% This is lecture no. 7 of BU8201/: Business Finance.

\chapter{The Cost of Capital}%
\label{cha:the_cost_of_capital}

A firm's primary objective is to maximize its shareholder's value.
The principle way value is increased is by investing in projects that earn more than their cost of capital.

\section{The Weighted Average Cost of Capital}%
\label{sec:the_weighted_average_cost_of_capital_wacc_}

When deciding what to invest money into (projects, etc.) a company will have to compare the future cash flows of this investment against its cost.
But the oversight here is to assume that so long as the future cash flows outweigh the upfront cost of capital that the investment is worth venturing into.

\bigbreak

The future cash flows must also be compared against the WACC, which describes how the capital can otherwise be used to earn interest in other ways.
The WACC considers three capital components that are investor-supplied items: debt, preferred stock, and common equity.
The cost of each component is called its component cost.
These costs are then combined to form a WACC, which is used in the firm's capital budgeting analysis.

\bigbreak

The target proportions of debt, preferred stock, and common equity, along with the costs of those components, are used to calculate the firm's weighted average cost of capital (WACC):

\[
	\textit{WACC} = w_dr_d(1-T) + w_pr_p + w_cr_s
.\]

\subsection{Cost of Debt, $r_d(1-T)$}%
\label{sub:cost_of_debt_r_d_1_t_}

\begin{definition}
	Before-tax Cost of Debt.
	This is the interest rate a firm must pay on its new debt.
	Firms can estimate this value by asking their bankers what it will cost to borrow or by finding the yield to maturity on their currently outstanding debt.
\end{definition}

However, the after-tax cost of debt, should be used to calculate the weighted average cost of capital:
\begin{align*}
	\text{After-tax cost of debt} & = \text{Interest rate on new debt} - \text{Tax savings}\\
				      & = r_d-r_dT\\
				      & = r_d(1-T)
\end{align*}

In effect the government pays part of the cost of debt because interest is tax deductible.
Therefore if a company can borrow at an interest rate of 10\%, and it's tax rate is 40\%, its after tax cost of debt will be 6\%.

The cost of debt is the interest rate on new debt, not outstanding debt because the primary concern with the cost of capital is its use in capital budgeting decisions.

We can find $r_d$ using the equation found in subsection \ref{sub:measuring_yield} of lecture \ref{cha:bonds_&_their_valuation}.

\subsection{Cost of Preferred Stock, $r_p$}%
\label{sub:cost_of_preferred_stock_r_p_}

The component cost of preferred stock, $r_p$, used to calculate the WACC is the preferred dividend, $D_p$, divided by the current price of the preferred stock, $P_p$:
\[
r_p = \frac{D_p}{P_p}
.\]

\subsection{Cost of Retained Earnings, $r_s$}%
\label{sub:cost_of_retained_earnings_r_s_}

\begin{definition}
	Cost of Retained Earnings, $r_s$.
	The rate of return required by stockholders on a firm's common stock.
\end{definition}
The cost of common equity is based on the rate of return that investors require on the company's common stock.

\bigbreak
\noindent
New common equity is raised in two ways:
\begin{enumerate}
	\item By retaining some of the current year's earnings.
	\item By issuing new common stock.
\end{enumerate}

We use the symbol $r_s$ to designate the cost retained earnings and $r_e$ to designate the cost of new common stock, or external equity.

\begin{definition}
	Cost of New Common Stock, $r_e$.
	The cost of external equity based on the cost of retained earnings, but increased for flotation costs necessary to issue new common stock.
\end{definition}

The reason new common equity has to be factored into the WACC calculation is due to the fact that it represents the opportunity cost that stockholders could have received the earnings as dividends and invested that money in other stocks.

The firm needs to earn at least as much on any earnings retained as the stockholders could earn on alternative investments of comparable risk.
If the firm cannot invest retained earnings to earn at least the required rate of return, it should pay those funds to its stockholders and let them invest directly in stocks or other assets that will provide that return.

To calculate this value for required rate of return, we must recall that if a stock is in equilibrium, its required rate of return must be equal to its expected rate of return.
From previous chapters we derive the following equation:
\begin{align*}
	r_s = r_{RF} + RP & = \frac{D_1}{P_0} + g = \hat{r}_s\\
	\text{Required rate of return} & = \text{Expected rate of return}
\end{align*}
The left term is based on the CAPM model, and the right term is based on the discounted dividend model.

\subsection{Cost of New Common Stock, $r_e$}%
\label{sub:cost_of_new_common_stock_r_e_}

The cost of new common stock, $r_e$ is not the same as the cost of retained earnings even though they both measure the cost of new common equity.
This is due to the fact that new common stock has to account for flotation cost.

\begin{definition}
	Flotation Cost.
	Flotation cost is the percentage cost of issuing new common stock.
\end{definition}

If there are flotation costs, the issuing firm receives only a portion of the capital provided by investors, with the remainder going to the underwriter.
To provide investors with their required rate of return on the capital they contributed, each dollar the firm actually receives must work harder.
Each dollar must earn a higher rate of return than the investors' required rate of return.

\bigbreak
For example, suppose investors require a 13.7\% return on their investment, but flotation costs represent 10\% of the funds raised.
Therefore, the firm actually keeps and invests only 90\% of the amount that investors supplied.
In that case, the firm must earn about 14.3\% on the available funds in order to provide investors with a 13.7\% return on their investment.

\bigbreak
\noindent
The DCF approach can be used to estimate the effects of flotation costs:
\[
	r_e = \frac{D_1}{P_0(1-F)} + g
.\]
Here $F$ is the flotation cost required to sell the new stock, so $P_0(1-F)$ is the net price per share received by the company.

The flotation cost adjustment can be calculated as such:
\[
	\text{Flotation cost adjustment} = \text{Adjusted DCF cost} - \text{Pure DCF cost}
.\]

Note that $r_e$ and $r_s$ are mutually exclusive in determining the value of the WACC.
\newpage

\section{Factors that Affect the WACC}%
\label{sec:factors_that_affect_the_wacc}

\subsection{Factors the firm cannot control}%
\label{sub:factors_the_firm_cannot_control}

The three most important factors that the firm cannot directly control are:
\begin{enumerate}
	\item Interest rates in the economy.
	\item The general level of stock prices.
	\item Tax rates.
\end{enumerate}

If interest rates in the economy rise, the cost of debt increases because the firm must pay bondholders more when it borrows.

\bigbreak
Similarly, if stock prices in general decline, pulling the firm’s stock price down, its cost of equity will rise.
Also, because tax rates are used in the calculation of the component cost of debt, they have an important effect on the firm’s cost of capital.

\bigbreak
Taxes also affect the cost of capital in other less apparent ways.
For example, when tax rates on dividends and capital gains were lowered relative to rates on interest income, stocks became relatively more attractive than debt; consequently, the cost of equity and WACC declined.

\subsection{Factors the firm can control}%
\label{sub:factors_the_firm_can_control}

A firm can directly affect its cost of capital in three primary ways:
\begin{enumerate}
	\item By changing its capital structure
	\item By changing its dividend payout ratio
	\item By altering its capital budgeting decision rules to accept projects with more or less risk than projects previously undertaken.
\end{enumerate}

\section{Adjusting the Cost of Capital for Risk}%
\label{sec:adjusting_the_cost_of_capital_for_risk}

Projects should be accepted if and only if their estimated returns exceed their costs of capital.
Thus, the cost of capital is a `hurdle rate'.
A project’s expected rate of return must “jump the hurdle” for it to be accepted.

\bigbreak
Moreover, investors require higher returns on riskier investments.
Consequently, companies that are raising capital to take on risky projects will have higher costs of capital than companies that are investing in safer projects.

\bigbreak
Therefore, each project’s hurdle rate should reflect the risk of the project, not the risk associated with the firm’s average project as reflected in its composite WACC.
