Question

Bloomberg Inc. is an all-equity firm and it will pay a dividend of $14.02/share next year and a liquidating dividend of $120 at the end of the 2nd year. Bloomberg has determined that market conditions will only allow the company to operate for the next 2 years. There are 500,000 shares outstanding and the total market value of the firm is $57.93 million. Ignore taxes and assume a discount rate of 8%.

1. You own 1,000 shares in Bloomberg. If you were to use homemade dividends to generate equal dividends over the next two years, how many shares would you need to buy or sell at the end of the first year? Assume fractional shares can be bought and sold. Use two decimal places on per-share dividends and whole numbers (no decimals) for total dividends.

Answer is to sell 458.56 shares - need in-depth solution.

2. Suppose instead that you, as a very picky holder of 1,000 shares, want exactly $6.48 per share at time 1. How many shares would you be buying or selling at time 1 to achieve this goal? Assume fractional shares can be bought and sold. Use two decimal places on per-share dividends and whole numbers (no decimals) for total dividends.

Answer is to buy 67.86 shares at time 1 - need in-depth solution.

Answer 1

a)

Share price today= $57.93 million / 500,000 = $115.86

Share price after one year = Value of $120 dividend at t=1

= 120/1.08 = $111.11

Let X be the no. of shares sold

So, total income =$14.02*1000 + X*111.11

Total income after one year from (1000-X) shares = 120* (1000-X)

=> 14020 + 111.11X = 120000 - 120X

=> 231.11 X = 105980

=> X = 458.57 shares

So, one needs to sell 458.57 shares at the end of 1st year to get

b) As the income at time 1 is $14.02 , to get $6.48 per share, one needs to buy some shares.

Suppose X shares were bought to get exactly $6.48 per share at time 1

total income =$14.02*1000 - X*111.11

So income per share = (14.02*1000 - X*111.11)/ 1000 = 6.48

=> 6480 = 14020 - 111.11X

=> 111.11 X = 7540

=> X = 67.86

So one needs to buy 67.86 shares at time 1 to get $6.48 income per share