Question

Starset, Inc., has a target debt-equity ratio of 0.71. Its WACC is 11.5 percent, and the tax rate is 34 percent.

If the company's cost of equity is 16.5 percent, what is the pretax cost of debt?

If instead you know that the aftertax cost of debt is 5.9 percent, what is the cost of equity?

Answer 1

Given that, debt/equity=0.71
Adding denominator to numerator in both the sides, we get
(debt+equity)/equity=1.71/1
Inverting both the sides, we get
equity/(debt+equity)=1/1.71
This means that the weight of equity is 1/1.71

Again, debt/equity=0.71
Inverting both the sides, we get
equity/debt=1/0.71
Adding denominator to numerator in both the sides, we get
(equity+debt)/debt=(1+0.71)/0.71
(equity+debt)/debt=1.71/0.71
Inverting both the sides, we get
debt/(equity+debt)=0.71/1.71
This means that the weight of debt=0.71/1.71

Formula to calculate weighted average cost of capital or WACC=Weight of equity*Cost of equity + Weight of debt*Cost of debt*(1-Tax rate)
=>WACC=(1/1.71)*Cost of equity + (0.71/1.71)*Cost of debt*(1-Tax rate)
Now, given that the tax rate=34% and WACC=11.5%

=>WACC=(1/1.71)*Cost of equity + (0.71/1.71)*Cost of debt*(1-34%)
11.5%=(1/1.71)*Cost of equity + (0.71/1.71)*Cost of debt*(0.66)
11.5%=(1/1.71)*Cost of equity + (0.71/1.71)*(0.66)*Cost of debt
11.5%=(1/1.71)*Cost of equity + (0.71/1.71)*(0.66)*Cost of debt

Part 1:
Given that the cost of equity=16.5%
Substituting this value in the above equation, we get
11.5%=(1/1.71)*Cost of equity + (0.71/1.71)*(0.66)*Cost of debt
=>11.5%=(1/1.71)*16.5% + (0.71/1.71)*(0.66)*Cost of debt
=>11.5%-(1/1.71)*16.5%=(0.71/1.71)*(0.66)*Cost of debt
=>0.115-0.096491228=0.274035088*Cost of debt
=>0.018508772/0.274035088=Cost of debt
So, the pretax cost of debt=0.067541614 or 6.75%

Part 2:
Given that the after tax cost of debt=5.9%, it means Cost of debt*(1-Tax rate)=5.9%
=>WACC=(1/1.71)*Cost of equity + (0.71/1.71)*Cost of debt*(1-Tax rate)
11.5%=(1/1.71)*Cost of equity + (0.71/1.71)*5.9%
=>0.115=(1/1.71)*Cost of equity + 0.024497076
=>0.115-0.024497076=(1/1.71)*Cost of equity
=>0.090502924=0.584795322*Cost of equity
=>Cost of equity=0.090502924/0.584795322=0.15476 or 15.48%