## Tax and the Weighted Average Cost of Capital

##### Published: Jan 2004

Last month, we introduced the concept of the Weighted Average Cost of Capital (WACC). We explained how WACC could be calculated using the following formula:

$$WACC = \frac{D}{v} \: \times \: r_d \: + \: \frac{E}{v} \: \times \: r_e$$

Where D is the company’s outstanding debt, rd is the expected return on debt, E is the market value of the company’s issued shares, re is the expected return on equity and V is the total value of the company defined as V = D + E .

However, this formula does not acknowledge the fact that interest payments on debt instruments are tax-deductible. In order to reflect this, we need to amend the formula to reflect this.

The after-tax WACC can be calculated using the following formula:

$$WACC = 1 \: – T \:\times\:\frac{D}{v} \: \times \: r_d \: + \: \frac{E}{v} \: \times \: r_e$$

Where T is the company’s marginal tax rate, or the rate at which any rebate on interest payments are received.

#### An illustration of the impact of tax on WACC

Using the same example as last month, it is possible to identify the impact of the tax rebate on the overall WACC.

Last month, we showed that the WACC of Company X was 5.77%. Company X issued 200,000 shares now selling at 12.25 a share and has \$1.75m of outstanding debt. Its average cost of borrowing is 4.75% and the shares are currently offering a return of 6.5%. If its marginal tax rate is 30%, what is the effect on WACC if that is included in the calculation?

$$WACC = 1 \: – T\:\times \:\frac{D}{v} \: \times \: r_d \: + \: \frac{E}{v} \: \times \: r_e$$

$$WACC = 1 \: – 0.3\: \times \:\frac{1.75}{4.2} \: \times \: 0.0475 \: + \: \frac{2.45}{4.2} \: \times \: 0.065 = 0.05177 \: or \: 5.177\%$$

This shows how the tax-deductibility of interest payments lowers the cost of debt and therefore the WACC.

#### Expanding the WACC equation

The model we have examined also assumes two sources of finance – debt and equity. However, it is likely that the company will have a range of alternative sources of finance. Each of these sources will offer different expected returns to the investors. It is possible to accommodate these in the WACC calculation. For example, if Company X had issued preferred stock in addition to equity, the WACC formula could be amended to read:

$$WACC = 1 \: – T\:\times \:\frac{D}{v} \: \times \: r_d\:+\:\frac{P}{V}\times r_p \: + \: \frac{E}{v} \: \times \: r_e$$

Where P is the value of the company’s preferred stock and r p is the expected return on this stock. This equation can be expanded to cope with any number of different financing instruments. It is important to remember, though, that any instrument for which interest is taxdeductible should be multiplied by (1 T ) and all additional instruments should be incorporated in the company’s value (V ). For instance, in this example, V is now equal to D + E + P .

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