Mulligan Manufacturing (MM) has a current market value of $100 million and has $80 million in debt. MM’s current assets are expected to be worth either $80 million or $130 million next year with equal probability. MM also has a project that in one year has a 20% probability a $25 million payoff and an 80% probability of a -$10 million payoff. For simplicity assume the discount rate is zero. What is the expected value of the project? How much better/worse off would MM shareholders be if they engage in the project? How much better/worse off are MM shareholders if they engage in the project, but bondholders can convert their bonds to 80% of MM’s equity?
Expected value of the project = 20% x 25 + 80% x (-10) = - $ 3 million
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Equity value = max (V - D, 0)
State 1 | State 2 | |
Firm's value | 80 | 130 |
[-] Debt | 80 | 80 |
Equity value | 0 | 50 |
Probability | 50% | 50% |
Hence, expected equity value without the project = 50% x 0 + 50% x 50 = $ 25 million
When the project is undertaken, there are 4 states possible now:
State 1 | State 2 | State 3 | State 4 | |
Current Assets value (A) | 80 | 80 | 130 | 130 |
Project's value (B) | 25 | -10 | 25 | -10 |
[-] Debt (C) | 80 | 80 | 80 | 80 |
Equity value (D) = Max (A + B - C, 0) | 25 | 0 | 75 | 40 |
Probability | 10% | 40% | 10% | 40% |
Hence, expected equity value with the project = 10% x 25 + 40% x 0 + 10% x 75 + 40% x 40 = $ 26 million
Hence, the MM shareholders will be better off by 26 - 25 = $ 1 million if they engage in the project.
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if they engage in the project, but bondholders can convert their bonds to 80% of MM’s equity
State 1 | State 2 | State 3 | State 4 | |
Current Assets value (A) | 80 | 80 | 130 | 130 |
Project's value (B) | 25 | -10 | 25 | -10 |
Debt (C) | 80 | 80 | 80 | 80 |
Debt Value if converted to equity (D) = 80% x (A + B) | 84 | 56 | 124 | 96 |
Will bond holders convert? {Yes if D > C, No otherwise} | Yes | No | Yes | Yes |
Value to bondholders E = max (C, D) | 84 | 80 | 124 | 96 |
Equity value to shareholders F = max (A + B - E, 0) | 21 | 0 | 31 | 24 |
Probability | 10% | 40% | 10% | 40% |
Hence, expected equity value with the project = 10% x 21 + 40% x 0 + 10% x 31 + 40% x 24 = $ 14.80 million
Hence, the MM shareholders will be worse off by 25 - 14.80 = $ 10.2 million if they engage in the project and bondholders can convert their bonds to 80% of MM’s equity
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