Question

Robert Campbell and Carol Morris are senior vice-presidents of the Mutual of Chicago Insurance Company. They are co-directors of the company’s pension fund management division. A major new client has requested that Mutual of Chicago present an investment seminar to illustrate the stock valuation process. As a result, Campbell and Morris have asked you to analyze the Bon Temps Company, an employment agency that supplies word processor operators and computer programmers to businesses with temporarily heavy workloads. You are to answer the following questions.

1. What is the difference between common stock and preferred stock? What are some of the characteristics of each type of stock?
2. (1) Write a formula that can be used to value any stock, regardless of its dividend pattern.

      (2) What is a constant growth stock? How do you value a constant growth stock?

(3) What happens if the growth is constant, and g > r_s? Will many stocks have g > r_s?

3. Bon Temps has an issue of preferred stock outstanding that pays stockholders a dividend equal to $10 each year. If the appropriate required rate of return for this stock is 8%, what is its market value?
4. Assume that Bon Temps is a constant growth company whose last dividend (D₀, which was paid yesterday) was $2 and whose dividend is expected to grow indefinitely at a 6% rate. The appropriate rate of return for Bon Temps’ stock is 16%.

      (1) What is the firm’s expected dividend stream over the next 3 years?

      (2) What is the firm’s current stock price?

      (3)

What is the stock’s expected value one year from now?

      (4) What are the expected dividend yield, the capital gains yield, and the total return during the first year?

5. Assume that Bon Temps’ stock is currently selling at $21.20. What is the expected rate of return on the stock?
6. Assume that Bon Temps is expected to experience supernormal growth of 30% for the next 3 years, then to return to its long-run constant growth rate of 6%. What is the stock’s value under these conditions? What are its expected dividend yield and its capital gains yield in Year 1? In Year 4?
7. Suppose Bon Temps is expected to experience zero growth during the first three years and then to resume its steady-state growth of 6% in the fourth year. What is the stock’s value now? What are its expected dividend yield and its capital gains yield in Year 1? In Year 4?

Answer 1

a. A preferred stock is a share of ownership in a public company. It has some qualities of a common stock and some of a bond. Preferred stocks pays dividend like common stocks. The difference is that preferred stocks pay an agreed-upon dividend at regular intervals. This quality is similar to that of bonds. Common stocks may pay dividends depending on profit of the company. Preferred stock dividends are often higher than common stock dividends. However, voting rights are granted only to common stock holders and not to preferred stock holders.

Characteristics of Common Stock:

• Common stock gives you the voting rights of the company.
• Existing stockholders have the right to purchase on a pro rata basis any additional shares sold by the firm. This right protects (1) control of present stockholders, and (2) existing stockholders against a dilution of wealth.

Characteristics of Preferred Stock:

• Preferred stock has characteristics of both common stock and a bond; it is sometimes referred to as a hybrid security.
• Preferred stocks have priority in Earnings and Assets of the company at the time of dissolution.
• Preferred stock rank ahead of common stockholders but behind bondholder.

b. 1) The value of any stock is the present value of its expected dividend stream:

However, some stocks have dividend growth patterns which allow them to be valued using short-cut formulas

b. 2) A constant growth stock is one whose dividends are expected to grow at a constant rate forever. Many companies have dividends which are expected to grow steadily into the foreseeable future, and such companies are valued as constant growth stocks.

For a constant growth stock: D₁ = D₀(1 + g)

D₂ = D₁(1 + g) = D₀(1 + g)², and so on.

With this regular dividend pattern, the general stock valuation model can be simplified to the following very important equation:

.

This is the well-known “Gordon,” or “constant-growth” model for valuing stocks. Here D₁, is the next expected dividend, which is assumed to be paid 1 year from now, r_s is the required rate of return on the stock, and g is the constant growth rate.

b. 3). The formula is derived mathematically, and the derivation requires that r_s > g. If g is greater than r_s, the model gives a negative stock price, which is not possible. The model simply cannot be used unless:

(1) r_s > g,

(2) g is expected to be constant,

Stocks may have periods of super normal growth, where g_s > r_s; however, this growth rate cannot be sustained indefinitely. In the long-run ,g < r_s..

c. The formula to calculate market value of preferred stock is:

= 10/0.08

P_{0 =} 125

d. 1) Bon Temps is a constant growth stock, and its dividend is expected to grow at a constant rate of 6 percent per year. Expressed as a time line, we have the following setup. Just enter 2 in your calculator; then keep multiplying by 1 + g = 1.06 to get D₁, D₂, and D₃:

0 1 2 3
|    |    |   |

D₀ = 2.00 2.12 2.247 2.382

d. 2) Since the stock is growing at a constant rate, its value can be estimated using the constant growth model:

= 2.12/ (0.16 - 0.06)

= 2.12/ 0.10

= $21.20

d. 3) After one year, D₁ will have been paid, so the expected dividend stream will then be D₂, D₃, D₄, and so on. Thus, the expected value one year from now is:

= $2.247/ (0.16 - 0.06)

= $22.47

d. 4) The expected dividend yield in any year n is

While the expected capital gains yield is

Thus, the dividend yield in the first year is 10 percent, while the capital gains yield is 6 percent:

Total return = 16.0%

Dividend yield = $2.12/$21.2 = 10.0%

Capital gains yield = 6.0%

e. The constant growth model can be rearranged to this form:

Here the current price of the stock is known, and we solve for the expected return.

r_s= $2.12/$21.2 + 0.060 = 0.10 + 0.060 = 16%.

g. If dividends are not expected to grow at all, then its dividend stream would be a perpetuity.

P₀ = PMT/r_s = $2.00/0.16 = $12.50.