Question

1. Suppose that firms face 40% income tax rate on positive profits and that net losses receive no credit. (Thus, if profits are positive, after-tax income is (1 – 0.4) * profit, while if there is a loss, after-tax income is the amount lost.) Firms A and B have the same cash flow distribution as in problem 5 above. Suppose the appropriate effective annual discount rate for both firms is 10%?
   1. What is the expected pre-tax profit for A and B?
   2. What is the expected after-tax profit for A and B?
   3. What would Firms A and B pay today to receive next year’s expected cash flow for sure, instead of the variable cash flows described above?

Here I attach problem 5, so you can see the info for problem 6, problem 6 is the one that I want to get the answer.

Problem 5.

1. Suppose that firms face 40% income tax rate on all profits. In particular, losses receive full credit. Firm A has 50% probability of a $1000 profit and a 50% probability of a $600 loss each year. Firm B has a 50% probability is a $300 profit and a 50% probability of a $100 profit each year.

Answer 1

Given,

Tax rate = 40% or 0.40

Discount rate = 10% or 0.10

Firm A's 50% probability of profit = $ 1000

Firm A's 50% probability of loss = -$ 600

Firm B's 50% probability of profit = $ 300

Firm B's 50% probability of profit = $ 100

Solution :-