Assume that the acquisition of Titan Tech by Apex AI will result in savings of $2million annually in perpetuity for the combined firm. The required rate of return on the combined firm is 8%. The transaction costs will amount to $1 million. Both Apex AI and Titan Tech have no debt outstanding. 

Requirement :

a. What is the present value of the net gain from the merger? 

b. If a cash offer of $60 million is accepted by Titan Tech's shareholders, what is the value created for Apex AI's shareholders? 

c. If shares are offered in such a way that Titan Tech's shareholders would possess one-third of the merged entity, what is the value created for Apex AI's shareholders