Mantle Corporation is considering two equally risky investments: (1)(2)What is the break-even corporate tax rate which makes the company indifferent between the two investments?
A) 33.17%
B) 34.00%
C) 37.97%
D) 42.15%
E) 42.86%

Question

Quizplus · Accepted Answer

To find the break-even corporate tax rate, we need to set the NPV of the two investments equal to each other and solve for the tax rate. Thus, we have:
$12,000 = $8,000/(1 - T_c) + $10,000/(1 - T_c)^2
Simplifying the equation, we get:
$12,000(1 - T_c)^2 = $8,000(1 - T_c) + $10,000
$12,000 - $24,000T_c + $12,000T_c^2 = $8,000 - $8,000T_c + $10,000
$12,000T_c^2 - $16,000T_c + $6,000 = 0
Solving for T_c using the quadratic formula, we get:
T_c = (0.333 + sqrt(0.111))/0.24 or T_c = (0.333 - sqrt(0.111))/0.24
T_c ≈ 1.407 or T_c ≈ 0.530
Since the tax rate cannot exceed 100%, the break-even tax rate is approximately 53%. Therefore, investment 1 is preferred when the corporate tax rate is below 53% and investment 2 is preferred when the tax rate is above 53%. As a result, the best choice is investment 1 for corporate tax rates below 53%, and investment 2 for corporate tax rates above 53%.

Mantle Corporation Is Considering Two Equally Risky Investments: (1)(2)What Is