A company had net income of $20,000 this year on equity of $100,000 last year. I

Q: A company had net income of $20,000 this year on equity of $100,000 last year. I

a) ROE = 20000/100000 = 20% b) New equity = 100000 + 40%*20000 = 108000 Earnings = 108000*20% = 21600 Dividends = (1-40%)*21600 = 12960 c) g = ROE * retention ratio = 20%*40% = 8% As ROE and rention are constant dividend also grows at 8% d) discount rate = 5% + 1*(10% - 5%) = 10% e) Dividend per share = 60%*20000/20000 = 0.6 Price = 0.6*(1+8%) / (10% - 8%) = 32.4

ID: 2793242 • Letter: A

Question

A company had net income of $20,000 this year on equity of $100,000 last year. Its ROE is expected to be constant. Answer the following questions:

(a) What is its ROE?

(b) The company retains 40% of its earnings. What are earnings next year expected to be? What are dividends next year expected to be?

(d) The beta of the returns on the stock has been 1. The risk-free rate is 5% and the return on the market is expected to be 10%. What is the discount rate (OCC) on the company’s stock?

(e) The company has 20,000 shares outstanding. What should the price per share be today?

Explanation / Answer

ROE = 20000/100000 = 20%

New equity = 100000 + 40%*20000 = 108000

Earnings = 108000*20% = 21600

Dividends = (1-40%)*21600 = 12960

g = ROE * retention ratio = 20%*40% = 8%

As ROE and rention are constant dividend also grows at 8%

discount rate = 5% + 1*(10% - 5%) = 10%

Dividend per share = 60%*20000/20000 = 0.6

Price = 0.6*(1+8%) / (10% - 8%) = 32.4

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