Question

A firm has an unlevered cost of capital of 10%, a cost of debt of 9%, and a tax rate of 34%. If it desires a cost of equity of 14%, what should be the weight of debt?

Answer 1

Suppose weight of debt is wd. Here we will use the formula for weighted average cost of capital as per below:

WACC = we * re + wd* rd * (1 - t)

where,wd = Percentage of debt = 40

we = Percentage of equity = 1 - wd

re = Cost of equity = 14%

t = Tax rate = 34%

rd = Cost of debt = 9%

WACC = 10%

Now, putting these values in the WACC formula, we get,

10% = ((1- wd) * 14%) + (wd * 9%) * (1 - 34%))

0.10 = 0.14 - 0.14wd  + (0.09wd * 0.66)

0.10 = 0.14 - 0.14wd + 0.0594wd

0.10 - 0.14 = -0.14wd + 0.0594wd

-0.04 = - 0.0806wd

wd = 0.04 / 0.0806

wd = 0.4963 or 49.63%

So, weight of debt should be 49.63%