Question

Your corporation is interested in acquiring XYZ Limited. Currently, it is expected that XYZ Limited will generate $1,000,000 of free cash flows at the end of each year, in perpetuity. Your corporation believes that it will be able to manage XYZ Limited more efficiently. In particular, XYZ Limited, under the management of your company, will be able to generate $1.000.000 of free cash flows at the end of year one, and the amount will grow by 4% per year thereafter, in perpetuity. The cost of equity is 10% per year, and the weighted average cost of capital is 8%. These discount rates are expected to remain constant in perpetuity. The corporate tax rate is 25%.

a. If you want to ensure that the net present value of this acquisition is not negative, what is the maximum amount that your corporation should pay to acquire XYZ Limited? Show your work. Currently, your corporation has a share price of $20 per share and 10,000,000 shares outstanding, while XYZ Limited has 1,000,000 shares outstanding. After a few rounds of negotiation, XYZ Limited agrees to be acquired by your corporation at a price of $20,000,000. Your corporation can choose to complete the acquisition either in the form of cash or shares. b. Calculate the net present value of the acquisition and the new share price of the merged corporation if your corporation chooses to use cash as the means of payment. Show your work. c. Calculate the net present value of the acquisition and the new share price of the merged corporation if your corporation chooses to use shares as the means payment. Show your work.

Answer 1

a) To discount free cashflows, WACC should be used

As per Gordon's constant growth formula

Value of the firm = Free cashflows in year 1/ (WACC -constant growth rate)

= $1,000,000/ (0.08-0.04) = $25,000,000

So, the maximum amount that your corporation should pay to acquire XYZ Limited is $25,000,000

b) If acquisition is done by cash

Present value of acquisition (Value created for the shareholders) = $25,000,000 - $20,000,000 = $5,000,000

So, Value per share = $5,000,000/ 10,000,000 shares = $0.5 per share

So, New Share price = $20+$0.5 = $20.5 per share

c) If shares are used for acquisition

No of new shares to be issued = $20,000,000/ $20 per share = 1,000,000

New No of shares of the corporation = 10 million +1 million =11 million

Present value of acquisition = $25 million (as no cash is spent)

Current value of the corporation = $20 per share * 10 million shares = $200 million

New value after acquisition= $200 million +$25 million = $225 million

So, New Value per share = $225 million/11 million shares = $20.45 per share