Debt and Taxes

The tax shield

In the US (and most of the world), interest expense is deductible from corporate income for tax purposes. Dividends are not. This gives debt-financed firms a tax advantage that all-equity firms don’t have.

Consider $1M of interest expense at a 25% corporate tax rate:

• All-equity firm: pays $1M to equity. No tax saving.
• Levered firm: pays $1M to debt holders, deducts it from taxable income, saves $0.25M in taxes. Net cost to firm: $0.75M.

The $0.25M in tax savings is the interest tax shield. Over the life of the debt, these annual savings accumulate.

PV of the tax shield (perpetuity case)

If a firm holds $D$ of debt at rate $r_D$ permanently, annual interest is $r_D \cdot D$ and annual tax savings are $t \cdot r_D \cdot D$, where $t$ is the corporate tax rate.

Discounted at $r_D$ as a perpetuity:

$$PV(\text{tax shield}) = \frac{t \cdot r_D \cdot D}{r_D} = t \cdot D.$$

So the PV of the tax shield is simply $t \cdot D$.

MM with corporate taxes

Add this to MM I:

$$V_L = V_U + t \cdot D.$$

Firm value grows linearly with debt. If $t = 0.25$ and you add $300M of permanent debt, you add $75M of tax-shield value to the firm.

Pushed to its logical conclusion, this says firms should be 100% debt-financed. Empirically they aren’t, of course — financial distress costs (next lesson) push back. But MM-with-taxes is the right starting baseline.

WACC with taxes

Re-derive WACC including the deductibility:

$$\text{WACC} = \frac{E}{V} r_E + \frac{D}{V} r_D (1 - t).$$

The $(1 - t)$ on the debt side is exactly the tax shield showing up. As debt rises (and equity falls), the weighted average tips toward the cheaper (tax-adjusted) debt rate. WACC declines with leverage — at least until distress costs kick in.

Play with it

Unlevered cost of equity: 10.0%Risk-free debt rate: 5.00%Corporate tax rate: 21%Distress sensitivity α: 0.50

Optimal D/V ≈ 80%, min WACC ≈ 8.32%

With no taxes or distress (MM I), WACC is flat across leverage. Add a tax shield (raise tax rate) and WACC slopes down with D/V. Add distress costs (raise α) and WACC bends back up — the trade-off theory of capital structure.

Slide the tax rate from 0 to 0.5. Watch WACC bend downward more sharply at higher tax rates. Now drop the distress sensitivity to 0 — WACC declines monotonically with $D/V$, just as MM-with-taxes predicts. Then raise distress sensitivity above 1 — WACC bends back up at high leverage, hinting at the optimal capital structure (next lesson).

A worked numerical example

Same firm from the prior lesson: $r_U = 12\%$, perpetual EBIT $100M. Add a 25% corporate tax rate.

Unlevered value:

$$V_U = \frac{100 \times (1 - 0.25)}{0.12} = \frac{75}{0.12} = \$625\text{M}.$$

(After-tax cash flows are smaller; value drops by 25%.)

Now issue $300M of perpetual debt at 5%. Tax-shield value:

$$PV(\text{TS}) = 0.25 \times 300 = \$75\text{M}.$$

Levered firm value:

$$V_L = 625 + 75 = \$700\text{M}.$$

The capital structure decision added $75M to firm value. Equity holders get most of it (because debt holders just earn $r_D$ on their face value).

How big is the tax shield, really?

For a typical US firm:

• Average leverage ratio (D/V) ~ 30%.
• Corporate tax rate ~ 21% (post-TCJA, pre-any reform).
• So tax-shield value as a fraction of firm value is ~ 0.21 × 0.30 = ~6% of firm value.

That’s not nothing — for a $10B firm, it’s $600M of value. But it’s also not enormous, which is why the full capital-structure story has to include distress costs and other frictions, not just tax shields.

What the model misses

MM-with-taxes is the model that says “more debt is always better.” Empirically:

1. Firms don’t lever to 100% — distress costs and agency costs matter, not just taxes.
2. Firms with low effective tax rates (NOLs, R&D credits) have smaller tax shields and indeed carry less debt.
3. Personal taxes complicate the picture. Miller (1977) extended MM to account for differential personal tax treatment of debt vs equity returns; the result is that the corporate-only tax- shield calc somewhat overstates the benefit.

Each of these adds nuance. The simple $t \cdot D$ formula remains the right starting point.

What’s next

The next lesson adds the cost side: financial distress. Together, the two sides produce the trade-off theory — the workhorse positive theory of capital structure.