Current value of the firm to the owners = Total vaue - amount owed to the debt h

Question

Current value of the firm to the owners = Total vaue - amount owed to the debt holders

= $ 700,000 - $ 500,000

= $ 200,000

If the company undertakes the project, then expected total value is calculated by multiplying the potential total value resulting from the project with the corresponding probability and then adding the resulting two numbers together.

Expected total value = Loss of entire value * 50% + gain in value of $ 500,000 * 50% = 0 * 50% + 1200000*50% = $ 600,000

Expected Value of the firm after undertaking the project = $ 600,000 - $ 500,000 = $ 100,000

This in expectation decreases the firm's value from $ 200,000 to $ 100,000

However, in spite of that, if the owners have a high risk propensity, (risk takers), then they would want to undertake the project, because the utility of expectation of gaining $ 500,000 is higher for them, than the loss of entire value.

Explanation / Answer

Scenario 3

(length: 0.5 - 1 pg)

A struggling company currently has a total value of $700,000. It owes $500,000 from debt financing (assume these are loans from the bank if you wish). The value of the company to the owners is the difference between the total value and the amount owed to the debt holders. What is the current value of the firm to the owners? Now assume that a project is presented to the owners that results in a loss of the entire value of the company with a probability of 50% and results in a gain in value of $500,000 with probability 50% (resulting in a total value of $1,200,000). Show that this in expectation decreases the firm's value, and explain why, in spite of that, the owners of the company would want to undertake the project.

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