Backcountry Adventures is a$$ Colorado$-$based outdoor travel agent that operates a series of backcountry huts.$$ Currently, the value of the firm is $ $4$ million. But profits will depend on the amount of$$ snowfall: If it is a good$$ year, the firm will be worth $ $5\mathrm{.}1$million$,$ and if it is a bad year it will be worth $ $2\mathrm{.}3$ million. Suppose managers always keep the debt to equity ratio of the firm at $25\%,$ 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.