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 firm F and an unlevered firm F0. The tree also provides the probability of each state. Let us denote by Z the node at time 0, by U and D the nodes at time 1, and by UU, UM, UD, DU, DM, DD the nodes at time 2 (U stands for up move, M for middle move, and D for 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) in the following order: 1) interest to debtholders, 2) taxes, 3) face value of debt to debtholders, and 4) the rest to shareholders. Remark: The notation X+ stands for node X right after cash flows have been distributed. Firm F issues 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%.

(e) (2 points) At which nodes does firm F default?

PREVIOUS QUESTION FOR CONTEXT: (a) (4 points) Compute the cash flows to shareholders of firm F0 at nodes UU, UM, UD, DU, DM, DD, U, and D (CFS0 (UU), CFS0 (UM), CFS0 (UD), CFS0 (DU), CFS0 (DM), CFS0 (DD), CFS0 (U), CFS0 (D))

PREVIOUS QUESTION FOR CONTEXT: (b) (3 points) Compute the value of firm F0 at nodes U+, D+, and Z (S0(U+), S0(D+), S0(Z))

PREVIOUS QUESTION FOR CONTEXT: (c) (4 points) Compute the tax savings of firm F at nodes UU, UM, UD, DU, DM, DD, U, and D (CFT S(UU), CFT S(UM), CFT S(UD), CFT S(DU), CFT S(DM), CFT S(DD), CFT S(U), CFT S(D))

PREVIOUS QUESTION FOR CONTEXT: (d) (3 points) Compute the tax shields (the present value of expected tax savings) of firm F at nodes U+, D+, and Z (T S(U+), T S(D+), T S(Z))

ax rate is 30%. 4000 P1 = 0.15 P2 = 0.25 500 (3000 P3 = 0.6 p=0.5 1200 O 1200 1- p=0.5 P1 = 0.1 P2 = 0.4 100 1000 P3 = 0.5 500 Figure 1: Evolution of the EBIT of firms F and Fo