Question

Your all-equity firm generates $60M per year in perpetual free cash flows. The firm pays out the entire free cash flows to stockholders each year and is about to pay the $60M generated this year. Analysis of comparable firms tells you that your asset cost of capital is 15 percent. Assume that there are 1M shares outstanding and the capital market is perfect.

a)What is the price per share for this firm att=0 just before the firm paysout the $60M?This price is called the cum-dividend price.

b)Suppose the firm chooses to pay out the $60M as a dividend.What is the price per shareat t=0 just after the dividend is paid out?This price is called the ex-dividend price.

c)The firm would like to pay$100M worth of dividends at t=0 and thus needs another $40M. The firm plans to issue shares today (t=0) at the cum-dividend price from (a) so that it will have the extra $40M.
i.How many additional shares does the firm have to issue to raise $40M?
ii.Whatwould the price per share be at t=0 just before this $100M dividend is paid out? (but directly after the additional $40M was raised via equity issuance)(Hint: The firm added $40M of cash to its assets throughthe equity issuance. That is,the firm’s asset value is $40M higher than before.)
  iii.What would the price per share be at t=0 just after the $100M dividend is paid out?

d)Which of the following is true? Explainyour answer.①.Investors prefer the usual dividend in (b).②.Investors prefer the boosted dividend in (c).③.Investors are indifferent between the usual and boosted dividends

Answer 1

A) Value of the firm = perpetual free cash flow / cost of capital

= $60M / 15% = $ 400M

Price per share = value of the firm/ no. Of outstanding share

= $400M / 1M =$400

B) dividend paid per share = total dividend paid/ no. Of outstanding shares =$60 M / 1M = $60

Ex dividend price = price per share - dividend per share = $400 - $60 =$340

C)i) the cum-dividend price per share = $400 as calculated in a)

We need to raise $40 M

No. Of shares to be issued = $40M / $400 = 100000 = 0.1 M

ii)New value of the firm = ealier value of the firm + new cash raised through equity = $400M + $40 M=$440 M

No. Of outstanding shares = 1M + 0.1 M = 1.1 M

Price before dividend payment per share = $440/ 1.1 = $400

iii) new value of the firm = ealier value of the firm + new cash raised through equity = $400M + $40 M=$440 M

Ex dividend price per share =($440M -$100M) / (1M +0.1M)

= $340/ 1.1= $309.09

d) Investors are indifferent between usual and boosted dividends because overall value that goes to investors pocket is same i.e. $400 per share ( dividend +final value per share)