Question

Nonlinear Alchemy has a market value of $9 Billion. It has 300 Million shares outstanding and holds $3 Billion in cash and other short term investments. Markets are efficient and there are no taxes.

a) What is the share price?

Suppose that Nonlinear wants to pay out all its cash as a special dividend next year.

b) What is the special dividend per share?

c) What is the ex-dividend share price?

Suppose Nonlinear repurchases shares for $3B instead.

d) What is the share price after the repurchase?

e) How many shares does Nonlinear have to repurchase?

Suppose that dividends are taxed at a rate of 15% and Nonlinear has to pay a transaction cost for their repurchase. The transaction cost is 20% of the repurchase value.

Suppose that Nonlinear decides to pay out its cash purely in form of a dividend.

f)      What is stock price after the ex-dividend date?

g) What is the stock price right before the ex-dividend date?

h) How much does the stock price change when the dividends are announced?

i) How much does total shareholder wealth decrease when the dividends are announced

j) How much money does the state get from the dividend tax?

Suppose Nonlinear decides to pay out its cash purely in form of a repurchase.

k) If Nonlinear has to pay the transaction cost in cash, what is the dollar value of shares it can buy back? Remember that the transaction cost is 20% of the repurchase value.

l1) How many shares does Nonlinear have to buy?

l2) What is the share price after the repurchase?

m) What is the total change (in billions) in shareholder value from the repurchase?

n) How much money does Nonlinear have to pay in transaction fees in total?

Answer 1

a) Share price = Market value / no of shares outstanding = $ 9 B/ 300 M = $30 per share

b) Special dividend per share = $3B/300M =$10 per share

c) Ex Dividend per share = Share price- Dividend paid = $ 30-$10 = $ 20 per share

d) Share price after repurchase = (Market value - Amount paid to repurchase) / No of outstanding shares

= $ (9B-3B)/(300M-100M) = 6B/200M = $30 per share

e) No of Shares purchased = $3B/30 per share = 100Million shares

f) Ex-dividend Share price = 28.70 - 8.70 = $20 per share

Cash = $3B, Dividend Tax = 0.15

Dividend paid after Tax = $3B/115 =2.61 B

Dividend per share = 2.61B/300M = $8.70 per share

g) Share price before dividend = (9B-0.39B)/ 300M = $28.70 per share

h) Stock price changes by = 30-28.70 = $1.30 per share

i) Decrease in shareholder's wealth =$ 3B

J) Total Dividend Tax paid to state = $3B*15/115 = $0.39B

k) Dollar value of Buy back of shares = $3B/1.20 = $2.5 Billion

l1) No of Shares buy back = $2.5B/28.33 =88.25 Million shares  

Share price = (9B-0.5B)/300M= $28.33 per share

l2) Share price after repurchase = $6B /211.75M = $ 28.33 per share

m) Total change in sharevalue after repurchase = $3Billion

n) Transaction cost = 3B/1.20 * 20 =0.50 Billion