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Optimizing the Capital Structure

The capital structure of a company is the mix of equity and debt the company uses to finance its capital

expenditures $($CAPEX$).$

Companies have two ways of funding their CAPEX: equity and debt, that is why in the balance sheet

assets equal equity plus liabilities $(A=E+L).$

Equity can take two forms: common equity and preferred equity.

Debt can take many forms: loans, accounts payable, notes, bonds, etc.

The company you will be analyzing uses bonds, common equity, and preferred equity.

The capital structure is crucial because it determines the cost of capital of the company. The cost of

capital is vital for the NPV calculation.

Since the cost of capital is made up of the cost of debt, the cost of common equity, and the cost of

preferred equity, the cost of capital is an average of the three costs. You should remember from your

introduction to finance class the concept of weighted average cost of capital $($WACC$).$

wacc$=w_d*r_d*(1-T)+w_e*r_e+w_p*r_p$

Where $w_d,w_e,$ and $w_p$ are the weights or proportions or debt, common equity, and preferred equity the

firm uses in the capital structure. $T$ is the tax rate. $r_d,r_e,$ and $r_R$ are the costs of debt, common equity,

and preferred equity, respectively. The cost of debt, $r_d,$ is multiplied by $(1-T)$ to find the after$-$tax cost

of debt because interest payments are tax deductible. Common and preferred dividends are not tax

deductible.

Your objective is to determine the proportions of debt $(r_d),$ common equity $(c_{{?}_{?}}()),$ and preferred equity

$(r_n)$ the firm must use to minimize the WACC.

Remember that:

The total amount of debt $($D$)$ is equal to the number of bonds $(x)$ times the price of each bond.

The total amount of common equity $(E)$ is equal to the number of shares $(y)$ times the stock

price.

The total amount of preferred equity $(P)$ is equal to the number of shares $(z)$ times the preferred

stock price.

$w_d=\frac{D}{D+E+P},w_e=\frac{E}{D+E+P},$ and $w_p=\frac{P}{D+E+P}$

The cost of debt $(r_d)$ is equal to the YTM of the company's bond issue.

The cost of equity $(r_{{?}_{?}})$ is calculated with the CAPM equation $r_e=r_f+*[E(r_M)-r_f].$

The cost of preferred equity is $r_p=\frac{\text{P}\text{r}\text{e}\text{f}\text{e}\text{r}\text{r}\text{e}\text{d}\text{d}\text{i}\text{v}\text{i}\text{d}\text{e}\text{n}\text{d}}{\text{P}\text{r}\text{e}\text{f}\text{e}\text{r}\text{r}\text{e}\text{d}\text{s}\text{t}\text{o}\text{c}\text{k}\text{p}\text{r}\text{i}\text{c}\text{e}}$

The company you are analyzing will use

$x$ number of $7$ percent coupon bonds, with $20$ years to maturity, par value $$1,000,$ and a quoted

price of ${93}^1.$ These bonds pay interest semiannually.

$y$ shares of common stock selling for $$45$ per share. The stock has a beta of $1\mathrm{.}2.$

$z$ shares of preferred equity selling for $$93$ per share and a preferred dividend of $$5\mathrm{.}58$ per

share.

The expected return on the market is $12$ percent, the risk$-$free rate is $4$ percent, and the tax rate

is $35$ percent.

With all the information above, you must set up an optimization model in Excel to determine the

number of bonds $(x),$ common stock shares $(y),$ and preferred stock shares $(z)$ that will minimize the

WACC of the company subject to the following constraints:

The debt$-$to$-$equity ratio $(\frac{D}{E+P})$ should not exceed $40\%.$

The proportion of preferred stock $(w_p)$ should not exceed $10\%.$

The total capital raised by the company $(D+E+P)$ should be at least $$6,000,000.$

The number of bonds $(x),$ common stock shares $(y),$ and preferred stock shares $($z$)$ should be

integers.

Questions:

What is the YTM of the bond issue?

What is the cost of equity?

What is the cost of preferred equity?

How many bonds should the company issue?

How many shares of common stock should the company issue?

How many shares of preferred stock should the company issue?

What is the optimal capital structure of the company? That is how much are $w_d,w_e,$ and $$