Backcountry Adventures is a Colorado-based outdoor travel agent that operates a series of backcountry huts. Currently, the value of the firm is 3.5$ million. But profits will depend on the amount of snowfall: If it is a good year, the firm will be worth 5 $ million, and if it is a bad year it will be worth 2.5$ million. Suppose managers always keep the debt to equity ratio of the firm at 25% and the debt is riskless. Calculate the percentage change in the value of the firm, its equity and its debt once the level of snowfall is revealed, but before the firm adjusts the debt level to achieve its target debt to equity ratio. The inital amount of debt is equal to 0.74 and equity 2.96
PLEASE FILL OUT THE TABLE AND PROVIDE PRECISE CALCULATIONS
Good state Bad state
Change in firm value 42.86% -28.57%
Change in equity value
Change in debt value

                                               Good state                Bad state

Change in firm value                  42.86%                   -28.57%

Change in equity value              26.69%                   -36.66%

Change in debt value                 68.91%                    -15.54%

Explanation:

The following are given in the question:

Current firm value = $3.5 million

Firm value in good state = $5 million

Firm value in bad state = $2.5 million

Initial debt amount = $0.74 million

Initial equity amount = $2.96 million

Percentage of debt finance = debt to equity ratio = 25%

Percentage of equity finance = 1 - debt to equity ratio = 100% - 25% = 75%

We can therefore calculate as follows:

Percentage change in firm value in good state = [(Firm value in good state - Current firm value) / Current firm value] * 100 = ((5 - 3.5) / 3.5) * 100 = (1.5 / 3.5) * 100 = 42.86%

Percentage change in firm value in bad state = [(Firm value in bad state - Current firm value) / Current firm value] * 100 = ((2.5 - 3.5) / 3.5) * 100 = (-1.00 / 3.5) * 100 = -28.57%

Equity amount in good state = Firm value in good state * Percentage of equity finance = $5 million * 75% = $3.75 million

Percentage change in equity in good state = [(Equity amount in good state - Initial equity amount) / Initial equity amount] * 100 = ((3.75 - 2.96) / 2.96) * 100 = (0.79 / 2.96) * 100 = 26.69%

Equity amount in bad state = Firm value in bad state * Percentage of equity finance = $2.5 million * 75% = $1.875 million

Percentage change in equity in bad state = [(Equity amount in bad state - Initial equity amount) / Initial equity amount] * 100 = ((1.875 - 2.96) / 2.96) * 100 =  (-1.085 / 2.96) * 100 = -36.66%

Debt amount in good state = Firm value in good state * Percentage of debt finance = $5 million * 25% = $1.25 million

Percentage change in debt in good state = [(Debt amount in good state - Initial debt amount) / Initial debt amount] * 100 = ((1.25 - 0.74) / 0.74) * 100 = (0.51 / 0.74) * 100 = 68.91%

Debt amount in bad state = Firm value in bad state * Percentage of debt finance = $2.5 million * 25% = $0.625 million

Percentage change in debt in bad state = [(Debt amount in bad state - Initial debt amount) / Initial debt amount] * 100 = ((0.625 - 0.74) / 0.74) * 100 = (-0.115 / 0.74) * 100 = -15.54%