How Interest Tax Shields Affect the After-Tax Cost of Debt

# Logic behind Tax Shield of debt


# Logic behind Tax Shield of debt












I don't understand the logic behind the idea of tax shield of interest payments. This question seems to support the idea of comparison behind two firms (with and without debt) to show the reduced tax expense. But all the expenses are actual cashflows and the firm with debt gets lower earnings. How is the lower tax amount a "Tax Shield" ?

This is further built into the post-tax weighted average cost of capital. There it acts to lower the debt cost further with a (1-Tax rate) component. Please help me understand this.

## Answer by João (score 1, accepted)

https://quant.stackexchange.com/a/83888

The cost of debt capital must always reflect current market conditions.

This principle must be applied to existing sources of debt financing.

- The historical cost of these sources only reflects past market conditions.

- Such information is of little importance for determining the current cost of using debt capital for the company.

We are interested in considering the after-tax cost of debt capital since, as we know, this source of financing is associated with a significant tax saving (tax shield).

Consider this:

This company is studying if it should use debt or not.

(Assuming a interest rate of 5% and a tax of 20%) we construct the income statement:

Note that:

-EBIT is not affected by the capital structure.

-Without debt, the company pays no interest; with debt (of 750), the interest amounts to 37.5.

-The tax payable depends on the capital structure: without debt it is 20; with debt (of 750) it is only 12.5.

The difference between 20 and 12.5 (7.5) in taxes results from the fact that interest is tax-deductible that is, it generates a tax saving.

In our case:

$$ \text{Taxshield} = r_d \cdot D \cdot t $$

$$ \text{Taxshield} = 0.05 \cdot 750 \cdot 0.2 = 7.5 $$

In your example:

The tax shield doesn’t mean the firm is better off in absolute profit, it just means it pays less tax.

Firm B still pays interest in cash to lenders (30,000), which is why net income is lower (56,000 vs 80,000). The shield’s benefit is relative without the deduction, Firm B’s taxes would be higher (20,000 instead of 14,000).

In a cash flow perspective (what matters in finance)

Firm A has no interest expense → all operating profit goes to equity holders after taxes.

Firm B gives part of operating profit to debt holders → less for equity holders.

But because the government “shares” part of the interest cost (through the deduction), the total amount available to debt + equity holders is higher than if interest weren’t deductible.