An unlevered firm adds debt to its capital structure. The interest rate on the firm's debt is $10\%.$ Its unlevered cost of equity is $14\%.$ The marginal tax rate is $35\%.$ The firm starts with a capital structure of $10\%$ debt and $90\%$ equity in year $1,$ where the debt level is $$10$ million. The firm increases its debt level by $$5$ million per year in year $2$ and year $3,$ but then debt remains constant at $$20$ million beyond year $3.$ What is the present value of the interest tax shield?

Question $3$ options:

a$)$

$$5\mathrm{.}23$ million

b$)$

$$7\mathrm{.}57$ million

c$)$

$$6\mathrm{.}54$ million

d$)$

$$4\mathrm{.}70$ million