**FORMULA AND DERIVATION**

\[WACC=\frac{\left(r_d\times D\right)+\left(r_e\times E\right)}{D+E}\]

Where,

\(r_d\) is the net cost of debt

\(D\) is the market value of debt

\(r_e\) is the cost of equity

\(E\) is the market value of equity

Cost of debt refers to the overall return that a company provides to all its debt holders. The cost of debt of a company depends generally on its credit worthiness expressed as a credit rating. A lower credit ranking will be assigned to companies that have a very low asset cover or interest cover, high level of gearing, high beta resulting in high volatility of profits. And thus, a company with a low credit ranking will require to pay out more to its debt holders for the higher risk assumed by them. On the other hand, a company with high credit rank would have a relatively low cost of debt.

Cost of debt (interest paid to debt holders) can be deducted from pre-tax profits, which means a company can reduce its tax liability by deducting interest cost from its profits before tax. Thus, the net cost of debt is considered instead of gross cost of debt.

\[Net\ cost\ of\ debt=gross\ cost\ of\ debt\times (1-tax\ rate)\]

Cost of equity refers to the return that the company provides to its shareholders. Cost of equity is generally higher than a company’s cost of debt, to represent the higher returns expected by shareholders to compensate for the higher amount of risks assumed by them. Cost of equity for a company can be determined by various models like the Capital Asset Pricing Model (CAPM), Gordon model etc.

**EXAMPLES**

Example 1

A company has a total debt of \(\$1000000\) (market value). The gross redemption yield available on its debt instruments is \(10\%\) . The company pays taxes on its profits at the rate of \(30\%\). The market value of the company’s equity is \(\$1000000\). The shareholders expect a risk premium of \(5\%\) over the yield available to the debt holders. The company needs to know the rate of return that it has to generate from its existing portfolio of projects to be able to provide sufficient returns to its investors.

The return that the company has to generate must be equal to its WACC (or greater).

In this case,

Gross cost of debt = \(10\%\)

Net cost of debt = \(10\%\times \left(1-30\%\right)=0.07=7\%\)

Cost of equity= \(10\%+5\%=15\%\)

Thus,

\[WACC=\frac{\left(0.07\times 1000000\right)+\left(0.15\times 1000000\right)}{1000000+1000000}\]
\[WACC=\frac{70000+150000}{2000000}\]
\[WACC=0.11=11\%\]

This means that the company has to generate \(11\%\) return on its investment (projects) to provide sufficient return to its investors.

Example 2

A company’s total equity is valued at \(\$100000\) and the cost of equity is \(12\%\). Its total debt is \(\$100000\) and the net cost of debt is \(8\%\). The company needs to ascertain its WACC.

\[WACC=\frac{\left(0.08\times 100000\right)+\left(0.12\times 100000\right)}{100000+100000}\]
\[WACC=\frac{8000+12000}{200000}\]
\[WACC=0.1=10\%\]

Example 3

Consider the same company in example 1. The company is planning to obtain \(\$100000\) more debt at the same cost. It wants to know what the WACC be, if it does so.

The total debt would be \(\$100000+\$100000=\$200000\) .

So,

\[WACC=\frac{\left(0.08\times 200000\right)+\left(0.12\times 100000\right)}{200000+100000}\]
\[WACC=\frac{16000+12000}{300000}\]
\[WACC=0.0933=9.3\%\]