Shares outstanding: 10

Market cap: $100

Market price per share: $10

If the firm were to repurchase one share of it's own stock, what would be the fair price to pay (i.e., the price where the remaining shareholders and the selling shareholder obtain the same value from the transaction)? What would be the new share price if the firm had to pay a $1 per share premium to entice that shareholder to sell? What would be the new share price if the firm could convince a shareholder to sell at a $1 discount? Assume that the market cap changes by the amount of the buyback.