions for this firm? Use the security market line with a given risk free rate a projects above the security market line should be accepted, the project below the Security Market Line should be rejected.