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.

a. What is the difference between common stock and preferred stock? What are some of the characteristics of each type of stock?

b. (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 > rs? Will many stocks have g > rs?

c. 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?

d. 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?

e. Assume that Bon Temps' stock is currently selling at $21.20. What is the expected rate of return on the stock?

f. 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?

g. 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

Ans: part (a)

Basically a Company issues two types of stocks in order to raise Capital :

(i) Equity shares ie. Common Stock &

(ii) Preference Shares ie. Preferred Stock

Following are the major differences between the two stocks on the basis of which they are distinguished:

• First major difference is that as the name says Preferred Stock Holders have a preferential right over the Common Stock Holders with regard to payment of any Dividends.
• Also such Preferential Right is given to the Preferred Stock Holders while disbursement of funds at time of Liquidation of Company.
• Dividends Payments are Guarenteed in case of Preferred Stocks Unlike Common Stock.
• Unlike Common Stock, Preferred Stock have to be redeemed from the market after a predetermined time.
• Finally, Preferred Stock can be converted to a fixed number of Common Stock, but Common Stock don't have this benefit.

So based on above differences we can point out following Major Characteristics of the above two stocks:

Characteristics of Preferred Stocks

1. Preference in dividends,
2. Preference in assets, in the event of liquidation,
3. Convertibility to common stock
4. No Voting Rights

Characteristics of Common Stock

1. Common Stocks Represent Ownership
2. Carries Voting Rights

Ans: part (b)

(1) Value of any Stock is basically Presents values of future Benefits that shareholders would get from such stock. In other Words we find out the Value of Stock by Discounting Future Expected Dividends hence this Approach is called Discounting Dividend Approach. Whatever we pay today to buy anything is the value of benefits we are gonna get from such product. Same goes for the Valuation of Stocks.

Hence FORMULA for Calculating Value of any Stock would be:

Po = D₁/(1+Ke)¹+D₂/(1+Ke)2 . . . . . . . . . .. . . . . + Dn/(1+Ke)ⁿ + Price at end of Holding Period/(1+Ke)ⁿ

Now difficulties arise to Discount stream of Dividends of n^th years as it is not feasible to do such calculation Hence came various Valuation Models to value such Stocks.

(2) Constant Dividend Growth Model {Gordon Model} : It is a Model/Theory to Calculate Theoratical Market Price of Company's Stock. Some other models of stock's valuation ignored the Dividend factor while valuing the stocks. Whereas this Theory contends that Dividend is relevant for Stock Valuation. In other words, it is used to value stocks based on the net present value of the future dividends.Here in this Model the main Assumption used is that the Dividends of Stocks grows at a constant rate every year which is definately not Practical.

Here , P₀ = D₁ / (Ke-g)

where, Po : Price of Stock

D1 : Expected Dividend of Year1

Ke : Discounting Factor/Cost of Equity

g : Growth rate of Dividends

(3) If Growth Rate (ie. g) is greater than Cost of Equity (ie. Ke) than this Model will reflect a Negative Stock Value which is practically impossible. Hence in that case this Model FAILS. Also one of the Assumptions of this Model is that Ke > g. No this is not a usual situation hence many stocks wont satisfy this.

Ans: part (c)

Price of Stocks= Dividend / Discounting Rate

= 10 / .08

= $125

Ans: part (d)

D₀ = $2

g = 6%

Ke = 16%

(1) Expected Stream of Dividends for next 3 years:

D₁ = D₀ (1+g)

= 2 (1+0.06)

= $2.12

D₂ = D₁ (1+g)

= 2.12(1.06)

=$2.2472

D₃ =D₂(1+g)

=2.2472(1.06)

=$2.382032

(2) P₀ = D₁ / (ke-g)

= $ 21.2 ( by solving above)

(3) P₁ = D₂ / (ke-g)

= $22.472

(4) Dividend Yield during 1st Year = D₁/P₀ * 100

= 10%

Capital Gain Yield during 1st Year = (P₁-P₀) / P₀ * 100

= 6%

Total Return during 1st Year = Div Yield + Cap Gain Yield

16%

Ans: part (e)

If P₀ = $21.2 , D₁=$2.12 , g=6%

then putting above values in Formula Po= D1 / ( ke-g)

we get Ke = 16%

Part (f) & Part (g) are also to be solved in same way by just putting respective values in Above Formula discussed above to value stock { ie. P₀ = D₁ / (Ke-g) } . Question is just changing the Variables and asking same thing repeatedly. Hope you are clear with the question & its solution now.