# Weighted Average Cost of Capital

Weighted average cost of capital (WACC) is the average of the minimum after-tax required rate of return which a company must earn for all of its security holders (i.e. common stock-holders, preferred stock-holders and debt-holders). It is calculated by finding out cost of each component of a company’s capital structure, multiplying it with the relevant proportion of the component to total capital and then summing up the proportionate cost of components. WACC is a very useful tool because it tells whether a particular project is increasing shareholders’ wealth or just compensating the cost.

## Formula

For a company which has two sources of finance, namely equity and debt, WACC is calculated using the following formula:

WACC = r(E) × w(E) + r(D) × (1 – t) × w(D)

### Cost of equity

In the formula for WACC, r(E) is the cost of equity i.e. the required rate of return on common stock of the company. It is the minimum rate of return which a company must earn to keep its common stock price from falling. Cost of equity is estimated using different models, such as dividend discount model (DDM) and capital asset pricing model (CAPM).

### After-tax cost of debt

In the WACC formula, r(D) × (1 – t) represents the after-tax cost of debt i.e. the after-tax rate of return which the debt-holders need to earn till the maturity of the debt. Cost of debt of a company is based on the yield to maturity of the relevant instruments. If no yield to maturity is available, the cost can be estimated using the instrument's current yield, etc. After-tax cost of debt is included in the calculation of WACC because debt offers a tax shield i.e. interest expense on debt reduces taxes. This reduction in taxes is reflected in reduction in cost of debt capital.

### Weights

*w(E)* is the weight of equity in the company’s total capital. It is calculated by dividing the market value of the company’s equity by sum of the market values of equity and debt.

*w(D)* is the weight of debt component in the company’s capital structure. It is calculated by dividing the market value of the company’s debt by sum of the market values of equity and debt.

Ideally, WACC should be estimated using target capital structure, which is the capital structure the company’s management intends to maintain in the long-run. For practical purposes, market values are usually used and where the market values are not available, book values may be used to find out the weight.

## Example

Sanstreet, Inc. went public by issuing 1 million shares of common stock @ $25 per share. The shares are currently trading at $30 per share. Current risk free rate is 4%, market risk premium is 8% and the company has a beta coefficient of 1.2.

During last year, it issued 50,000 bonds of $1,000 par paying 10% coupon annually maturing in 20 years. The bonds are currently trading at $950.

The tax rate is 30%. Calculate the weighted average cost of capital.

### Solution:

First we need to calculate the proportion of equity and debt in Sanstreet, Inc. capital structure.

Current Market Value of Equity = 1,000,000 × $30 = $30,000,000

Current Market Value of Debt = 50,000 × $950 = $47,500,000

Total Market Value of Debt and Equity = $77,500,000

Weight of Equity = $30,000,000 / $77,500,000 = 38.71%

Weight of Debt = $47,500,000 / $77,500,000 = 61.29%, or

Weight of Debt = 100% minus cost of equity = 100% − 38.71% = 61.29%

Now, we need estimates for cost of equity and after-tax cost of debt.

We can estimate cost of equity using either dividend discount model (DDM) or capital asset pricing model (CAPM).

Cost of equity (DDM) = expected dividend in 1 year /current stock price + growth rate

Cost of equity (CAPM) = risk free rate + beta coefficient × market risk premium

In the current example, the data available allow us to use only CAPM to calculate cost of equity.

Cost of Equity = Risk Free Rate + Beta × Market Risk Premium = 4% + 1.2 × 8% = 13.6%

Cost of debt is equal to the yield to maturity of the bonds. With the given data, we can find that yield to maturity is 10.61%. It is calculated using hit and trial method. We can also estimate it using MS Excel RATE function.

For inclusion in WACC, we need after-tax cost of debt, which is 7.427% [= 10.61% × (1 − 30%)].

Having all the necessary inputs, we can plug the values in the WACC formula to get an estimate of 9.82%.

WACC = 38.71% × 13.6% + 61.29% × 7.427% = 9.8166%

It is called weighted average cost of capital because as you see the cost of different components is weighted according to their proportion in the capital structure and then summed up.

### Importance of WACC

Weighted average cost of capital is the discount rate used in calculation of net present value (NPV) and other valuations models such as free cash flow valuation model. It is the hurdle rate in the capital budgeting decisions.

WACC represents the average risk faced by the organization. It would require an upward adjustment if it has to be used to calculate NPV of projects which are riskier than the company's average projects and a downward adjustment in case of less risky projects. Further, WACC is after all an estimation. Different models for calculation of cost of equity may yield different values.

Written by Obaidullah Jan, ACA, CFA