Mutual of Chicago Insurance Company

ROBERT BALIK AND CAROL KIEFER ARE SENIOR VICE-PRESIDENTS OF THE MUTUAL OF CHICAGO INSURANCE COMPANY. THEY ARE CO-DIRECTORS OF THE COMPANY'S PENSION FUND MANAGEMENT DIVISION, WITH BALIK HAVING RESPONSIBILITY FOR FIXED INCOME SECURITIES (PRIMARILY BONDS) AND KIEFER BEING RESPONSIBLE FOR EQUITY INVESTMENTS. A MAJOR NEW CLIENT, THE CALIFORNIA LEAGUE OF CITIES, HAS REQUESTED THAT MUTUAL OF CHICAGO PRESENT AN INVESTMENT SEMINAR TO THE MAYORS OF THE REPRESENTED CITIES, AND BALIK AND KIEFER, WHO WILL MAKE THE ACTUAL PRESENTATION, HAVE ASKED YOU TO HELP THEM.

TO ILLUSTRATE THE COMMON STOCK VALUATION PROCESS, BALIK AND KIEFER 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. DESCRIBE BRIEFLY THE LEGAL RIGHTS AND PRIVILEGES OF COMMON STOCKHOLDERS.

ANSWER: [SHOW S8-1 THROUGH S8-5 HERE.] THE COMMON STOCKHOLDERS 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 STOCKHOLDERS HAVE THE RIGHT TO ELECT ITS FIRM'S DIRECTORS, WHO IN TURN ELECT THE OFFICERS WHO MANAGE THE BUSINESS.

2. COMMON STOCKHOLDERS OFTEN HAVE THE RIGHT, CALLED THE PREEMPTIVE RIGHT, TO PURCHASE ANY ADDITIONAL SHARES SOLD BY THE FIRM. IN SOME STATES, THE PREEMPTIVE RIGHT IS AUTOMATICALLY INCLUDED IN EVERY CORPORATE CHARTER; IN OTHERS, IT IS NECESSARY TO INSERT IT SPECIFICALLY INTO THE CHARTER.

B. 1. WRITE OUT A FORMULA THAT CAN BE USED TO VALUE ANY STOCK, REGARDLESS OF ITS DIVIDEND PATTERN.

ANSWER: [SHOW S8-6 HERE.] 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.

B. 2. WHAT IS A CONSTANT GROWTH STOCK? HOW ARE CONSTANT GROWTH STOCKS VALUED?

ANSWER: [SHOW S8-7 AND S8-8 HERE.] 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, kS IS THE REQUIRED RATE OF RETURN ON THE STOCK, AND g IS THE CONSTANT GROWTH RATE.

B. 3. WHAT HAPPENS IF A COMPANY HAS A CONSTANT g THAT EXCEEDS ITS ks? WILL MANY STOCKS HAVE EXPECTED g > ks IN THE SHORT RUN (THAT IS, FOR THE NEXT FEW YEARS)? IN THE LONG RUN (THAT IS, FOREVER)?

ANSWER: [SHOW S8-9 HERE.] THE MODEL IS DERIVED MATHEMATICALLY, AND THE DERIVATION REQUIRES THAT ks > g. IF g IS GREATER THAN ks, THE MODEL GIVES A NEGATIVE STOCK PRICE, WHICH IS NONSENSICAL. THE MODEL SIMPLY CANNOT BE USED UNLESS (1) ks > 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 > ks; HOWEVER, THIS GROWTH RATE CANNOT BE SUSTAINED INDEFINITELY. IN THE LONG-RUN, g < ks.

C. ASSUME THAT BON TEMPS HAS A BETA COEFFICIENT OF 1.2, THAT THE RISK-FREE RATE (THE YIELD ON T-BONDS) IS 7 PERCENT, AND THAT THE REQUIRED RATE OF RETURN ON THE MARKET IS 12 PERCENT. WHAT IS THE REQUIRED RATE OF RETURN ON THE FIRM'S STOCK?

ANSWER: [SHOW S8-10 HERE.] HERE WE USE THE SML TO CALCULATE BON TEMPS REQUIRED RATE OF RETURN:

ks = kRF + (kM - kRF)bBon Temps = 7% + (12% - 7%)(1.2)

= 7% + (5%)(1.2) = 7% + 6% = 13%.

D. ASSUME THAT BON TEMPS 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 PERCENT RATE.

1. WHAT IS THE FIRM'S EXPECTED DIVIDEND STREAM OVER THE NEXT 3 YEARS?

ANSWER: [SHOW S8-11 HERE.] 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

1.88

1.76

1.65

.

.

.

D. 2. WHAT IS THE FIRM'S CURRENT STOCK PRICE?

ANSWER: [SHOW S8-12 HERE.] WE COULD EXTEND THE TIME LINE ON OUT FOREVER, FIND THE VALUE OF BON TEMPS' DIVIDENDS FOR EVERY YEAR ON OUT INTO THE FUTURE, AND THEN THE PV OF EACH DIVIDEND DISCOUNTED AT k = 13%. FOR EXAMPLE, THE PV OF D1 IS $1.8761; THE PV OF D2 IS $1.7599; AND SO FORTH. NOTE THAT THE DIVIDEND PAYMENTS INCREASE WITH TIME, BUT AS LONG AS

ks > 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:

= = = = $30.29.

D. 3. WHAT IS THE STOCK'S EXPECTED VALUE ONE YEAR FROM NOW?

ANSWER: [SHOW S8-13 HERE.]