Mini Case $5\mathrm{.}1$

The entrepreneur establishes a limited liability company today $(t=0)$ and expects the following state$-$

dependent company's cash flows after one period $(t=1)$ :

Market participants are risk$-$neutral and the relevant interest rate is $12\%.$

To take advantage of the tax benefit, the entrepreneur wants to finance the investment costs of $2,220$

million at $t=0$ by issuing debt. If the company value at the end of the period is lower than the claims of

creditors, the company goes bankrupt. The bankruptcy costs at $t=1$ amount to $150$ million, and the

remaining assets of the company are distributed to the creditors.

Risk management could smooth the company's cash flows and would cost $10$ million today. We

assume that the cost of implementing the risk management system is born by the entrepreneur.

a$)$ What is the face value of the debt if the entrepreneur does not implement risk management?

What is the present value of debt and the present value of equity in this case?

b$)$ What is the face value of the debt if the entrepreneur implements risk management? What is

the present value of debt and the present value of equity in this case?

c$)$ Should the entrepreneur implement risk management?