Question

Backcountry Adventures is a Colorado-based outdoor travel agent that operates a series of backcountry huts. Currently, the value of the firm is $3.8 million. But profits will depend on the amount of snowfall: If it is good year, the firm will be worth $5.2 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 30%, and the debt is riskless.

a. What is the initial amount of debt?
b. 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.
c. Calculate the percentage change in the value of outstanding debt once the firm adjusts to its target debt-equity ratio.
d. What does this imply about the riskiness of the firm's tax shields. Explain.

Answer 1

a.
Debt	$                                                      0.88
equity	$                                                      2.92	3.8/(1+0.3)
total	$                                                      3.80
b.
	% change in Firm value	% change in	% change in Debt value
		Equity value
Good state	36.84%	47.89%	0%
Bad state	-34.21%	-44.47%	0%
	(5.2-3.8)/3.8	36.84%
	(2.5-3.8)/3.8	-34.21%
	(4.32-2.92)/2.92	47.89%
	(1.62-2.92)/2.92	-44.47%
C
	% change in Firm value	% change in	% change in Debt value
		Equity value
Good state	36.84%	36.84%	36.84%
Bad state	-34.21%	-34.21%	-34.21%
	(5.2-3.8)/3.8	36.84%
	(2.5-3.8)/3.8	-34.21%
	(4-2.92)/2.92	36.84%
	(1.92-2.92)/2.92	-34.21%
	(1.2-1)/0.88	36.84%
	(1-0.88)/0.88	-34.21%
d.
Because the debt is riskless, the only risk to the tax shields is the amount of outstanding debt. This risk is identical to the risk of the firm as a whole, so the riskiness of the tax shields are identical to the riskiness the firm as a whole.