Chapter 17, Problem 10P

a)

Summary Introduction

To determine: The value of IA.

Explanation of Solution

$\begin{array}{c}{\text{V}}_U={\text{S}}_U=\frac{\text{EBIT}}{r_{sU}}\\ =\frac{\$1,600,000}{0.11}\\ =\$14,545,455\\ V_L=V_U=\$14,545,455\end{array}$

b)

Summary Introduction

To determine: The values of WACC, rs and effect of leverage.

Explanation of Solution

$\begin{array}{c}{\text{r}}_{sL}=r_{sU}+\left(r_{sU}-r_d\right)\left(\frac{D}{S}\right)\\ =11\%+\left(11\%-6\%\right)\left(\frac{\$6,000,000}{\$8,545,455}\right)\\ =14.51\%\\ WACC=\left(\frac{D}{V}\right)r_d+\left(\frac{S}{V}\right)r_s\\ =\left(\frac{\$6,000,000}{\$14,545,455}\right)6\%+\left(\frac{\$8,545,455}{\$14,545,455}\right)14.51\%\\ =11\%\end{array}$

$\begin{array}{c}{r}_{sL}=11\%+5\%\left(\frac{\$10,000,000}{\$4,545,455}\right)\\ =22\%\\ WACC=\left(\frac{\$10,000,000}{\$14,545,455}\right)6\%+\left(\frac{\$4,545,455}{\$14,545,455}\right)22\%\\ =11\%\end{array}$

Leverage holds no impact on business esteem, which may be a steady $14,545,455 since the weighted average cost of capital could be a steady 11percent. This can be since the fetched of value is expanding with use, and this increment precisely balances the benefit of utilizing below the cost of debt financing.

c)

Summary Introduction

To determine: The new market values for IA.

Explanation of Solution

$\begin{array}{c}{\text{V}}_U=\frac{\left[\left(EBIT-1\right)\left(1-T\right)\right]}{r_{sU}}\\ =\frac{\left(\$1,600,000-0\right)\left(1-0.4\right)}{0.11}\\ =\$8,727,273\\ V_L=V_U+TD\\ =\$8,727,273+\left(0.4\times \$6,000,000\right)\\ =\$11,127,273\end{array}$

d)

Summary Introduction

To determine: The values of WACC and rs and plot relationship between value of firm and debt proportion.

Explanation of Solution

$\begin{array}{c}{V}_L=V_U+TD\\ =\$8,727,273+\left(0.4\times \$6,000,000\right)\\ =\$11,127,273\\ r_{sL}=r_{sU}+\left(r_{sU}-r_d\right)\left(1-T\right)\left(\frac{D}{S}\right)\\ =11\%+\left(11\%-6\%\right)0.6\times \left(\frac{\$6,000,000}{\$5,127,273}\right)\\ =14.51\%\\ WACC=\left(\frac{D}{V}\right)r_d\left(1-T\right)+\left(\frac{S}{V}\right)r_s\\ =\left[\left(\frac{\$6,000,000}{\$11,127,273}\right)\times 6\%\times 0.6\right]+\left[\left(\frac{\$5,127,273}{\$11,127,273}\right)14.51\%\right]\\ =8.63\%\end{array}$

$\begin{array}{c}{\text{V}}_L=\$8,727,273+\left(0.4\times \$10,000,000\right)\\ =\$12,727,273\\ r_{sL}=11\%+\left(5\%\times 0.6\right)\left(\frac{\$10,000,000}{\$2,727,273}\right)\\ =22\%\\ WACC=\left(\frac{\$10,000,000}{\$12,727,273}\times 6\%\times 0.6\right)+\left(\frac{\$2,727,273}{\$12,727,273}\times 22\%\right)\\ =7.54\%\end{array}$

e)

Summary Introduction

To determine: The highest dollar value of debt funding that can be applied and the value of the company at this debt level.

Explanation of Solution

$\begin{array}{c}{V}_L=V_U+TD\\ \$8,727,273+0.4D=D\\ D=\$8,727,273\\ V=\$14,545,455\end{array}$

$\begin{array}{c}{V}_L=\frac{\$1,600,000}{0.11}\\ =\$14,545,455\end{array}$

f)

Summary Introduction

To determine: The manner in which each of the following factors tend to change the values plotted.

Explanation of Solution

• Rising intrigued rates would cause rd and thus $r_d\left(1-T\right)$ to extend, pulling up weighted average cost of capital. These variation would lead V to increase less steeply, or indeed to decrease.
• Expanded hazard causes rs to rise speedier than anticipated by MM. Hence, weighted average cost of capital would increment and V would diminish.