House of Haddock has 5,000 shares outstanding and the stock price is $140. The company is expected to pay a dividend of $20 per share next year and thereafter the dividend is expected to grow indefinitely by 5% a year. The president, George Mullet, now makes a surprise announcement: He says that the company will henceforth distribute half the cash in the form of dividends and the remainder will be used to repurchase stock. A) What is the total value of the company before and after the announcement? What is the value of one share. B) What is the expected stream of dividends per share for an investor who plans to retain his shares rather than sell them back to the company

Answer & Explanation:

(a) Gordon growth model:

Gordon growth model is a type of dividend discount model in which not only the dividends are factored in and discounted but also a growth rate for the dividends is factored in and the stock price is calculated based on that.

Formula:

P =  D1   / (r − g)

where:

P = Current stock price

g = Constant growth rate expected for

dividends, in perpetuity

r = expected return in the stock

D1  = Value of next year’s dividends

As House of Haddock has 5,000 shares outstanding and the stock price is $140 and the company is expected to pay a dividend of $20 per share next year and thereafter the dividend is expected to grow indefinitely by 5% a year.

Therefore by putting the values in the above formula, we get

140 = 20 / ( r - .05 )

r = .192857

As the stock price is $140

So total value of the company = 140 * 5,000

total value of the company = 700,000

If the dividend growth rate is cut to 2.5%

P = 20/(.192857-.025)

P (one share) = 119.14

So the total value of the company becomes 595,745.

(b)

The expected stream of dividends per share for an investor who plans to retain his shares rather than sell them back to the company can be found be multiplying the previous dividend per share with 1.025

Expected stream of dividends per share = 20 * 1.025

= 20.5

Expected stream of dividends per share = 20.5 * 1.025

= 21.01

Expected stream of dividends per share for an investor = 20, 20.50, 21.01, 21,54 and so on.

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