## Cost of Capital Formula

The formula for calculating the cost of capital is typically represented as the Weighted Average Cost of Capital (WACC). The WACC is the average rate of return a company is expected to provide to all its different investors: the holders of its debt, equity, and preferred equity.

Here is the formula for WACC:

\(\text{WACC} = \frac{E}{V} \cdot r_e + \frac{D}{V} \cdot r_d \cdot (1 – \text{T}_c) \)

Where:

- E is the market value of the company’s equity
- D is the market value of the company’s debt
- V is the total market value of equity and debt (E + D)
- R
_{e}is the cost of equity (which can be calculated using different models, such as the Capital Asset Pricing Model (CAPM)) - R
_{d}is the cost of debt (the yield to maturity on the company’s debt) - T
_{c}is the corporate tax rate

In this formula, E/V represents the proportion of company financing that comes from equity, and D/V represents the proportion that comes from debt. The cost of equity is typically higher than the cost of debt, reflecting the higher risk borne by equity investors. The term Rd * (1 – Tc) represents the after-tax cost of debt, as interest payments are often tax-deductible.

Please note that the calculation of WACC requires a number of assumptions and estimates, such as the risk-free rate, the company’s beta (in the CAPM), and the company’s tax rate, among others. As such, it should be used as a guide and not a definitive measure of a company’s cost of capital.

## Example of Cost of Capital Formula

Let’s consider a hypothetical company, we’ll call it Alpha Corporation.

Let’s assume the following:

- Alpha Corporation has a market value of equity (E) of $10 million.
- It has a market value of debt (D) of $5 million.
- The cost of equity (R
_{e}) for Alpha is 12%. - The cost of debt before tax (R
_{d}) is 7%. - The corporate tax rate (T
_{c}) is 25%.

The total market value of Alpha’s equity and debt (V) is $10 million (E) + $5 million (D) = $15 million.

We can plug these values into the WACC formula:

\(\text{WACC} = \frac{E}{V} \cdot r_e + \frac{D}{V} \cdot r_d \cdot (1 – \text{T}_c) \)

Substituting in the values:

\(\text{WACC} = \frac{\text{\$10 million}}{\text{\$15 million}} \cdot \text{12%} + \frac{\text{\$5 million}}{\text{\$15 million}} \cdot \text{7%} \cdot (1 – \text{25%}) \)

This gives:

\(\text{WACC} = (0.67 \cdot \text{12%}) + (0.33 \cdot \text{7%} \cdot 0.75) \)

\(\text{WACC} = \text{8% + 1.75% = 9.75%} \)

So, in this example, Alpha Corporation’s weighted average cost of capital (WACC) is 9.75%. This means that Alpha must strive to earn a return on its invested capital that is greater than 9.75% in order to create value for its investors. If it earns less than this, it would be destroying value because it’s not meeting the return expectations of its debt and equity holders.