Answer: 9.03%.
Explanation:
Given: The Two Dollar Store has a cost of equity of 11.9 percent, the YTM on the company's bonds is 6.2 percent, and the tax rate is 40 percent.
Debt to equity ratio is .54
i.e. [tex]\dfrac{debt}{equity}=\dfrac{0.54}{1}\ ...(i)[/tex]
Adding denominator to numerator on both the sides, we get,
[tex]\dfrac{debt+equity}{equity}=\dfrac{1.54}{1}\\\\\Rightarrow\ \dfrac{equity}{debt+equity}=\dfrac{1}{1.54}[/tex]
i.e. Weighted equity = [tex]\dfrac{1}{1.54}\ ....(ii)[/tex]
From (i)
[tex]\dfrac{equity}{debt}=\dfrac1{0.54}\[/tex]
Adding denominator to numerator on both the sides we get,
[tex]\dfrac{equity+debt}{debt}=\dfrac{1+0.54}{0.54}[/tex]
[tex]\dfrac{equity+debt}{debt}=\dfrac{1.54}{0.54}[/tex]
Thus, weight of debt=[tex]\dfrac{1.54}{0.54}[/tex]
Now,
Weighted average cost of capital=(Weight of equity) × (cost of equity)+(Weight of debt)×(Cost of debt)×(1-tax rate)
[tex]\dfrac{1}{1.54}\times (0.119)+\dfrac{0.54}{1.54}\times(0.062)\times(1-0.40)\\\\=0.07727+0.02174(0.60)\\\\=0.07727+0.02174(0.60)\\\\=0.07727+0.013044\\\\=0.090314\approx9.03\%[/tex]
Hence, the weighted average cost of capital is 9.03%.
