3.APV Approach

Consider the tree provided in Figure 1. This tree describes the earnings before interest and taxes (EBIT) at time 0, time 1, and time 2 of a levered firmFand an unlevered firmF0. The tree also provides the probability of each state. Let us denote byZthe node at time 0, byUandDthe nodes at time 1, and byUU,UM,UD,DU,DM,DDthe nodes at time 2 (Ustands for up move,Mfor middle move, andDfor down move). Failure to pay either interest or face value of debt to debtholders triggers default. The net income is distributed to shareholders. At time 2, both firms stop their business and use their EBIT to pay (if possible) inthe following order: 1) interest to debtholders, 2) taxes, 3) face value of debt to debtholders, and 4) the rest to shareholders.

Remark: The notationX+stands for nodeXright after cash flows have been distributed.

• FirmFissues a regular bond at time 0. Face value is 1000, coupon rate is 5%, maturity is 2 years,
• and coupon payments are made at time 1 and time 2.
• The cost of debt is 4%.
• In case of default, firms incur bankruptcy costs worth 20% of the EBIT.
• The cost of unlevered equity is 6%.
• The corporate tax rate is 30%.

4000 P1 = 0.15 P2 = 0.25 500 3000 P3 = 0.6 p = 0.5 1200 1200 90 = d - I P1 = 0.1 P2 = 0.4 100 1000 P3 = 0.5 500