# Weighted Average Cost of Capital

The weighted average cost of capital (WACC) is the minimum return a company must earn on its projects. It is calculated by weighing the cost of equity and the after-tax cost of debt by their relative weights in the capital structure.

WACC is an important input in capital budgeting and business valuation. It is the discount rate used to find out the present value of cash flows in the net present value technique. It is the basic hurdle rate to which the internal rate of returns of different projects are compared to decide whether the projects are feasible. It is also used in the free cash flow valuation model to discount the free cash flow to firm (FCFF) to find a company's intrinsic value.

## Formula

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

WACC = k_{e} × | E | + k_{d} × (1 − t) × | D |

E + D | E + D |

Where,

*k _{e}* is the cost of equity,

*E*is the market value of equity,

*k*is the pre-tax cost of debt,

_{d}*t*is the tax rate,

*D*is the market value of debt, and

*E/(E + D)*and

*D/(E + D)*are the respective weights of equity and debt in the company's capital structure.

### Cost of Equity

Cost of equity is 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

After-tax cost of debt represents 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 calculated by finding the yield to maturity of the company's bonds and other loans. 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.

### Equity and Debt Weights

E/A 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.

D/A 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.

## 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.

If 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.

#### Calculating Capital Structure Weights

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.

#### Estimating Cost of Equity

We can estimate cost of equity using either the 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%

#### Estimating Cost of Debt

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%)].

#### Calculating WACC

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.

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. Further, different models for calculation of cost of equity may yield different values.

by Obaidullah Jan, ACA, CFA and last modified on

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