Your all-equity firm has a 60 percent chance of producing expected cash flows of $7.0M in perpetuity and a 40 percent chance of producing expected cash flows of $14.50M in perpetuity. These cash flows are unrelated to the state of the economy and investors have access to a risk-free rate of 5 percent.
What is the value of your all-equity firm?

You are considering issuing debt to retire shares and obtain the valuable tax shield cash flows from interest payments. Specifically, if you issued debt valued at D, the value if your firm from (a) would increase by:
V(tax shield) = 0.04 * D
However, increasing debt would also increase your probability of financial distress, which would decrease firm value due to the potential costs paid to bankruptcy lawyers. Your financial analysts inform you that if you issued debt valued at D, then the value of your firm from (a) would decrease by:
V(bankruptcy costs) = 0.0025 * D^2
For example, if you issued $10M in debt to retire equity, then the value of your tax shield would be 0.40 * $10M =$4M and the value lost due to bankruptcy costs would be 0.0025 * 10M^2= $0.25M. That is ,if you issued $10M in debt to retire equity, then the value of your firm would increase by $3.75M.

b) Your firm can choose a level of debt anywhere between zero and $120M.Create a graph that contains the level of debt on the x-axis and the change in the value of the firm on the y-axis.

c) What is the optimal level of debt you should issue to maximize the change in value for your firm? You should be able to use Excel or calculus to answer this question?