###### Pricing and Valuation of Interest Rate ...

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A company’s cost of capital is the overall required rate of return of a company’s suppliers of capital, estimated using the company’s weighted average required rates of return for the different sources of capital.

For a company with creditors and common shareholders, WACC is expressed as:

$$\text{WACC}=\frac{\text{MVD}}{\text{MVD}+\text{MVCE}}\text{r}_{d}(1-\text{Tax rate})+\frac{MVCE}{\text{MVD}+\text{MVCE}}\text{r}$$

Where:

\(\text{MVD}=\) Market value of debt.

\(\text{MVCE}=\) Market value of common equity.

\(\text{r}_{\text{d}}(1-\text{Tax rate})=\) After-tax required rate of return on debt.

\(\text{r}=\) Required rate of return on common equity.

It is more appropriate to use a company’s marginal tax rate rather than its current effective tax rate because the effective tax rate can reflect nonrecurring items. A cost of capital based on the marginal tax rate usually better reflects a company’s future costs in raising funds.

A company’s current capital structure may differ substantially from what it will be in the future. For this reason, analysts use target weights instead of using current market value weights when calculating WACC. Target weights provide a good approximation of the WACC in cases where the company’s current weights mispresent its normal capital structure.

The before-tax required rate of return on debt is estimated using the expected Yield to Maturity of the company’s debt based on current market values.

Consider the following inputs for estimating the cost of capital (all dollar values in $ million):

$$\small{\begin{array}{l|r}\text{Book value of the company’s common stock} & $10 \\ \hline\text{Market value of the company’s common stock} & $15 \\ \hline\text{Book value of the company’s debt} & $20 \\ \hline\text{The market value of the company’s debt} & $25 \\ \hline\text{The required rate of return on equity} & 7\% \\ \hline \text{The required rate of return on debt} & 3.50\% \\ \hline\text{Tax rate} & 25\% \\\end{array}}$$

The WACC is *closest* to:

$$\begin{align*}\text{Weight of debt in the capital structure}&=\frac{\text{MVD}}{\text{MVD}+\text{MVCE}}\\&=\frac{25}{25+25}=0.625\end{align*}$$

$$\begin{align*}\text{Weight of equity in the capital structure}&=\frac{\text{MVD}}{\text{MVD}+\text{MVCE}}\\&=\frac{15}{25+15}=0.375\end{align*}$$

$$\text{WACC}=0.625\times(1-0.25)\times3.50\%+(0.375\times7\%)=4.27\%$$

## Question

Which of the following required rates of return would be

most appropriatewhen estimating the total value of a firm with both debt and equity in its capital structure?

- Rate of return on equity.
- Rate of return on debt.
- Weighted average cost of capital.
## Solution

The correct answer is C.The weighted average cost of capital is the rate of return that is used to discount a firm’s cash flow to arrive at its value when it has both debt and equity in its capital structure.

A is incorrect.The rate of return on equity is used to estimate the value of equity for a firm.

B is incorrect.The rate of return on debt is used to estimate the payment amount the firm makes on its debt

Reading 21: Return Concepts

*LOS 21 (g) Explain and calculate the weighted average cost of capital for a company.*