# Value of equity and expected value of the firm

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C3. Now, suppose that Michigan Mining and Manufacturing's assets of $102 million and debt of $100 million. This debt must be paid off very soon. Prior to paying off the debt, MMM has an opportunity to make a high-risk investment which will cost $20 million and pay off either $40 million or $0. (The time between investment and pay off is negligible, so the NPV of the project will be either $20 million or <$20 million>. The investment would be paid for with the firm's liquid cash holdings.

a. If the $40 million payoff (NPV = $20 million) occurs, what will be the value of MMM's equity? What will be the value of debt?

b. If the $20 million payoff (NPV = <$20 million>) occurs, what is the value of MMM's equity? What will be the value of its debt?

c. Assume the probability of the high payoff is 0.25 and the probability of the low payoff is 0.75. What is the expected value of the firm? What is the expected value of its equity? What is the expected value of its debt?

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a. Firm pays for the investment using its assets. Thus, the assets of the firm will now be 102-20 = 82M. In the good state, the value will rise to 82+40 = 122M. Thus ...

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