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# Michigan Mining payoff, value of equity and value of debt

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Michigan Mining and Manufacturing has a debt obligation of \$100 million and assets with a value of \$90 million. This debt must be paid off very shortly. When this happens, the value of the debt will be \$90 million and the value of equity will be \$0. Prior to paying off the debt, MMM has an opportunity to make a high-risk investment. MMM is considering an investment of \$20 million (from existing assets) that will pay off \$40 million or zero. The investment would have an NPV of either \$20 million or - \$20 million (NPV = the value of the payoff minus the investment). The investment would be paid for with the firm's liquid cash holdings.

1. If the \$40 million payoff (NPV = \$20 million) occurs, what is the value of equity? What is the value of debt?
2. If the zero payoff (NPV = - \$20 million) occurs, what is the value of equity? What is the value of debt?
3. Assume the probability of the high payoff is 0.25 and the probability of the low payoff is 0.75. What is the expected NPV of the investment? What is the expected value of the firm?
4. What is the expected value of equity? What is the expected value of debt?
5. How can stockholders benefit from a negative-NPV project?

#### Solution Preview

Question 1
Value of the company = 90+20 = 110
Value of equity = 10 million
Value of debt = 100 million

Question 2
Value of the company = 90-20 = 70
Value of equity = ZERO
Value of debt = 70 million

Question 3
Expected payoff = 40x0.25 + 0x0.75 = 10 million
Expected NPV = - 20 million + 10 million = - 10 million
Expected value of ...

#### Solution Summary

The solution examines Michigan Mining and Manufacturing as a debt obligation. The NPV of investments is determined.

\$2.19