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Little oil has outstanding 1 million shares with a total market value of 26 million. The firm is expected to pay 1.00 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 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 percent in each subsequent year.
(a) At what price will the new shares be issued in year 1?
(b) How many shares will the firm need to issue?
(c) What will be the expected dividend payments on these new shares, and what therefore will be paid out to the old shareholders after year 1?

Sagot :

batolisis

Answer:

a) $26

b) 1,038,462 shares

c) i) 0.037 ,  ii) 0.963

Explanation:

Total market value = 26 million

a) Determine the price at which the new shares will be issued in year 1

number of shares issued after year 1 = ( 1,000,000 + x )

x = new shares

p = price of new share

Total value of firm = Total market value + Dividend payment

                              = $26 million + $1 million = $27 million

p = Total value / x  = 27 million / x  ----- ( 1 )

also : x * ( p ) = $1,000,000

back to equation 1

P = $27,000,000 / ( 1,000,000 + x )

p ( 1,000,000 + x ) = $27,000,000

∴ ( 1,000,000 * P ) + 1,000,000 = $27,000,000

hence P = $26,000,000 / 1,000,000

price at which share new share will be issued = $26

b) Determine the number of shares the firm will issue

P( 1,000,000 + x ) = $27,000,000

= 26 ( 1,000,000 + x ) = $27,000,000

x =  ( 27,000,000 / 26 ) - 1,000,000

number of shares ≈ 38462

Number of new shares that the firm will need to issue

=  ( 1,000,000 + 38462 ) = 1,038,462 shares

c) Determine the expected dividend payments on these new shares and

dividend payment on new shares = New shares / Total outstanding shares

                                                        = 38462 / 1,038,462 = 0.037

dividend payment to old shareholder = 1 - 0.037

                                                              = 0.963

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