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Chapter 9: Problem 8

Ezzell Corporation issued perpetual preferred stock with a \(10 \%\) annual dividend. The stock currently yields \(8 \%\), and its par value is \(\$ 100\). a. What is the stock's value? b. Suppose interest rates rise and pull the preferred stock's yield up to \(12 \% .\) What is its new market value?

Short Answer

Expert verified
a. $125 b. $83.33

Step by step solution

01

Understand the Perpetual Preferred Stock

Perpetual preferred stock pays an annual dividend indefinitely. The dividend is calculated as a percentage of the par value.
02

Calculate the Annual Dividend

The annual dividend for the preferred stock is computed as \(10\%\) of its par value of \(\\(100\). \[ \text{Annual Dividend} = 0.10 \times 100 = \\)10 \]
03

Calculate the Stock's Value at 8% Yield

To find the stock's value when it yields \(8\%\), use the formula: \[ \text{Value} = \frac{\text{Annual Dividend}}{\text{Yield}} = \frac{10}{0.08} = \$125 \]
04

Calculate the New Market Value at 12% Yield

When the yield increases to \(12\%\), recalculate the stock's value:\[ \text{New Value} = \frac{\text{Annual Dividend}}{\text{New Yield}} = \frac{10}{0.12} \approx \$83.33 \]

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Key Concepts

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

Dividend Calculation
When dealing with perpetual preferred stock, understanding how to calculate the dividend is crucial. The annual dividend is determined based on a percentage of the stock's par value. Simply put, you multiply the par value by the dividend rate to find out what the stockholder earns each year. In our example, Ezzell Corporation's preferred stock has a par value of $100 and pays a 10% dividend. Therefore, the calculation is straightforward:
  • Annual Dividend = 10% of $100
  • Annual Dividend = $10
Every year, a stockholder with this preferred stock can expect to receive $10 in dividends.
Yield Impact on Valuation
The yield of a preferred stock has a direct impact on its valuation. When we discuss yield, we're looking at the returns that an investor earns from the stock. The formula to find the stock's value when you know the yield is the dividend divided by the yield percentage.
In this exercise, when the stock yields 8%, the formula is:
  • Stock's Value = Annual Dividend / Current Yield
  • Stock's Value = $10 / 0.08 = $125
This means that with an 8% yield, the stock's market value is $125. Changes in yield can significantly alter the stock's perceived market value.
Interest Rate Changes
Interest rate changes affect stock yields significantly. When interest rates fluctuate, they can drive changes in preferred stock yields because investors compare the rates of return across different investment options. If interest rates rise, investors might seek higher yields, causing stock prices to drop until the yield aligns with the new rate.
For instance, with Ezzell Corporation's preferred stock, if interest rates rise resulting in a 12% yield, the value of the stock needs adjustment:
  • New Market Value = Annual Dividend / New Yield
  • New Market Value = $10 / 0.12 鈮� $83.33
The increased yield from rising interest rates leads to a lower stock price in this case.
Financial Management Concepts
Understanding financial management is essential when evaluating investment opportunities like perpetual preferred stock. This involves recognizing how factors such as dividend policies, yield, and interest rate changes interact. When making investment decisions:
  • Know how dividends affect your income.
  • Understand that yield impacts how much investors value a stock.
  • Be aware that interest rate changes can make preferred stocks more or less attractive.
These concepts help investors balance risk and return, ensuring they make informed decisions and manage portfolios that suit their financial goals.

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Most popular questions from this chapter

Hart Enterprises recently paid a dividend, Do, of \(\$ 1.25 .\) It expects to have nonconstant growth of \(20 \%\) for 2 years followed by a constant rate of \(5 \%\) thereafter. The firm's required return is \(10 \%\) a. How far away is the terminal, or horizon, date? b. What is the firm's horizon, or terminal, value? c. What is the firm's intrinsic value today, \(\hat{\mathrm{P}}_{0} ?\)

Martell Mining Company's ore reserves are being depleted, so its sales are falling. Also, because its pit is getting deeper each year, its costs are rising. As a result, the company's earnings and dividends are declining at the constant rate of \(5 \%\) per year. If \(\mathrm{D}_{0}=\$ 5\) and \(\mathrm{r}_{\mathrm{s}}=15 \%\), what is the value of Martell Mining's stock?

Harrison Clothiers' stock currently sells for \(\$ 20.00\) a share. It just paid a dividend of \(\$ 1.00\) a share (that is, \(\mathrm{D}_{0}=\$ 1.00\) ). The dividend is expected to grow at a constant rate of \(6 \%\) a year. What stock price is expected 1 year from now? What is the required rate of return?

Warr Corporation just paid a dividend of \(\$ 1.50\) a share (that is, \(\left.\mathrm{D}_{0}=\$ 1.50\right) .\) The dividend is expected to grow \(7 \%\) a year for the next 3 years and then at \(5 \%\) a year thereafter. What is the expected dividend per share for each of the next 5 years?

What will be the nominal rate of return on a perpetual preferred stock with a \(\$ 100\) par value, a stated dividend of \(8 \%\) of par, and a current market price of (a) \(\$ 60,(\mathrm{b}) \$ 80,(\mathrm{c}) \$ 100,\) and (d) \(\$ 140 ?\)
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