1 (a) Hofzinger Inc. plans to pay a dividend of $10 per year on its common stock

Question

1 (a) Hofzinger Inc. plans to pay a dividend of $10 per year on its common stocks for the next 5 years and then increase the dividend to $12 per year for the next 6 years and to $15 per year thereafter. That is Dt = $10 for t = 1, 2,..., 5, Dt = $12 for t = 6, 7,... 11, and Dt = $15 for t=12,... If the required rate of return on the stocks is 9%, what is the current price of the stock?

(b) Jorgensen and Krugman, Inc. is a young start-up company. The company will not pay dividends for the next five years (i.e., D1=D2=...=D5=0), because the firm needs to plow back its earnings to fuel growth. However, the company is expected to pay a dividend of $3 per share every year for the subsequent 5 years and paid dividend of $5 per share every year thereafter. If the required rate of return on the stock is 12%, what is the current price of the stock?

(c) A company has just paid a dividend of $4 per share on its common stock (i.e., D0= $4). The required return on the the stock is 10%, and is it is assumed that this return is evenly divided between capital gains yield and dividend yield. If the company's policy to maintain a constant growth rate and its dividends, what is the current stock price?

(d) Colt 45 Brewing Co. is growing very rapidly Dividends are expected to grow at 18% per year for the next three years, with a growth rate falling off to a constant 5% per year thereafter. If the required return is 10% and the company just paid a dividend of $2 per share (i.e., D0=$2.00), what is the current price of this stock?

Explanation / Answer

For a constand dividend paying stock

Price = Dividend/rate

So, P12 = 15/0.09 = 166.67

To find the present value of the stock discount the future dividends and P12

P0 = 10/(1+0.09)^1 + 10/(1+0.09)^2 + 10/(1+0.09)^3 + 10/(1+0.09)^4 + 10/(1+0.09)^5 + 12/(1+0.09)^6 + 12/(1+0.09)^7 + 12/(1+0.09)^8 + 12/(1+0.09)^9 + 12/(1+0.09)^10 + 12/(1+0.09)^11 + 166.67/(1+0.09)^12 = 133.14

Current share price = $133.14

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