"atc has a value of $70,000 in a good economy and $55,000 in a recession. the firm has $60,000 of debt. the probability of a recession is 50 percent. the firm is considering a project that would change the firm values to $73,000 in a good economy and $50,000 in a recession. if the firm accepts this project, the firm value will and shareholder value will "

The firm value will decrease by $1,000 and shareholder value will increase by $1,500

Explanation:

Data provided in the question:

Value of ATC in a good economy = $70,000

Value of ATC in recession = $55,000

Debt = $60,000

Probability of a recession = 50%

Final firm value in a good economy = $73,000

Final firm value in recession = $50,000

Now,

Expected total value = ∑(value × Probability)

= ( $73,000 × 50% ) + ( $50,000 × 50% )

= $36,500 + $25,000

= $61,500

Therefore,

Shareholder value = Expected total value - Debt

= $61,500 - $60,000

= $1,500        [Positive value means an increase]

Expected change in firm value = ∑(Change in value × Probability)

= [ ($73,000 - $70,000) × 50% ] + [ ($50,000 - $55,000) × 50% ]

= $1,500 + (- $2,500)

= -$1,000                   [Here, negative value means a decrease ]

Hence,

The firm value will decrease by $1,000 and shareholder value will increase by $1,500

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