Question

1. The current price of the shares of Company XYZ is $50. There are N = 1 million shares outstanding. Next year’s (year 1) earnings and dividends per share are $4 and $2, respectively. Investors expected perpetual dividend growth at g = 8% per year. The expected rate of return demanded by investors is r=12%. (10 points)

1. What will be the dividend per share in the next 3 years (we are now in year 0)?

2. What is the current market value of the firm?

3. What will be the value of the firm next year after the payout?

Suppose that the company announces that it will increase its dividend from $2 per share to $4 per share next year （year1）, and the extra cash needed will be financed by issuing new shares. However, the dividends after next year follow the old schedule, as in part a).

4. What will be the price of the new shares that the firm issue in year 1? How many new shares will be issued?

5. How much dividend will the old shareholders get in year 2?

6. What should the current stock price be under the new policy?

Answer 1

A. Next 3 year dividend = $2 (1+growth rate)^3 = $2*(1.08)^3 = $2.519/share.
B. Market Value = 1 million shares * current price = $50 million.
C. Price of share next year = D(next year)/expected return - growth rate = 2(1.08)/(12%-8%) = $54
so, Market Value next year = 1 million * 54 = 54 million.
D. Extra Cash Needed = $2 * 1 million shares = $2million.
Market Value of share next year will be $ 54 (computed above)
So, actual shares issued = 2 million / 54 = 37,037.03 shares.
E. Dividend old shareholders get in Year 2 = $2(1.08)^2 * 1 million = $2.33 million.