7.8. Volcker Company follows the residual theory of dividends. It has 8 million

Question

7.8. Volcker Company follows the residual theory of dividends. It has 8 million shares of common stock, and it maintains its optimal debt/assets ratio at 25%. Its EBIT next year is expected to be $25 million, with a standard deviation of $5 million. The income tax rate of Volcker is 37% and it has to pay $3.5 million in interest. It would like to finance $15 million in new projects from retained earnings and new borrowings. Find the probability that it will be able to give a dividend of at least 45¢ next year.

ANSWER: 33.93% PLEASE SHOW SOLUTIONS

Explanation / Answer

Expected Dividend:

Expected EBIT = $ 25 Million

Interest Expense = $ 3.5 Million

EBT= 25-3.5 = 21.5 Million

Tax Expenses = 21.5*37% = 7.955 Million

Net Income = $ 13.545 Million

Retained Earning Required = Total Finance required*(1-debt/assets ratio)

Retained Earning Required = 15*(1-25%)

Retained Earning Required = $ 11.25 Million

Maximum Dividend declared as per Expected EBIT = 13.545-11.25

Maximum Dividend declared as per Expected EBIT = $ 2.295 Million

Expected Dividend Per share = Maximum Dividend declared as per Expected EBIT / No of Outstanding share

Expected Dividend Per share = 2.295/8

Expected Dividend Per share = 0.286875

Standard Deviation of Dividend per share = Standard Deviation of EBIT*(1-tax rate)/No of oustanding share

Standard Deviation of Dividend per share = 5*(1-37%)/8

Standard Deviation of Dividend per share = 0.39375

Z = (X- Expecetd Dividend per share)/Standard Deviation

Z = (0.45-0.286875)/0.39375

Z = 0.414285

Using Excel formula for normal distribution probability

Probability of getting a dividend of at least 45¢ next year = 1- normsdist(z)

Probability of getting a dividend of at least 45¢ next year = 1-normsdist(0.414285)

Probability of getting a dividend of at least 45¢ next year = 33.93%

Answer

Probability of getting a dividend of at least 45¢ next year = 33.93%

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