Question

Firms A and B are competitors. Both have similar
assets and business risks and are all-equity firms.
Firm A has aftertax cash flow of $20,000 per year
forever and firm B has aftertax cash flow of $150,000
per year forever. If the two firms merge, the perpetual
aftertax cash flow will be $179,000. If the appropriate
discount rate is 15% what is the MOST B will pay for
A?
A) $9,000
B) $20,000
C) $60,000
D) $133,333
E) $193,333

Answer 1

What is the MOST B will pay for A?

Answer: E) $193,333

Maximum amount that B will pay for A will be the additional benefit receivable by B from the merger. Additional benefit is the increase in value of business due to merger. Additional benefit can be measured in terms of present value of future cash flows of B before and after the merger.

Reason

Maximum amount payable for A should be the additional benefit receivable by B. If B is paying anything more than the additional benefit receivable then there is no benefit for B in merger.

Since all future cash flows given in the problem are perpetual, for calculating the present value of future cash flows (Value of Business) we can use the following formula

Present value of future cash flows (Value of business) = Cash flow ÷ discount rate

1. Value of B before merger = $150,000 ÷ .15

=$1,000,000

2. Value of B after merger = $179,000 ÷ .15

= 1,193,333

Additional benefit for B from merger = Value after merger – Value Before merger

                                                            = $1,193,000 - $ 1,000,000

                                                            = $193,333