Question

Capital injection as a screening device. Suppose we have a firm that needs $200 to invest in a project that will yield a random payoff one period hence and that the lender will require 10% loan rate. The firm knows the probability distribution of the project’s cash flow, but no one else does. All that others know is that the project can be type C or type D. If it is type C, then it will yield a cash flow of $300 with probability 0.9 and zero with probability of 0.1. If it is type D, the project will yield a cash flow of $600 with probability 0.5 and zero with probability 0.5.

The corporate tax rate is now 20%. Now though bank cannot tell whether the borrower has a type C or a type D project, the bank wish to separate out each type of borrower correctly. The key to resolving this informational asymmetry is to use capital from the borrower as a signal. As a banker, how would you deal with those borrowers, assuming that the borrower type is either project C or project D?

Answer 1

Prinicple = $200

Rate of interest = 10%

Interest expense = $20

Tax rate = 20%

Case 1: Project is type C

Payoff on project = $300

Probability = 0.90

Expected return = Payoff * probability = $300 * 0.90 = $270

Earnings before tax = Payoff - interest expense = 270 - 20 = $250

After tax return = 250 * ( 1 - Tax ) = 250 * ( 1 - .20 ) = $200

Percentage return on project = ( After tax return - initial investment ) / initial investment = ( 200 - 200 ) / 200 = 0%

Case 2 : Project is type D

Payoff on project = $600

Probability = 0.50

Expected return = Payoff * probability = $600 * 0.50 = $300

Earnings before tax = Payoff - interest expense = 300 - 20 = $280

After tax return = 250 * ( 1 - Tax ) = 280 * ( 1 - .20 ) = $224

Percentage return on project = ( After tax return - initial investment ) / initial investment = ( 224 - 200 ) / 200 = 12%

A banker would prefer project D since it provides a greater percentage of return. If the borrower is not disclosing the type of project, a banker should give out the loan because in either case, the borrower would be able to pay the interest due to the bank.