a. Assume the following capital structure for the Morgan Corp. The following facts are also provided: Compute the weighted average cost of capital. b. If there is $30 million in retained earnings, at what dollar value will the marginal cost of capital go up? If the flotation cost on common stock is

Question

a. Assume the following capital structure for the Morgan Corp.

Debt	35%
Preferred stock	15%
Common equity	50%

The following facts are also provided:

Bond yield to maturity	9%
Corporate tax rate	35%
Dividend, preferred stock	$ 8.50
Price, preferred stock	$ 100
Flotation cost, preferred stock	$ 2
Dividend, common stock	$ 1.20
Price, common stock	$ 30
Growth rate, common stock	9%

Compute the weighted average cost of capital.

b. If there is [latex]\$30[/latex] million in retained earnings, at what dollar value will the marginal cost of capital go up? If the flotation cost on common stock is [latex]\$1.50[/latex], what will be the cost of new common stock?

Accepted Answer

a. First compute the cost of the components in the capital structure.

[latex] \begin{aligned} \mathrm{K}_{\mathrm{d}}( ext { aftertax cost of debt }) &= ext { Yield }(1-\mathrm{T}) \ &=9 \%(1-.35)=5.85 \% \end{aligned} [/latex] (11-2)

[latex]\mathrm{K}_{\mathrm{p}} ext { (cost of preferred stock)}=\frac{\mathrm{D}_{\mathrm{p}}}{\mathrm{P}_{\mathrm{p}}-\mathrm{F}}[/latex] (11-3)

[latex] \begin{array}{l} \mathrm{D}_{\mathrm{p}}= ext { Dividend, preferred stock }=\$ 8.50 \ \mathrm{P}_{\mathrm{p}}= ext { Price, preferred stock }=\$ 100 \end{array} [/latex]

[latex]\mathrm{F}=[/latex] Flotation cost, preferred stock [latex]=\$ 2[/latex]

[latex] \mathrm{~K}_{\mathrm{p}}=\frac{\$ 8.50}{\$ 100-\$ 2}=\frac{\$ 8.50}{\$ 98}=8.67 \% [/latex]

[latex]\mathrm{K}_{\mathrm{e}}[/latex] (cost of common equity in the form of retained earnings) [latex]=\frac{\mathrm{D}_{1}}{\mathrm{P}_{0}}+\mathrm{g}[/latex] (11-6)

[latex]\mathrm{D}_{1}=[/latex] Dividend, common stock [latex]=\$ 1.20[/latex]

[latex]\mathrm{P}_{0}=[/latex] Price, common stock [latex]=\$ 30[/latex]

[latex]\mathrm{g}=[/latex] Growth rate, common stock [latex]=9 \%[/latex]

[latex]\mathrm{K}_{\mathrm{e}}=\frac{\$ 1.20}{\$ 30}+9 \%=4 \%+9 \%=13 \%[/latex]

Now, combine these with the weights in the capital structure to compute the weighted average cost of capital.

		Cost	Weights	Weighted Cost
Debt	[latex]K_{d} [/latex]	5.85%	35%	2.05%
Preferred stock	[latex]K_{p} [/latex]	8.67	15	1.30
Common equity (retained earnings)	[latex]K_{e} [/latex]	13.00	50	6.50
Weighted average cost of capital ([latex]K_{a} [/latex])				9.85%

b. The marginal cost of capital will go up when there is no longer enough retained earnings to support the capital structure. This is point [latex]\mathrm{X}[/latex]. Solve for [latex]\mathrm{X}[/latex] :

[latex] \begin{aligned} X &=\frac{ ext { Retained earnings }}{ ext { Percent of retained earnings in the capital structure }} \ &=\frac{\$ 30 ext { million }}{.50}=\$ 60 ext { million } \end{aligned} [/latex]

At this point, new common stock will be used instead of retained earnings in the capital structure. The cost of the new common stock is:

[latex] \begin{aligned} \mathrm{K}_{\mathrm{n}} &=\frac{\mathrm{D}_{1}}{\mathrm{P}_{0}-\mathrm{F}}+\mathrm{g} \end{aligned} [/latex] (11-7)

[latex] \begin{aligned}\mathrm{K}_{\mathrm{n}} &= ext { Cost of new common stock } \end{aligned} [/latex]

The only new term is [latex]\mathrm{F}[/latex] :

[latex] \begin{aligned} \mathrm{D}_{1} &=\$ 1.20 \ \mathrm{P}_{0} &=\$ 30 \ \mathrm{~F} &= ext { Flotation cost, new common stock } \$ 1.50 \ \mathrm{~g} &=9 \% \end{aligned} [/latex]

[latex] \mathrm{K}_{\mathrm{n}}=\frac{\$ 1.20}{\$ 30-\$ 1.50}+9 \%=\frac{\$ 1.20}{\$ 28.50}+9 \%=4.21 \%+9 \%=13.21 \% [/latex]

Question 11.2: a. Assume the following capital structure for the Morgan Cor...

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