A project with uncertain return costs $50 to finance today and pays out (next year) $150 with probability .4 and $0 with probability .6. Assume the time premium is 10%. Also assume capital markets are perfect and that all investors are risk-neutral.
a. Assume a manager fully finances this project with a $50 bond. What is the face value of the bond?
b. What is the promised rate on the bond?
c. Now assume the manager finances the project with a $20 bond and finances the remainder by himself. What is the PV of this “levered”equity scheme?
d. True or false: Given the hypotheses, the promised rate on the bond is independent of the amount (i.e. initial value) of the bond.
e. Find the optimal (profit-maximizing) mix of debt and equity for this project.