Question

An entrepreneur has a choice of two mutually exclusive investment projects, Project
A and Project B. Each lasts for one time period and the firm has no other projects.
Project A will result in a cash flow of £27 million in the good state and £10 million in
the bad state. Each outcome is equally likely. Project B will result in a cash flow of
£34 million in the good state and zero in the bad state. Each outcome is equally
likely. Assume the entrepreneur is able to choose which project to undertake after
the finance has been raised.
Each project requires an initial investment of £6 million. Assume risk-neutrality and a
discount rate of zero.

Assume for parts (a) to (c) that the investment is financed by debt.
(a) If Project A is chosen, what is the expected value of the firm and the payoffs
to the debtholders and the entrepreneur?
(b) If Project B is chosen, what is the expected value of the firm and the payoffs
to the debtholders and the entrepreneur? Which is the better project? Which
one will the entrepreneur choose?
(c) Assume the debtholders are fully aware of the firm’s possible investment
choices. They decide to use a bond covenant to stipulate that the face value
of the debt will be £9.2 million if the entrepreneur decides to take on the riskier
project. Which project does the entrepreneur choose now? Is this different
from your answer in part (b)? Why/why not?
(d) Suppose the entrepreneur chooses instead to finance the project with outside
equity. Which project will be chosen? What fraction of the project’s payoff will
the outside equityholders ask for? What is the payoff to the entrepreneur and
the expected value of the firm?
(e) Explain the risk-shifting (asset substitution) agency problem identified by
Jensen and Meckling (1976), with reference to your results in parts (a) to (d).
Is the solution to use as much outside equity as possible? Explain.

Please provide detailed answers, thank you!

Answer 1

a). Project A:

Firm value = sum of (probability of a state*cash flow in that state)

= (50%*27) + (50%*10) = 18.50 million

For both states, payoff to debt remains 6 million, so expected debt payoff is (50%*6) + (50%*6) = 6 million

Equity payoff (for good state) = cash flow - debt payoff = 27-6 = 21 million

Equity payoff (for bad state) = cash flow - debt payoff = 10-6 = 4 million

Expected equity payoff = (50%*21) + (50%*4) = 12.50 million

b). Project B:

Firm value = (50%*34) + (50%*0) = 17 million

Debt payoff (for good state) = 6 million

Debt payoff (for bad state) = 0 million (as there is no cash flow to pay the debtholders)

Equity payoff (for good state) = 34-6 = 28 million

Equity payoff (for bad state) = 0 million

Expected equity payoff = (50%*28) + (50%*0) = 14 million

Project A is better due to higher firm value and lower risk but the entrepreneur will choose Project B as the equity payoff is higher compared to Project A.

c). If the entrepreneur chooses Project B and the debt face value is now 9.2 million then equity payoff becomes 50%*(34-9.2) + 50%*0 = 12.40 million. This equity payoff is now less than the equity payoff from Project A so the entrepreneur's preference will shift to Project A.

d). If project is funded with equity rather than debt then for

Project A outsider equity fraction of project payoff = initial investment/firm value = 6/18.50 = 32.43%

Entrepreneur payoff is 18.50 - 6 = 12.50 million

Project B outsider equity fraction of project payoff = 6/17 = 35.29%

Entrepreneur payoff is 17-6 = 11 million

e). Equityholders prefer to take on risky projects due to higher payoffs even if the projects have overall lower value. Debtholders would prefer that the less risky, higher value projects be taken on so even if debt financing is taken with the understanding that the less risky projects will be chosen, once funding is secured then the managers may go with the riskier projects. This results in wealth transfer from debtholders. One way of curtailing this, is for bondholders to use covenants (as shown in part c).

If projects are financed with external equity then there are agency costs associated with them which decrease payoff for the owners as profits have to be shared with the external equityholders. So, an optimal capital structure is a trade-off between choosing the agency cost of debt or agency cost of external equity.