Question

Example: agency problem between stockholders and bondholders – asset substitution (over-investment problem)

A firm is at the verge of bankruptcy. It has outstanding debt of $100k, and its total assets amount to also $100k only. (Amount equity=0) The debt has a 10% annual interest, and the firm is confronted with the following two mutually exclusive projects with their respective initial and terminal cash flows.

CF=Cash flow

CF₀ =at t=0

Project	Initial cost, CF0 $	Terminal cash flows, CF1
		Economy Doom, 50% chance	Economy Boom, 50% chance
A	$100k	$90k	$110k
B	$100k	0	$200k

Assuming information asymmetry (information is not equally distributed, the stock holder (in the board) within it the firm know more about the firm rather then the bondholder (not on the board)) exists between stockholders and bondholders at t=0. Else, bondholders may choose to liquidate the firm at t=0.

Which project will the stockholders instruct the managers to accept? Why?

Expected payoff for project A =

Expected payoff for project B =

Expected bondholders’ payoff for project A =

Expected bondholders’ payoff for project B =

Expected stockholders’ payoff for project A =

Expected stockholders’ payoff for project B =

Answer 1

Part A

Expected payoff = Sum of probability x payoff

                                 = (0.50 x 90K) + (0.50 x 110 K)

                                = 100 K

Part B

Expected payoff = Sum of probability x payoff

                                 = (0.50 x 0K) + (0.50 x 200 K)

                                = 100 K

Part C

Payoff to bondholders = sum of probability x interest

                                             = 0.50 x 100K x 10%    + 0.50 x 100K x 0.10

                                             = 10K

Part D

Payoff to bondholders = sum of probability x interest

                                             = 0.50 x 100K x 10%    + 0.50 x 100K x 0.10

                                             = 10K