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.

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 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?

l1) How many shares does Nonlinear have to buy?

l2) What is the share price after the repurchase?

Answer 1

Market cap of nonlinear = $9Bn= $9000mn

No of outstanding shares =300mn

Price per share= Mcap/no of outstanding shares = 9000/300 =$30/share

Cash company holds = $3bn= $3000mn

transaction cost for a repurchase = 20% of $3000mn

Net value company have for share buy back or effective value net of transaction cost= (1-20%)*$3000mn

= 0.8*3,000,000= $2,400mn = Dollar value of shares it can buy back

total number of Shares that it can buy back = effective value for buyback/price of share

= $2,400/30 = 80mn shares

Net outstanding shares after buyback = 300mn-80mn = 220mn

Assuming P/E remains same before and after buyback

lets say company makes $Xmn of PAT

P/E (before buy back) = share price /Earnings per share = $30/(PAT/No of outstanding shares)

= $30/(X/300mn)= 30*300/X ..................(1)

P/E (after buy back )= Shareprice /Earnings per share = Share price /(PAT/No of outstanding shares) = Share price/(X/220mn)

= Share price*220mn/X..................(2)

Since P/E before and after buyback should remain same

hence equating eq 1 and 2

Share price = 3*300/220mn = $40.9/ share