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    Using the t-test to Determine Risk of Bankruptcy

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    Please see attached problem.
    Ralston Enterprises has assets that will have a market value in one year as shown below:

    Probability 1% 6% 24% 38% 24% 6% 1%
    Value ($ million) 70 80 90 100 110 120 130

    That is, there is a 1% chance the assets will be worth $70 million, a 6% chance the assets will be worth $80 million, and so on. Suppose the CEO is contemplating a decision that will benefit her personally but will reduce the value of the firm's assets by $10 million. The CEO is likely to proceed with this decision unless it substantially increases the firm's risk of bankruptcy.
    a. If Ralston has debt due of $75 million in one year, the CEO's decision will
    increase the probability of bankruptcy by what percentage?
    b. What level of debt provides the CEO with the biggest incentive not to
    proceed with the decision?

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    Solution Preview

    What you are doing here is testing the relation between two values, one of which is a random variable (asset value) and the other is a constant (the debt). The standard test to do this is to use the t-test.

    But before we do that we need to find the mean of the random variable, the asset value. This is done as follows:

    Mean = Sum(Asset Value * Probability of Occurrence)

    This gives you

    Mean = Sum (70*.01+80*.06+90*.24+100*.38+110*.24+120*.06+130*.01) = 100

    Then we need to find the variance. The formula to ...

    Solution Summary

    The expert examines using the t-test to determine the risk of bankruptcy.