# Weighted average cost of capital

(WACC).

Weighted average cost of capital is used as:

- a discount rate in net present value analysis and
- a hurdle rate in internal rate of return analysis.

The WACC is the average cost of capital of a firm, taking into account:

(1) All sources of capital

(2) Weighted by their current market values.

## WACC calculations

For a firm with both equity and debt capital, the WACC would be calculated as:

WACC = Ke x *proportion of equity* + Kd(1-t) x *proportion of debt*

= Ke x E/(D + E) + Kd(1 - t) x D/(D + E)

*Where:*

Ke = cost of equity.

Kd(1 -t) = after-tax cost of debt.

E = market value of equity.

D = market value of debt.

**Example 1: Equal equity and debt**

Where:

Ke = cost of equity = 10%

Kd(1-t) = after-tax cost of debt = 3.6%

E = market value of equity = $100m

D = market value of debt = $100m

WACC = Ke x E/(D + E) + Kd(1 - t) x D/(D + E)

= 10 x 100/(100 + 100) + 3.6 x 100/(100 + 100)

= 10 x 100/200 + 3.6 x 100/200

= 10 x 1/2 + 3.6 x 1/2

= 5 + 1.8

= **6.8%**

This weighted average is exactly mid-way between the cost of equity (10%) and the after-tax cost of debt (3.6%), because the proportions of equity and debt are exactly equal in this first example.

**Example 2: Increasing equity, reducing debt**

Making a number of simplifying assumptions, if the proportion of equity were increased to 75% (= 0.75), the proportion of debt would fall to 25% and the WACC might theoretically increase to:

= 10 x 0.75 + 3.6 x 0.25

= 7.5 + 0.9

= **8.4%**

**Example 3: Reducing equity, increasing debt**

If the firm was 'geared up' to reduce the proportion of equity to 25%, and increase the proportion of debt to 75%, again simplifying, the WACC might in theory fall to:

= 10 x 0.25 + 3.6 x 0.75

= 2.5 + 2.7

= **5.2%**

However, the simplified second and third calculations above ignore the change in the *risk* to shareholders and to debt holders when the firm's capital structure is changed in this way.

In practice both the cost of equity and the cost of debt would normally change, following the change in capital structure, leading to a more complex analysis.

In order to create or add shareholder value, the managers of this firm would need to earn:

- An after-tax rate of return on their investment projects

- Of
__more than__the WACC - of, for example in Example 1 above, 6.8%.

## See also

- Adverse selection
- Capital management
- CertICM
- Cost of capital
- Cost of debt
- Cost of equity
- Discount rate
- Economic value added
- Hurdle rate
- Internal rate of return
- Net present value
- Opportunity cost
- Optimal capital structure
- Shareholder value