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Chapter 9: Problem 1

Warr Corporation just paid a dividend of \(\$ 1.50\) a share (i.e., \(D_{0}=\$ 1.50\) ). The dividend is expected to grow 5 percent a year for the next 3 years, and then 10 percent a year thereafter. What is the expected dividend per share for each of the next 5 years?

Short Answer

Expert verified
Year 1: $1.575, Year 2: $1.65375, Year 3: $1.7364375, Year 4: $1.91008125, Year 5: $2.101089375.

Step by step solution

01

Identify the Initial Dividend

The initial dividend just paid is \( D_0 = 1.50 \). This is the starting point for calculating future dividends.
02

Calculate Year 1 Dividend

Use the growth rate for the next 3 years of 5% to calculate the Year 1 dividend. The formula is \( D_1 = D_0 \times (1 + g) \), where \( g = 0.05 \). Thus, \( D_1 = 1.50 \times 1.05 = 1.575 \).
03

Calculate Year 2 Dividend

Apply the 5% growth rate again: \( D_2 = D_1 \times (1 + g) = 1.575 \times 1.05 = 1.65375 \).
04

Calculate Year 3 Dividend

Use the same 5% growth rate: \( D_3 = D_2 \times (1 + g) = 1.65375 \times 1.05 = 1.7364375 \).
05

Calculate Year 4 Dividend

From Year 4 onwards, dividends grow at 10%. Therefore, \( D_4 = D_3 \times (1 + 0.10) = 1.7364375 \times 1.10 = 1.91008125 \).
06

Calculate Year 5 Dividend

Using the 10% growth rate again: \( D_5 = D_4 \times (1 + 0.10) = 1.91008125 \times 1.10 = 2.101089375 \).

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Key Concepts

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

Dividend Calculation
Dividend calculation is a vital concept in corporate finance, representing the process of determining the amount shareholders receive from a company's profits. In the context of growing dividends, as seen in Warr Corporation's case, the calculations take into account a series of growth rates.

When calculating future dividends, you need to start with the initial dividend, often denoted as \(D_0\). With Warr Corporation, \(D_0\) was \$1.50.
  • To calculate the dividend for Year 1, apply the growth rate: \( D_1 = D_0 \times (1 + g) \).
  • Repeat this approach annually, using the previous year's dividend to find the next. For example, \(D_2 = D_1 \times (1 + g)\), and so forth.
Understanding each step ensures accuracy and allows for projections into future earnings that take compounding of growth into account. This sequential accumulation is what gives investors a predicted future income from their investment.
Financial Analysis
Financial analysis involves evaluating a company's financial statements to make better economic decisions. This includes the calculation of expected dividends, which can tell us a lot about a company's future performance and financial health.

Analyzing Warr Corporation's case means looking at how the dividends grow year over year. The growth rate reflects the company's policy of increasing shareholder value over time.
  • The initial growth rate of 5% may indicate steady, consistent growth expectations.
  • A shift to a 10% growth rate suggests a potential increase in company performance or profitability.
Evaluating these growth patterns helps in assessing the risk and return involved in the company鈥檚 securities. By understanding these dividend changes, investors can gauge potential returns on their equity investments.
Growth Rate
The growth rate in dividends is crucial as it shows how much the dividend is expected to increase each year. For Warr Corporation, the growth rate shifted from 5% over the first three years to 10% in subsequent years.

A growth rate is presented as a percentage and signifies the annual compounding effect on dividends. To calculate it:
  • Start with the known dividend and use the growth factor to project future dividends over a period of time.
  • The formula \( g = (D_{n} - D_{0}) / D_{0} \) can be helpful to understand the rate from start to end over a specified period.
Managing and calculating growth rates allow companies and investors to forecast future performances and understand potential returns better. A rising growth rate can also imply an expectation of increased profitability or company expansion, resulting in greater shareholder value.

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Most popular questions from this chapter

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. a. If \(\mathrm{D}_{0}=\$ 1.60, \mathrm{k}=10 \%,\) and \(\mathrm{g}_{\mathrm{n}}=6 \%,\) what is TTC's stock worth today? What are its expected dividend yield and capital gains yield at this time? b. Now assume that TTC's period of supernormal growth is to last for 5 years rather than 2 years. How would this affect its price, dividend yield, and capital gains yield? Answer in words only. c. What will be TTC's dividend yield and capital gains yield 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 yield and capital gains yield over time?

Ezzell Corporation issued preferred stock with a stated dividend of 10 percent of par. Preferred stock of this type currently yields 8 percent, and the par value is \(\$ 100\). Assume dividends are paid annually. a. What is the value of Ezzell's preferred stock? b. Suppose interest rate levels rise to the point where the preferred stock now yields 12 percent. What would be the value of Ezzell's preferred stock?

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 \(\mathrm{k}_{\mathrm{s}}=15 \%,\) what is the value of Martell Mining's stock?

It is now January \(1,2002 .\) 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 \(2002,2003,2004,2005,\) and 2006 b. Calculate the value of the stock today, \(\hat{\mathrm{P}}_{0}\). Proceed by finding the present value of the dividends expected at the end of \(2002,2003,2004,2005,\) and 2006 plus the present value of the stock price that should exist at the end of \(2006 .\) The year-end 2006 stock price can be found by using the constant growth equation. Notice that to find the December \(31,2006,\) price, you use the dividend expected in \(2007,\) which is 5 percent greater than the 2006 dividend. c. Calculate the expected dividend yield, \(D_{1} / P_{0}\), the capital gains yield expected in 2002 , and the expected total return (dividend yield plus capital gains yield) for 2002 . (Assume that \(\mathrm{P}_{0}=\mathrm{P}_{0},\) and recognize that the capital gains yield is equal to the total return minus the dividend yield.) Also calculate these same three yields for 2007 . 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" in this example? 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 normal growth rate will be only 4 percent. Without doing any calculations, what general effect would these growthrate 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. Again, without doing any calculations, how would the higher required rate of return affect the price of the stock, its capital gains yield, and its dividend yield? Again, assume that the firm's normal growth rate will be 4 percent.

Fee Founders has preferred stock outstanding that pays a dividend of \(\$ 5\) at the end of each year. The preferred stock sells for \(\$ 60\) a share. What is the preferred stock's required rate of return?
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