I simplified it a bit before in the past but the reality is in a company you have
Net Assets = Net Liabilities + Owners' Equity
Lets say a company has $10 bill assets $5 bill liabilities and $5 bill Owners Equity @ 1$ each
book value per share is 10/5 = $ 2 per share
Owners' equity, also called capital, is any debt owed to the business owners.
If a company buys it's own shares, lets say 2 bill then 2 bill from the cash asset gets reduces 2bill of Owners equity
so you are left with
8 bill net assets = 5 net liabilities + 3 bill owner equity
book value per share is 8 / 3 = $ 2.66 per share
so a share buy back increases book value per share.
In addition in a public company you have market value of the shares and the shares may be worth $1 on the market but an increase in book value to $2.66 would also restrict supply and increase stock price further.
Ryan
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