Firms A and B are competitors. Both have similar assets and business risks and are all-equity firms. Firm A has after-tax cash flow of $20,000 per year forever and firm B has after-tax cash flow of $150,000 per year forever. If the two firms merge, the perpetual after-tax 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

Question

Quizplus · Accepted Answer

The value of a perpetuity is calculated as the annual cash flow divided by the discount rate. The value of Firm A is $20,000 / 0.15 = $133,333, and the value of Firm B is $150,000 / 0.15 = $1,000,000. The combined firm's value is $179,000 / 0.15 = $1,193,333. The maximum B would pay for A is the increase in value due to the merger minus the standalone value of A, which is $1,193,333 - $1,000,000 - $133,333 = $60,000. However, this calculation is incorrect based on the provided options and the premise of the question. The correct approach should consider the synergy value directly: The combined value is $1,193,333, and the value of B alone is $1,000,000. Subtracting the standalone value of A ($133,333) from the combined value gives us $1,193,333 - $133,333 = $1,060,000, which is not directly an option. The mistake here is in the interpretation of how much B would pay for A based on the given options and the calculation mistake in the explanation. The correct approach is to look at the additional value created by the merger ($179,000 - $150,000 - $20,000 = $9,000) and how this translates into a valuation, but the provided calculation and options lead to confusion. Given the options and the scenario, none directly align with the correct calculation method, indicating a misunderstanding in the explanation provided. The correct answer should reflect the value B places on A based on the synergies created by the merger, which is not accurately captured in the explanation. The premise of calculating the maximum B will pay for A should consider the synergy and how it affects the overall valuation, which is not correctly addressed with the provided options and calculations.

Firms a and B Are Competitors