Question

At time t=0 a firm has a project which costs $160 today and will yield $200 at time t=2 with probability 1/2 and $100 at time t=2 with probability 1/2. At time t=1 the firm learns what the payoff will be from the original project (i.e., whether the payoff will be $200 or $100) and, assuming they invested at t=0, the firm can choose to fund a follow-up project at time t=1 where the follow-up project requires spending an additional $100 at time t=1 and will increase eventual cash flows at time t=2 by $120. Assume risk-neutrality, a zero interest rate, no direct bankruptcy costs, and no taxes. The only asset that the firm has is the idea for this project.

(a) Suppose that when the firm funds investment projects it is committed to a policy of selling equity. Thus, if they fund the original project at t=0 or the follow-up project at t=1 they will sell new equity. What will the market value of old equity be at time t=0 before any financing takes place?

(b) Suppose that when the firm funds investment projects it is committed to a policy of selling junior debt at t=0 to fund the original project and senior debt at t=1 to fund the follow-up project. The firm can choose to fund both projects, neither project, or only the original project (skipping the original project and financing the follow-up one is not an option). However, any projects that the firm funds will be financed according to the financing policy that it has committed to. What will the market value of equity be at time t=0 before any financing takes place?

(c) Suppose that when the firm funds investment projects it is committed to a policy of selling senior debt at t=0 to fund the original project and junior debt at t=1 to fund the follow-up project. The firm can choose to fund both projects, neither project, or only the original project. However, any projects that the firm funds will be financed according to the financing policy that it has committed to. What will the market value of equity be at time t=0 before any financing takes place?

Answer 1

1.

Actual outflow in year 0 (t=0) = 160 $

Expected inflow in year 2 = (200*0.5) + (100*0.5)

= 150 $

So on the face this project should not be accepted.

Here value of old equity will be 150$.

2. If invested Rs. 100 in t=1 years then

Actual outflow = 160 + 100 = 260 $

Actual inflow will be increased by 120 $

So actual inflow will be 270 $.

Here inflow will be more than the outflow assuming zero interest rate. So this project should be acceptable as benefit of 10 $ will be arise in this project if 100 $ to be invested in t= 1 years.

Here the value of equity will be 270 $ if both the outflow are funding from equity.

In case if the funding is from debt, then if the return on project is more than the interest on debt then it would be have higher market value & vice versa.