Question

In this question, we will explore the irrelevance of dividend policy.

Suppose XYZ Inc currently has 1 million shares outstanding, and XYZ expects to make $1 million per year in perpetuity, all of which is paid out in dividends. Assume the relevant discount rate is 10%. (Ignore taxes and transaction costs, and assume the markets are efficient.Use the DDM to value the shares)

a.What is the value of one share of XYZ Inc? (Assume the next dividend payment is one year from today.)

b.Now assume XYZ Inc plans to change its dividend policy as follows: the company will skip the next dividend payment and instead it will repurchase $1 million worth of shares. In year 2, and in all subsequent years, the dividends will resume and all the income will be paid out as dividends. What is the current share price under this policy? Provide an explicit calculation of the share price given the new dividend payment stream.(Hint: Let P1 be the share price at time 1, immediately before the share repurchase. Calculate the number of shares repurchased, and then find the dividends per share for years 2 and beyond. Discount all this back in order to find the current share price.) Do not assume the M&M proposition that the dividend policy is irrelevant. Essentially, this question is meant to prove that fact.

c.Suppose you purchase 100 shares today, and sell them 2 years from now, immediately after the year 2 dividend is paid. What is your total profit under each dividend policy? Does this difference in profit violate the indifference of dividend policy? Expla

Answer 1

Answer to question No.A

Value of One share

Total Earning    =   $ 1 Million

No.of Share      =   $ 1 Million

Earning Per share = Earning/ No.of Share

EPS = 1 million/ 1 million = $1 Per share

Value of Share = EPS/ interest rate

Value of Share = $1 /0.10 = $ 10

Answer to question No.2

Current Share price for new policy

Company will not pay dividend for 1st year

Company will pay dividend for 2nd year and onwards

Using the concept of perpatuity, the total value of company on 2nd year= $1 million/0.10= $10 Million

we calculate the value for 1st year so pull the value upto 1st year

for that we will divide $10 million to the factor of interest rate

so the present value of $10 miliion = $10 million/ 1.10 = $9.09 Million

The income of 1st year is $1 million

Total value of the company before repurchase the share =$9.09 Million+$1 Million =10.09 $Million

Value per share before Repurchase = $10.09 Million/1 Million = $10.09 per share

No. of share repurchased = $1 Million/ 10.09 =0.099 Miliion Shares

Remaining No.of Share= 1 Million - 0.099 Million=0.901 Million Shares