Bond Binomial Pricing Model (please search an image if confused, hard to type out)

(c) > 4000

500 (d) > 3000

(a) > (e) > 1200

0

(b) > (f) > 1200

100 (g) > 1000

(h) > 500

(a): p = 0.5 (b): 1 - p = 0.5 (c): P1 = 0.15 (d): P2 = 0.25 (e): P3 = 0.6 (f): P1 = 0.1 (g): P2 = 0.4 (h): P3 = 0.5

Consider the tree above. The 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 probabilty of each state. Let us demote 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 debt holders triggers default. The net income is distributed to the shareholders. At time 2, both firms stop their business and use their EBIT to pay (if possible) in the following order: 1) interest to debt holders, 2) taxes, 3) face value of debt to debt holders, and 4) the rest to shareholders.

Remark: The notation X+ stands for node X right after cash flows have been distributed.

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

Question: Compute the present value of expected bankruptcy costs of firm F at nodes U+, D+, and Z

hint: Use the cost of unlevered equity to discount expected bankruptcy costs.