Question

Sam Strother and Shawna Tibbs are senior vice presidents of Mutual of Seattle. They are co-directors of the company's pension fund management division, with Strother having responsibility for fixed income securities (primarily bonds) and Tibbs responsible for equity investments. A major new client, the Northwestern Municipal Alliance, has requested that Mutual of Seattle present an investment seminar to the mayors of the cities in the association, and Strother and Tibbs, who will make the actual presentation, have asked you to help them. To illustrate the common stock valuation process, Strother and Tibbs have asked you to analyze the Temp Force 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.

a. Describe briefly the legal rights and privileges of common stockholders.

b. (1) Write out a formula that can be used to value any stock, regardless of its dividend pattern. (2) What is a constant growth stock? How are constant growth stocks valued? (3) What happens if a company has a constant g that exceeds its rs? Will many stocks have expected g > rs in the short run (i.e., for the next few years)? In the long run (i.e., forever)?

c. Assume that Temp Force has a beta coefficient of 1.2, that the risk-free rate (the yield on T-bonds) is 7.0%, and that the market risk premium is 5%. What is the required rate of return on the firm's stock?

d. Assume that Temp Force is a constant growth company whose last dividend (D0, which was paid yesterday) was $2.00 and whose dividend is expected to grow indefinitely at a 6% rate. (1) What is the firm's expected dividend stream over the next 3 years? (2) What is the firm's current intrinsic stock price? (3) What is the stock's expected value 1 year from now? (4) What are the expected dividend yield, the expected capital gains yield, and the expected total return during the first year?

Answer 1

Ans: (a)

The legal rights and privileges of common stockholders:

The common stockholders are the owners of a corporation, and as such, they have certain rights and privileges as described below:

• Ownership implies control. Thus, a firm's common stockholders have the right to elect its firm's directors, who in turn elect the officers who manage the business.
• Common stockholders often have the right, called the preemptive right, to purchase any additional shares sold by the firm. In some stated, the preemptive right is automatically included in every corporate charter, in others, it is necessary to insert it specifically into the charter.

Ans: (b) 1.

Formula that can be used to value any stock, regardless of its dividend pattern:

The value of any stock is the present value of its expected dividend stream:

P₀ = [ D₁ ÷ (1+r_s)^t ] + [ D₂ ÷ (1+r_s)² ] + [ D₃ ÷ (1+r_s)³ ] + ............ + [ D∞ ÷ (1+r_s)∞]

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

Ans: (b) 2.

Constant growth stock and How are constant growth stocks valued

A constant growth stock is one whose dividends are expected to grow at a constant rate forever. "Constant growth" means that the best estimate of the future growth rate is some constant number, not that we really expect growth to be the same each and every year. 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:

P₀ = [ D₁ ÷ ( r_s - g ) ] =  [ D₀ (1+g) ÷ (r_s -g ) ]₁

This is the well-known "Gordon" , or "constant-growth" model for valuing stocks. Here D_1. 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.

Ans: (b) 3.

The model is derives 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 nonsensical. The model simply cannot be used unless (1) r_s > g, (2) g is expected to be constant, and (3) g can reasonably be expected to continue indefinitely.

Stocks may have periods of supernormal growth where g, > r_{s ,} however, this growth rate cannot be sustained indefinitely. In the long-run, g < r_s.

Ans: (c)

Here we use the SML to calculate temp force's required rate of return:

r_s = r_RF + ( r_M - r_RF)b_{Temp Force} = 7% + ( 12% - 7% ) ( 1.2 )

= 7% + (5%) (1.2) = 7% + 6%

= 13%.

Ans: (d) 1.

Firm's expected dividend stream over the next 3 years:

Temp Force is a constant growth stock, and its dividend is expected to grow at a constant rate of 6% 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	4
D0 = 2.00	2.12	2.247	2.382
	1.88	1.76	1.65

Ans: (d) 2.

Firm's current intrinsic stock price:

We could extend the time line on out forever, find the value of Temp Force's dividends for every year on out into the future, and then the PV of each dividend, discounted at r = 13%. For example, the PV of D₁ is $1.76106; the PV of D₂ is $1.75973; and so forth. Note that the dividend payments increase with time, but as long as r_s > g, the present values decrease with time. If we extended the graph on out forever and then summed the PVs of the dividends, we would have the value of the stock. However, since the stock is growing at a constant rate, its value can be estimated using the constant growth model:

P₀ = D₁ ÷ ( r_s - g )

= $2.12 ÷ ( 0.13 - 0.06 )

= $2.12 ÷ 0.07

= $30.29.

Ans: (d) 3.

After one year, D₁ will have been paid, so the expected dividend stream will then be D₂, D_3, D₄ and so on. Thus, the expected value one year from now is $32.10:

P₁ =  D₂ ÷ ( r_s - g )

= $2.247 ÷ ( 0.13 - 0.06 )

= $2.247 ÷ 0.07

= $32.10.

Ans: (d) 4.

The expected dividend yield in any year n is

Dividend Yield = D_n ÷ P_{n-1 ,}

While the expected capital gains yield is

Capital Gains Yield = ( P_n - P_n-1 ) ÷ P_n-1

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

Total return	= 13.0%
Dividend yield = $2.12 / $30.29	= 7.0%
Capital gains yield	= 6.0%