Question

WRITE LEGIBLY

1. Consider a risky project which pays you $10 two years from now with 60% probability, or you have to pay $4 (i.e. negative cash flow) with 40% probability. There are no other cash flows.

   1. You do the math and decide you’d be willing to pay $3.44 to buy the project as an individual. You wouldn’t have to pay taxes on any profits. What is the discount rate you are using to value this project?

   2. Now suppose you are offered the same project except that you would be able to run the project through a corporation which would give you full liability protection if the project goes bad. If the cash flows are negative, you can just walk away and owe nothing. However, the corporation has to pay taxes on any profits. Using the discount rate in (a), what is the tax rate at which you are indifferent between running the project as in individual or through the corporation?

Answer 1

1) Let us first find expected cash flow

Expected cash flow after 2 years = $10 x 60% + - $4 x 40%

= 6$ - 1.6$

= 4.4 $

Now FV = 4.4 , PV = 3.44$ , n =no of year = 2 years ,r = rate of interest =?

FV = PV(1+r)^n

4.4 = 3.44(1+r)^n

1.2791 = (1+r)^2

1.1310 = 1+r

r = 0.1310

i.e 13.10%

2) if project is run through a corporation , then expected cash flow = 10$ x 60% + 0$ x 40%

= $6

Now the above cash flow is pre tax cash flow , so first we need to find after tax cash flow

FV = ? , PV = 3.44$ , n =no of year = 2 years ,r = rate of interest =13.10%

FV = PV(1+r)^n

= 3.44(1+13.10%)^2

= 3.44(1.1310)^2

= 3.44 x 1.279161

= 4.40 $

Thus After tax cash flow = 4.40$

Maximum tax rate that can be afford

After tax cash flow = Before tax cash flow(1-tax rate)

4.40 = 6(1-tax rate)

0.73333 = 1-tax rate

Tax rate = 0.2667

i.e 26.67%

Ths at tax rate of 26.67% one will be indifferent between running the project as in individual or through the corporation