Question

Sam Forbes and Jenny Hewes are senior vice-presidents of the First Creek Investment Council . They are co-directors of the company's pension fund management division, with Sam having responsibility for fixed income securities (primarily bonds) and Jneey being responsible for equity investments. A major new client has requested that council present an investment seminar to Executive Committee, and Forbes and Hewes, who will make the actual presentation, have asked you, a recent UCW graduate to help them.                                                                                                       

to illustrate the common stock valuation process, Sam and Jenny 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. Assume that Temp Force is a constant growth company whose last dividend (Do, which was paid yesterday) was $2.00, and whose dividend is expected to grow indefinitely at a 5 percent rate.                                                                                   

   (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 1 year from now?                                                                                                              

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

                                                                                                                  

c. Now assume that the stock is currently selling at $43.75. What is the expected rate of return on the stock? (                                                                                        

                                                                       

f. What would the stock price be if its dividends were expected to have zero growth?                                                                                                        

g. Now assume that Temp Force is expected to experience supernormal growth of 30 percent for the next 3 years, then to return to its long-run constant growth rate of 5 percent. What is the stock's value under these conditions? What is its expected dividend yield and capital gains yield in Year 1? In Year 4? (                                                                                                           

                                                                       

h. Is the stock price based more on long-term or short-term expectations? Answer this by finding the percentage of Temp Force current stock price based on dividends expected more than 3 years in the future.                                                                                          

                                                                                     

                                                                                                                  

i. Suppose Temp Force is expected to experience zero growth during the first 3 years and then to resume its steady-state growth of 5% in the fourth year. What is the stock's value now? What is its expected dividend yield and its capital gains yield in Year 1? In Year 4?                                              

                                                                                                                                               

j. Finally, assume that Temp Force’s earnings and dividends are expected to decline by a constant 6 percent per year, that is, g = -5%. Why would anyone be willing to buy such a stock and at what price should it sell? What would be the dividend yield and capital gains yield in each year?                                

l. Temp Force recently issued preferred stock. It pays an annual dividend of $1.60, and the issue price was $25 per share. What is the expected return to an investor on this preferred stock?                                                                                           

Answer 1

a.

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

1. Ownership implies control. Thus, a firm’s common shareholders have the right to elect its firm’s directors, who in turn elect the officers who manage the business.

2. Common shareholders may have the right, called the preemptive right, to purchase any additional shares sold by the firm.

b.

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

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

2. 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 that 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, rs is the required rate of return on the stock, and g is the constant growth rate.

3. The model is derived mathematically, and the derivation requires that rs > g. If g is greater than rs, the model gives a negative stock price, which is nonsensical. The model simply cannot be used unless (1) rs > 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 gs > rs; however, this growth rate cannot be sustained indefinitely. In the long-run, g < rs.

c.

Here we use the SML to calculate Temp Force’s required rate of return:

rs = rRF + (rM – rRF)bTemp Force = 5% + (9% – 5%)(1.2)

= 5% + (4%)(1.2) = 5% + 4.8% = 9.8%.

d.

1. Temp Force is a constant growth stock, and its dividend is expected to grow at a constant rate of 5% per year. Expressed as a time line, we have the following setup. Just enter 2 in your calculator; then keep multiplying by 1 + g = 1.05 to get D1, D2, and D3:

2. 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 = 9.8%. For example, the PV of D1 is $1.91; the PV of D2 is $1.83; and so forth. Note that the dividend payments increase with time, but as long as rs > 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:

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 $45.94:

4. The expected dividend yield in any year n is

Dividend yield = Dn/P̂n-1

While the expected capital gains yield is

Thus, the dividend yield in the first year is 4.8%, while the capital gains yield is 5%:
Total return = 9.8%

Dividend yield = $2.10/$43.75 = 4.8%

Capital gains yield = 5.0%

e.

The constant growth model can be rearranged to this form:

r̂s = D1/P0 + g

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

r̂s = $2.10/$43.75 + 0.05 = 0.048 + 0.05 = 9.8%.

f.

If Temp Force’s dividends were not expected to grow at all, then its dividend stream would be a perpetuity. Perpetuities are valued as shown below:

P0 = PMT/r = $2.00/0.098 = $20.41.

Note that if a preferred stock is a perpetuity, it may be valued with this formula.

g.

Temp Force is no longer a constant growth stock, so the constant growth model is not applicable. Note, however, that the stock is expected to become a constant growth stock in 3 years. Thus, it has a nonconstant growth period followed by constant growth. The easiest way to value such nonconstant growth stocks is to set the situation up on a time line as shown below:

Simply enter $2 and multiply by (1.30) to get D1 = $2.60; multiply that result by 1.3 to get D2 = $3.38, and so forth. Then recognize that after Year 3, Temp Force becomes a constant growth stock, and at that point can be found using the constant growth model. is the present value as of t = 3 of the dividends in year 4 and beyond.

With the cash flows for D1, D2, D3, and shown on the time line, we discount each value back to year 0, and the sum of these four PVs is the value of the stock today, P0 = $81.11.

The dividend yield in year 1 is 3.2%, and the capital gains yield is 6.6%:

During the nonconstant growth period, the dividend yields and capital gains yields are not constant, and the capital gains yield does not equal g. However, after Year 3, the stock becomes a constant growth stock, with g = capital gains yield = 5.0% and dividend yield = 9.8% – 5.0% = 4.8%.

h.

$38.26/$43.75 = 87%

Stock price is based more on long-term expectations, as is evident by the fact that 87% of Temp Force’s stock price is determined by dividends expected more than three years from now.

i.

Now we have this situation:

Again, in Year 4 Temp Force becomes a constant growth stock; hence g = capital gains yield = 5.0% and dividend yield = 4.8%.

j.

The company is earning something and paying some dividends, so it clearly has a value greater than zero. That value can be found with the constant growth formula, but where g is negative:

Since it is a constant growth stock:

g = Capital gains yield = –5.0%,

hence:

Dividend yield = 9.8% – (–5.0%) = 14.8%.

As a check:

Dividend yield = $1.90/$12.84 = 0.148 = 14.8%.

The dividend and capital gains yields are constant over time, but a high (14.8%) dividend yield is needed to offset the negative capital gains yield.

k.

Analysts often use the P/E multiple (the price per share divided by the earnings per share) or the P/CF multiple (price per share divided by cash flow per share, which is the earnings per share plus the dividends per share) to value stocks. For example, estimate the average P/E ratio of comparable firms. This is the P/E multiple. Multiply this average P/E ratio by the expected earnings of the company to estimate its stock price. The entity value (V) is the market value of equity (# shares of stock multiplied by the price per share) plus the value of debt. Pick a measure, such as EBITDA, sales, customers, eyeballs, etc. Calculate the average entity ratio for a sample of comparable firms. For example, V/EBITDA, V/customers. Then find the entity value of the firm in question. For example, multiply the firm’s sales by the V/sales multiple, or multiply the firm’s # of customers by the V/customers ratio. The result is the total value of the firm. Subtract the firm’s debt to get the total value of equity. Divide by the number of shares to get the price per share. There are problems with market multiple analysis. (1) It is often hard to find comparable firms. (2) The average ratio for the sample of comparable firms often has a wide range. For example, the average P/E ratio might be 20, but the range could be from 10 to 50. How do you know whether your firm should be compared to the low, average, or high performers?

l.

m.

Using the constant growth model, the price of a stock is P0 = D1/(rs – g). If estimates of g change, then the price will change. If estimates of the required return on stock change, then the stock price will change. Notice that rs = rRF + (rpM)bi, so rs will change if there are changes in inflation expectations, risk aversion, or company risk. The following table shows the stock price for various levels of g and rs.

n.

Equilibrium means stable, no tendency to change. Market equilibrium means that prices are stable—at its current price, there is no general tendency for people to want to buy or to sell a security that is in equilibrium. Also, when equilibrium exists, the expected rate of return will be equal to the required rate of return:

r̂ = D1/P0 + g = r = rRF + (rM – rRF)b.

o.

Securities will be bought and sold until the equilibrium price is established.

p.

The EMH in general is the hypothesis that securities are normally in equilibrium, and are “priced fairly,” making it impossible to “beat the market” over the long term.

Weak-form efficiency says that investors cannot profit from looking at past movements in stock prices—the fact that stocks went down for the past few days is no reason to think that they will go up (or down) in the future. This form has been proven pretty well by empirical tests, even though people still employ “technical analysis.”

Semistrong-form efficiency says that all publicly available information is reflected in stock prices, hence that it won’t do much good to pore over annual reports trying to find undervalued stocks.

Strong-form efficiency says that all information, even inside information, is embedded in stock prices. This form does not hold—insiders know more, and could take advantage of that information to make abnormal profits in the markets. Trading on the basis of insider information is illegal.