Question

1. 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. Assume that Bon Temps is expected to experience supernormal growth of 25% for the next 4 years, then to return to its long-run constant growth rate of 8%. 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 6? Assume that the required rate of return is 16%. The dividend paid yesterday was $2.00.

Answer 1

(a) Current Dividend = D0 = $ 2, Initial Supernormal Growth Rate = g1 = 25 % and Perpetual Constant Growth Rate = g2 = 8 %

Required Rate of Return = R = 16 %

Expectd Dividends: D1 = 2 x 1.25 = $ 2,5, D2 = 2.5 x 1.25 = $ 3.125, D3 = 3.125 x 1.25 = $ 3.90625, D4 = 3.90625 x 1.25 = 4.8828125, D5 = 4.882125 x 1.08 = $ 5.2734375

Current Stock Price = P0 = 2.5 / 1.16 + 3.125 / (1.16)^(2) + 3.90625 / (1.16)^(3) + 4.8828125 / (1.16)^(4) + [5.2734375 / (0.16-0.08)] x [1/(1.16)^(4)] = $ 41.0613 ~ $ 41.06

Price after 1 year = P1 = 3.125 /1 1.6 + 3.90625 / (1.16)^(2) + 4.8828125 / (1.16)^(3) + [5.2734375 / (0.16-0.08)] x [1/(1.16)^(3)] = $ 50.96

In year 1:

Capital Gains Yield In Year 1 = [(P1 - P0) / P0] x 100 = 24.11 %

Dividend Yield = (D1/P0) = (2.5/41.06) x 100 = 6.09 %

In year 6:

D5 = $ 5.2734375, D7 = D5 x (1.08)^(2) = $ 6.1509375, D6 = D5 x 1.08 = $ 5.6953125

P6 = [D7 / (0.16 - 0.08)] = [6.1509375 / (0.16 - 0.08)] = $ 76.88672

P5 = [D6 / (0.16 - 0.08)] = [5/6953125 / (0.16 - 0.08)] = $ 71.19141

Capital Gains Yield = [(P6 - P5) / P5] x 100 = [(76.88672 - 71.19141) / 71.19141] x 100 = 7.99%

Dividend Yield = (D6/P5) x 100 = (5.6953125 / 71.19141) x 100 = 7.99%