Question

Little Oil has outstanding one million shares with a total market value of $20 million. The firm is expected to pay $1 million of dividends next year, and thereafter the amount paid out is expected to grow by 5% a year in perpetuity. Thus the expected dividend is $1.05 million in year 2, $1.1025 million in year 3, and so on. However, the company has heard that the value of a share depends on the flow of dividends, and therefore it announces that next year’s dividend will be increased to $2 million and that the extra cash will be raised immediately afterwards by an issue of shares. After that, the total amount paid out each year will be as previously forecasted, that is, $1.05 million in year 2 and increasing by 5% in each subsequent year

a. At what price will the new shares be issued in year 1? (Do not round intermediate calculations. Round your answer to the nearest whole number.)

New share price            $

b. How many shares will the firm need to issue? (Do not round intermediate calculations. Round your answer to the nearest whole number.)

Number of shares              

c-1. What will be the expected dividend payments on the new shares at t₂? (Do not round intermediate calculations. Enter your answer in dollars not in millions. Round your answer to the nearest whole number.)

Total dividend            $

c-2. What will be paid out to the old shareholders at t₂? (Do not round intermediate calculations. Enter your answer in millions not in dollars. Round your answer to the nearest whole number.)

Total dividend            $   million

d-1. What is the present value of the cash flows to current shareholders under the revised dividend policy? (Do not round intermediate calculations. Enter your answer in millions not in dollars. Round your answer to the nearest whole number.)

Present value            $   million

Answer 1

Value per share = D1 / (cost of equity - dividend growth rate)

Value per share = Market value / no. of shares = 20,000,000 / 1,000,000 = $20

D1 = $1 and constant dividend growth rate = 5%

20 = 1/ (cost of equity -5%)

Cost of equity = 1/20 + 5% = 10%

If the firm $2 dividend in next year and then pay dividend of 1.05 next year and 5% growth each year

Price per share = D1 / (1+cost of equity) + D2 / (cost of equity - constant dividend growth)

= 2 / (1+10%) + (1.05) / (10%-5%)

a. Price per new share =$23

Total amount to be raised =increase in dividend * no. of shares outstanding = (2-1) *1,000,000 = $1,000,000

b. Number of shares to be issued = 1,000,000 / 22.8 = 43,825 no. of shares

C-1 Total expected dividend at period 2  = 1,050,000 ($1.05 million)

Total number of shares = 1,000,000 + 43,825 = 1,043,825

Dividend per shares on new shares = 1,050,000 / 1,043,825

Dividend per shares on new shares = $1

C-2. Total dividend paid on new shares =1.0059 * 43,825 = $44,084

Dividend paid to old shareholders = 1,050,000 - 44,084

Dividend paid to old shareholders = $1 million

d-1 - Present value of period 2 dividend to current shareholder is = 1,005,916 / (1+10%)^2

  Present value of period 2 dividend to current shareholder under revised policy is = $0.83 million