Question

Young & Creative Inc. has a debt-equity ratio of 0.70. The cost of equity is 15 percent and the aftertax cost of debt is 5 percent. What will the firm's cost of equity be if the debt-equity ratio is revised to 0.80?

10.89 percent

11.47 percent

11.70 percent

13.89 percent

15.59 percent

Answer 1

Answer: The correct option is 15.59 percent

Complete solution:

We are given that:
Debt-Equity ratio=0.70
Cost of equity=15%
After tax cost of debt=5%

Now, weighted average cost of capital is calculated as:
Weight of equity*Cost of equity + Weight of debt*After tax cost of debt
Here,

Debt/Equity=0.7
Let us denote debt as "d" and equity as "e".
So, d/e=.7
=>(d+e)/e=1.7 (adding denominator to numerator on both the sides)
=>e/(d+e)=1/1.7 (Inverting both sides)
This means weight of equity is 1/1.7

Again,
As d/e=.7 this implies that, e/d=1/.7

(e+d)/d=1+.7/.7=1.7/.7 (adding denominator to numerator on both sides)
d/(d+e)=.7/1.7 (Inverting both sides)
This means weight of debt is .7/1.7

Weighted average cost of capital=Weight of equity*Cost of equity + Weight of debt*After tax cost of debt
1/1.7*15%+.7/1.7*5%
=0.088235294+0.020588235
=0.108823529

Now, even after the debt to equity ratio is changed to .8, the weighted average cost of capital should remain the same.

Now, when the debt to equity ratio is revised to 0.8, we will have:

Debt/Equity=0.8
Let us denote debt as "d" and equity as "e".
So, d/e=.8
=>(d+e)/e=1.8 (adding denominator to numerator on both sides)
=>e/(d+e)=1/1.8 (Inverting both sides)
This means weight of equity is 1/1.8

Again,
As d/e=.8 this implies that, e/d=1/.8

(e+d)/d=1+.8/.8=1.8/.8 (adding denominator to numerator on both sides)
d/(d+e)=.8/1.8 (Inverting both sides)
This means weight of debt is .8/1.8

Let us assume that the cost of equity is x.
Weighted average cost of capital=Weight of equity*Cost of equity + Weight of debt*After tax cost of debt

After tax cost of debt=5%
So, weighted average cost of capital=x/1.8+5%*.8/1.8=0.108823529 (this is the value we calculated earlier for weighted average cost of capital when debt/equity=.7)

=>x/1.8+0.022222222=0.108823529
=>x/1.8=0.108823529-0.022222222
=>x/1.8=0.086601307
=>x=1.8*0.086601307
=>x=0.155882353 or 15.59% (rounded upto two decimal places)
Therefore, the new cost of equity would be 15.59% when the debt to equity ratio is revised to 0.80.