Question

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?

Answer 1

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