Question

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%.

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).

(d) What will be the price of the new shares that the firm issue in year 1? How many new shares will be issued?

(e) How much dividend will the old shareholders get in year 2?

(f) What should the current stock price be under the new policy?

Answer 1

Price for new issue in year 1 is given by

P(t) = D(t+1)/(Re-g)

Where

P(t) = price at t th period i.e.p(1)= ???

g = growth rate = 8%

D(t+1) = dividend at (t+1)th period i.e. D2 = D1(1+g) since dividend from year 2 onwards will be as per old schedule and D1 as per old shedule was 2 and D2 as per old schedule was 2(1.08) = 2.16

Re = 12%

P(1) = 2.16/(.12-.08) = 54

Part e

Let say no. Of share to be issued = N million

Total no. Of share will be (1+N)million

Old dividend per share at (time 1 )= 2 i.e. total funds as per old scheme was = 2×1million = 2million

New dividend per share = 4 i.e. total dividend as per new scheme will be = 4 ×(1+N)= 4 +4N

Extra funds required = 4+4N -2

These extra funds will be financed by new isse of N million shares at P(1) =54 i.e. = 54×N

Therefore

54N=4 + 4N -2

N= .04 million i.e. 40000 share

Part f

price today i.e. P0 = D1/Re +Present value of future price i.e.P(2)

P0= 4/1.12 + 54 /1.12 = 51.79$