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

Short Answer

Expert verified
The nominal rates are 13.33%, 10%, 8%, and 5.71% for market prices $60, $80, $100, and $140, respectively.

Step by step solution

01

Understanding the Concept

Nominal rate of return for a perpetual preferred stock is calculated using the formula: \( r = \frac{D}{P} \), where \( D \) is the annual dividend, and \( P \) is the current market price. In this problem, \( D = 8\% \times 100 = 8 \).
02

Calculate Rate for $60 Market Price

Using the formula, the nominal rate of return for a market price of \( \$60 \) is \( r = \frac{8}{60} = 0.1333 \) or \( 13.33\% \).
03

Calculate Rate for $80 Market Price

For a market price of \( \$80 \), the nominal rate of return is \( r = \frac{8}{80} = 0.10 \) or \( 10\% \).
04

Calculate Rate for $100 Market Price

For a market price equal to the par value, \( \$100 \), the nominal rate of return is \( r = \frac{8}{100} = 0.08 \) or \( 8\% \), which matches the stated dividend rate.
05

Calculate Rate for $140 Market Price

Finally, for a market price of \( \$140 \), the nominal rate of return is \( r = \frac{8}{140} = 0.0571 \) or \( 5.71\% \).

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Key Concepts

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

Perpetual Preferred Stock
Perpetual preferred stock is a type of equity security that pays a fixed dividend to its holders for as long as the company is operational. Unlike common stock, perpetual preferred stock does not have a maturity date, making it "perpetual." It's an appealing option for investors seeking stable income, as the dividend rate is predetermined and generally consistent. This stability arises from the company’s commitment to distribute fixed dividends before any dividends are paid to common stockholders.

Key characteristics of perpetual preferred stock include:
  • Fixed Dividends: Holders receive regular, fixed payments, making this investment attractive for income-focused investors.
  • No Maturity Date: This means the stock can exist indefinitely as long as the company remains in operation.
  • Priority in Earnings: These stocks have a higher claim on earnings compared to common stock.
Perpetual preferred stock often offers a lower yield compared to bonds, but higher than common stocks. They provide a balance between risk and return, offering stability during market volatility.
Dividend Yield
The dividend yield is a financial ratio that shows how much a company pays out in dividends each year relative to its stock price. It's an important tool for investors, as it indicates how much income they might earn from their investment.

The dividend yield for a preferred stock is calculated using the formula:\[ \text{Dividend Yield} = \frac{\text{Annual Dividend}}{\text{Current Market Price}} \times 100 \]
This calculation helps investors determine the return on investment they can expect from owning a share of the stock if the price remains the same.

It's worth noting that a higher dividend yield is not always better, as it could indicate that the stock's price is low because of poor market conditions or negative perceptions about the company's performance. Investors should carefully consider the company's financial health along with its dividend yield.
Financial Calculations
Financial calculations are essential for evaluating investments and ensure that investors make informed decisions by understanding potential returns. In our exercise, the nominal rate of return of perpetual preferred stock is calculated using a straightforward formula:\[ r = \frac{D}{P} \]where \( D \) is the annual dividend and \( P \) is the current market price.

In practical terms, this formula breaks down the expected annual earnings from dividends relative to the market price. Performing these calculations helps investors know whether the expected returns meet their targets. Errors or misunderstandings in these calculations can significantly impact an investor's perception of value, so accuracy is crucial. It's advisable for investors to practice these calculations frequently to become comfortable and confident in their investment analysis skills.
Investment Analysis
Investment analysis involves evaluating various investment opportunities to determine their potential for return and risk. The goal is to make informed decisions that align with one's financial objectives and risk tolerance.

When analyzing investments like perpetual preferred stocks, consider the following:
  • Nominal Rate of Return: Examine the potential returns relative to market price to assess profitability.
  • Market Trends: Stay informed about economic factors that might affect market prices and dividend stability.
  • Company Stability: Investigate the issuing company's financial health to ensure continued dividend payments.
Investment analysis helps differentiate between high-risk, high-reward opportunities, and low-risk, steady ones. By assessing elements such as nominal rate of return and dividend payouts, investors can tailor their portfolios to meet their specific goals. Strong investment analysis results in informed decision-making, aiming for maximum returns while safeguarding against significant losses.

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Most popular questions from this chapter

Assume that it is now January \(1,2006 .\) Wayne-Martin Electric Inc. (WME) has just developed a solar panel capable of generating 200 percent more electricity than any solar panel currently on the market. As a result, WME is expected to experience a 15 percent annual growth rate for the next 5 years. By the end of 5 years, other firms will have developed comparable technology, and WME's growth rate will slow to 5 percent per year indefinitely. Stockholders require a return of 12 percent on WME's stock. The most recent annual dividend (D), which was paid yesterday, was \(\$ 1.75\) per share. a. Calculate WME's expected dividends for \(2006,2007,2008,2009,\) and 2010 b. Calculate the value of the stock today, \(\hat{P}_{0}\). Proceed by finding the present value of the dividends expected at the end of \(2006,2007,2008,2009,\) and 2010 plus the present value of the stock price that should exist at the end of 2010 . The year-end 2010 stock price can be found by using the constant growth equation. Notice that to find the December 31,2010 , price, you must use the dividend expected in 2011 , which is 5 percent greater than the 2010 dividend. c. Calculate the expected dividend yield, \(D_{1} / P_{0}\), capital gains yield, and total return (dividend yield plus capital gains yield) expected for 2006 . (Assume that \(\hat{P}_{0}=P_{0 \prime}\) and recognize that the capital gains yield is equal to the total return minus the dividend yield.) Then calculate these same three yields for 2011 d. How might an investor's tax situation affect his or her decision to purchase stocks of companies in the early stages of their lives, when they are growing rapidly, versus stocks of older, more mature firms? When does WME's stock become "mature" for purposes of this question? e. Suppose your boss tells you she believes that WME's annual growth rate will be only 12 percent during the next 5 years and that the firm's long-run growth rate will be only 4 percent. Without doing any calculations, what general effect would these growth-rate changes have on the price of WME's stock? f. Suppose your boss also tells you that she regards WME as being quite risky and that she believes the required rate of return should be 14 percent, not 12 percent. Without doing any calculations, how would the higher required rate of return affect the price of the stock, the capital gains yield, and the dividend yield? Again, assume that the long-run growth rate is 4 percent.

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

C's beta coefficient is \(\mathrm{b}_{\mathrm{C}}=0.4,\) while Stock D's is \(\mathrm{b}_{\mathrm{D}}=-0.5 .\) (Stock \(\mathrm{D}^{\prime}\) s beta is negative, indicating that its return rises when returns on most other stocks fall. There are very few negative beta stocks, although collection agency stocks are sometimes cited as an example.) a. If the risk-free rate is 7 percent and the expected rate of return on an average stock is 11 percent, what are the required rates of return on Stocks \(C\) and \(D ?\) b. For Stock \(C\), suppose the current price, \(P_{0}\), is \(\$ 25\); the next expected dividend, \(D_{1}\), is \(\$ 1.50 ;\) and the stock's expected constant growth rate is 4 percent. Is the stock in equilibrium? Explain, and describe what would happen if the stock is not in equilibrium.

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

Taussig Technologies Corporation (TTC) has been growing at a rate of 20 percent per year in recent years. This same growth rate is expected to last for another 2 years, then to decline to \(g_{n}=6 \%\). a. If \(\mathrm{D}_{0}=\$ 1.60\) and \(\mathrm{r}_{\mathrm{s}}=10 \%\) what is TTC's stock worth today? What are its expected dividend and capital gains yields at this time, that is, during Year \(1 ?\) b. Now assume that TTC's period of supernormal growth is to last for 5 years rather than 2 years. How would this affect the price, dividend yield, and capital gains yield? Answer in words only. c. What will TTC's dividend and capital gains yields be once its period of supernormal growth ends? (Hint: These values will be the same regardless of whether you examine the case of 2 or 5 years of supernormal growth; the calculations are very easy. d. Of what interest to investors is the changing relationship between dividend and capital gains yields over time?

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