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Chapter 13: Problem 21

Calculating the Cost of Equity Floyd Industries stock has a beta of 1.50. The company just paid a dividend of \(\$ \mathbf{. 8 0}\), and the dividends are expected to grow at 5 percent per year. The expected return on the market is 12 percent, and Treasury bills are yielding 5.5 percent. The most recent stock price for Floyd is \(\$ 61\). 1\. Calculate the cost of equity using the DDM method. 2\. Calculate the cost of equity using the SML method. 3\. Why do you think your estimates in (a) and (b) are so different?

Short Answer

Expert verified
The cost of equity using the Dividend Discount Model (DDM) is 6.377%, while the cost of equity using the Security Market Line (SML) method is 15.25%. The estimates are different because the DDM method focuses on dividends and their expected growth rate, while the SML method considers the risk associated with the stock (beta) and the expected market return. Different factors and assumptions drive both methods, leading to different results. Additionally, the DDM assumes constant dividend growth, while the SML factors in market performance and the stock's sensitivity to market movements.

Step by step solution

01

Calculate the cost of equity using the DDM method.

First, we will find the cost of equity using the Dividend Discount Model, which can also be described with the Gordon growth model. The formula for cost of equity using the DDM method is given by: Cost of Equity = \(\dfrac{Dividend_{1}}{Price_{0}} + g\) Where: Dividend_{1} = Dividend at the end of year 1 Price_{0} = The most recent stock price g = The expected growth rate of dividends Using the given data, the expected dividend at the end of year 1 can be calculated as: Dividend_{1} = Dividend * (1 + g) = \(.8 * (1 + .05 = \)\(.84\) Price_{0} = $61 Now you can plug these values into the DDM formula: Cost of Equity = \(\dfrac{.84}{61} + .05 =\) \(0.01377 + 0.05 = 0.06377\) So, the cost of equity using the DDM method is 6.377%.
02

Calculate the cost of equity using the SML method.

To calculate the cost of equity using the Security Market Line (SML) method, we need to use the Capital Asset Pricing Model (CAPM). The CAPM formula is: Cost of Equity = Risk-free rate + (Beta * (Expected market return - Risk-free rate)) Given data: Risk-free rate = 5.5% = 0.055 Beta = 1.50 Expected market return = 12% = 0.12 Now you can plug these values into the CAPM formula: Cost of Equity = 0.055 + (1.50 * (0.12 - 0.055)) = 0.055 + (1.50 * 0.065) = 0.055 + 0.0975 = 0.1525 So, the cost of equity using the SML method is 15.25%.
03

Explain why the estimates are different.

The estimates from the DDM and SML methods are different because of the following reasons: 1. The DDM method is based on dividends and their expected growth rate, while the SML method is based on the risk associated with the stock (beta) and the expected market return. Different factors and assumptions drive both methods, leading to different results. 2. The DDM assumes that dividends will grow at a constant rate forever, which may not always be accurate in real-world scenarios, while the SML method factors in the performance of the overall market and the stock's sensitivity to market movements (beta). In conclusion, both methods provide estimates of the cost of equity based on their underlying assumptions, and the differences in estimates can be attributed to the different factors each method takes into consideration. It's essential to understand the limitations of each approach when making decisions based on these calculations.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Dividend Discount Model (DDM)
The Dividend Discount Model (DDM) is a popular method used to estimate the cost of equity for a company. It focuses primarily on the dividends that a company expects to pay its shareholders. According to the DDM, the value of a stock is the present value of all its future dividends. One common way to implement this model is the Gordon Growth Model, which assumes that dividends will grow at a constant rate forever. For this reason:
  • Formula: The cost of equity in the DDM is calculated as \(\text{Cost of Equity} = \dfrac{\text{Dividend}_{1}}{\text{Price}_{0}} + g\), where \(\text{Dividend}_{1}\) is the expected dividend next year, \(\text{Price}_{0}\) is the current stock price, and \(g\) is the dividend growth rate.
  • Assumptions: The model assumes that the dividend growth rate \(g\) is constant and the company is expected to continue this forever.
This approach is straightforward and useful for companies that distribute consistent dividends. However, it doesn't consider non-dividend-related factors, like changing company policies or macroeconomic conditions, that might affect stock prices.
Security Market Line (SML)
The Security Market Line (SML) is an essential concept within portfolio management and investment. It's used to determine a stock's expected return in relation to its risk by utilizing the Capital Asset Pricing Model (CAPM). The SML provides a graphical representation of the expected return of an investment as a function of its beta, which measures the stock's volatility relative to the market:
  • Representation: The SML is a straight line on a graph where the x-axis represents beta, and the y-axis represents the expected return.
  • CAPM Application: Using CAPM, the cost of equity is calculated as \(\text{Cost of Equity} = \text{Risk-free rate} + (\beta \times (\text{Expected market return} - \text{Risk-free rate}))\), where \(\beta\) indicates stock risk compared to the market.
This method takes into account broader market risks, offering a broader view of what investors might expect in terms of return based on a stock's volatility and market behavior. Unlike the DDM, the SML focuses more on the comparative risk of stocks and market influences rather than dividend growth.
Capital Asset Pricing Model (CAPM)
The Capital Asset Pricing Model (CAPM) is a foundational theory in finance, extensively used for calculating the cost of equity. This model offers insights into the relationship between expected return and risk of investing in a particular asset. The CAPM formula combines information from both the risk-free rate, market return, and the asset's beta:
  • Understanding Beta: Beta \(\beta\) measures the systematic risk or a stock's sensitivity to market movements. A beta greater than 1 indicates higher volatility, while a beta less than 1 suggests less volatility compared to the market.
  • Risk-Free Rate: This is typically the yield on government bills or bonds, representing the return on an investment with zero risk, which forms the baseline for return expectations.
  • Expected Market Return: This is the average return expected from the overall market portfolio, often determined by historical market data.
By incorporating these factors, the CAPM aids in understanding the compensation investors require for taking on additional risk beyond risk-free investments. Unlike models focusing almost solely on dividends, such as the DDM, CAPM emphasizes market conditions and inherent stock risks, providing an alternative perspective on equity valuation.

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Most popular questions from this chapter

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