Question

A company is expect to pay annual dividends of $10.00 per share in perpetuity on the 1 million shares outstanding. Shareholders require a 10% rate of return on the stock.

(a) What is the price of the stock?

(b) What is the aggregate market value of the equity?

The company decides to increase its dividend next year to $20.00 per share without changing its investment or borrowing plans. Thereafter, the company will revert to its policy of distributing $10 million in dividends per year. Only the existing shareholders receive the $20.00 dividend. The new shareholders do not receive the $20.00 per share dividend, but will receive the dividends paid thereafter along with the existing shareholders.

(c) How much new equity capital must the company raise to finance the extra dividend payment?

(d) What is the total present value of the dividends paid on the new shares?

(e) What is the value of the transfer of ownership from the old shareholders to the new shareholders?

(f) Did the old shareholders gain or lose total value?

Answer 1

a)Price of stock is nothing but present value of all dividend payments' since dividend are paid in annuity following formula can be used
PV = A/r
A=10$
r=10%
Price of share = 10/10% =100$

b) Market value of equity = no of shares*market price per share
=1 million shares *100 = $100 million

c) Amount to be raised = 1 million shares *10$( Assuming that company has 10$ to pay but to make payment of 20$ thet have to raise extra 10$)
=$10 million
No of shares to be issued = 10million /100 = 0.1 million shares

d) PV = (0.1*10)/10%
=1 million/10%
=$10 million