$(10$ points$)$ Suppose Arturu Corp has an equity beta of $1\mathrm{.}2$ and a debt beta of $0\mathrm{.}25.$ The firm' debt$-$equity ratio is $0\mathrm{.}25.$ Arturu Corp's WACC is $12$ percent, and its cost of debt is $8$ percent

a$.$ What is the company's cost of equity capital?

b$.$ What is the company's unlevered cost of equity capital?

c$.$ Estimate Arturu Corp's asset beta.

d$.$ Suppose Arturu Corp were to increase its leverage so that its debt$-$equity ratio is $0\mathrm{.}5.$Assuming its debt beta does not change, what should its cost of equity capital and equity

beta be after the increase in leverage?