Tax Shield with Debt Policy
Interest on debt is tax-deductible, so borrowing lowers a company's tax bill. That yearly saving is the interest tax shield, and its present value adds to the firm's value. These notes show how to calculate it and why it explains much of the pull toward debt.
The interest tax shield explained simply
Interest on debt is tax-deductible, so borrowing lowers a company's tax bill. The yearly saving is T_c × r_D × D, and for permanent debt its present value is T_c × D. In the example, $1,000 of debt at 8% with 25% tax saves $20 a year, worth $250, so the firm's value rises from $5,000 to $5,250.
What this tax shield lesson covers
- What an interest tax shield is and where the saving comes from
- How to calculate the annual tax shield: T_c × r_D × D
- Why the PV of the tax shield on permanent debt is simply T_c × D
- How M&M Proposition I changes once corporate taxes exist
- Why firms still don't borrow 100%: financial distress costs
Tax shield formulas, explained
- T_c
- corporate tax rate
- r_D
- interest rate on debt
- D
- amount of debt
- r_D
- discount rate for the tax savings, assumed as risky as the debt
- V_L
- value of the levered firm
- V_U
- value of the same firm with no debt
How to value the interest tax shield step by step (worked example)
An all-equity firm is worth $5,000. It borrows $1,000 permanently at 8% interest. The corporate tax rate is 25%. What is the tax shield and the new firm value?
- Annual interest = 8% × $1,000 = $80.
- Annual tax shield = 25% × $80 = $20.
- PV of tax shield = $20 ÷ 0.08 = $250 (same as 25% × $1,000).
- V_L = V_U + PV(tax shield) = $5,000 + $250 = $5,250.
Answer: The debt saves $20 of tax a year, worth $250 today, so the levered firm is worth $5,250.
Benefits vs costs of borrowing more
| Benefit | Cost | |
|---|---|---|
| What it is | Interest tax shield | Risk of financial distress |
| Grows with | More debt and higher tax rates | More debt and less stable profits |
| Shows up as | Lower taxes each year | Higher borrowing costs, lost customers, bankruptcy costs |
| Leads to | A pull towards debt | A limit on debt |
Harder tax shield questions
What if the tax rate were 30%?
The yearly shield becomes 0.30 × 80 = $24, worth 0.30 × 1,000 = $300, so the firm would be worth $5,300.
Then why don't companies borrow as much as possible?
Past some point, the expected costs of financial distress (bankruptcy costs, lost customers and suppliers, managers' hands tied) outweigh the extra tax savings. The trade-off between the two is why firms aim for a target mix.
Common tax shield questions
How do you calculate the interest tax shield?
Multiply the interest expense by the corporate tax rate: tax shield = T_c × interest = T_c × r_D × D. For example, $80 of interest at a 25% tax rate saves $20 of tax that year. To value it, discount those yearly savings back to today.
Why is the tax shield discounted at the cost of debt?
In the classic textbook case the firm keeps a fixed, permanent amount of debt, so the tax savings are about as risky as the interest payments themselves. That justifies discounting at r_D. If debt is rebalanced to a target ratio, many textbooks discount at the unlevered cost of capital instead.
What is the value of a levered firm with taxes?
Under M&M with corporate taxes, a levered firm is worth the unlevered firm plus the present value of its interest tax shields. For permanent debt this simplifies to V_L = V_U + T_c × D.
Does more debt always increase firm value?
Not in the real world. Each extra dollar of debt adds tax savings, but it also raises the chance and expected cost of financial distress: lost customers, legal fees, and bad investment choices. Trade-off theory says value peaks where those costs start to outweigh the tax benefit.