Question

2. 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. NO USE OF EXCEL

a. 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?

b. 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

a) Expected value of cashflows after two years = $10*0.6 + (-$4)*0.4 = $4.4

So, Discount rate r is given by

4.4/(1+r)^2 = 3.44

r = 0.6360 or 63.60% p.a.

b) Suppose the tax rate is t

Profit if cashflows are good = t*(10-3.44)

Expected value of cashflows = ($10-t*(10-3.44))*0.6 +0.4*0 (as one owes nothing if the cashflows are bad)

So, To be indifferent between running the project as in individual or through the corporation

Expected value of cashlflows = 4.4

=> (10-t*(10-3.44))*0.6 +0.4*0 =4.4

=>(10-t*(10-3.44) = 7.3333

t*6.56 = 2.6666

t = 0.4065 or 40.65%

So, tax rate is 40.65%