Optimal Capital Structure
“Why don’t companies just borrow more, if debt is cheaper?” This is the model that answers it. Step leverage up and three things happen at once: interest coverage falls, so the credit rating deteriorates and the spread widens; the tax shield eventually runs out of profit to shield; and the levered beta climbs, dragging the cost of equity with it. Somewhere in there the cost of capital bottoms out.
Built on the Damodaran cost-of-capital framework, including the circular rating solve — the rate sets the rating and the rating sets the rate.
The optimum has run past where the ladder can be trusted. A synthetic rating is fitted on companies that mostly sit at moderate leverage, so above roughly 65% debt it is extrapolating spreads nobody has observed. The model will happily tell you to borrow enormously, because the only thing stopping it is how fast the spreads widen. Steepen the spread multiplier below and watch the answer move — if the optimum is that sensitive to an assumption you cannot source, the honest output is a range, not a number.
The company
Cost of capital inputs
Relevering is what drives the curve. Beta Refresher walks the mechanics.
Cost of capital across the range
Cost of equity climbs steadily as leverage raises the levered beta. After-tax debt is cheaper but steps up each time the rating drops. WACC is the weighted blend, and its lowest point is the answer.
| D/(D+E) | D/E | Cover | Rating | Rate | Tax eff. | Kd post-tax | Beta | Ke | WACC |
|---|---|---|---|---|---|---|---|---|---|
| 0% | 0.00 | ∞ | AAA | 2.45% | 30.0% | 1.71% | 0.32 | 5.70% | 5.700% |
| 5% | 0.05 | 75.91x | AAA | 2.45% | 30.0% | 1.71% | 0.33 | 5.76% | 5.557% |
| 10% | 0.11 | 37.96x | AAA | 2.45% | 30.0% | 1.71% | 0.34 | 5.82% | 5.413% |
| 15% | 0.18 | 25.30x | AAA | 2.45% | 30.0% | 1.71% | 0.36 | 5.90% | 5.270% |
| 20% | 0.25 | 18.98x | AAA | 2.45% | 30.0% | 1.71% | 0.38 | 5.98% | 5.127% |
| 25% | 0.33 | 15.18x | AAA | 2.45% | 30.0% | 1.71% | 0.39 | 6.07% | 4.984% |
| 30% | 0.43 | 12.65x | AAA | 2.45% | 30.0% | 1.71% | 0.42 | 6.18% | 4.840% |
| 35% | 0.54 | 10.84x | AAA | 2.45% | 30.0% | 1.71% | 0.44 | 6.30% | 4.697% |
| 40% | 0.67 | 8.45x | AA | 2.75% | 30.0% | 1.93% | 0.47 | 6.45% | 4.638% |
| 45% | 0.82 | 7.51x | AA | 2.75% | 30.0% | 1.93% | 0.50 | 6.62% | 4.505% |
| 50% | 1.00 | 6.10x | A+ | 3.05% | 30.0% | 2.13% | 0.54 | 6.82% | 4.477% |
| 55% | 1.22 | 5.20x | A | 3.25% | 30.0% | 2.27% | 0.59 | 7.07% | 4.432% |
| 60% | 1.50 | 4.77x | A | 3.25% | 30.0% | 2.27% | 0.66 | 7.38% | 4.317% |
| 65% | 1.86 | 4.40x | A | 3.25% | 30.0% | 2.27% | 0.74 | 7.78% | 4.202% |
| 70% | 2.33 | 3.80x | A− | 3.50% | 30.0% | 2.45% | 0.84 | 8.31% | 4.209% |
| 75% | 3.00 | 3.54x | A− | 3.50% | 30.0% | 2.45% | 0.99 | 9.06% | 4.103% |
| 80% | 4.00 | 3.32x | A− | 3.50% | 30.0% | 2.45% | 1.22 | 10.18% | 3.996% |
| 85% | 5.67 | 3.13x | A− | 3.50% | 30.0% | 2.45% | 1.59 | 12.05% | 3.889% |
| 90% | 9.00 | 2.76x | BBB | 3.75% | 30.0% | 2.63% | 2.34 | 15.78% | 3.940% |
Once interest expense exceeds EBIT there is not enough profit left to shield, so extra borrowing stops buying a tax benefit while still buying risk. This one mechanic is what bends the curve upward.
Crossing BBB to BB is not one more notch of spread. Many institutional mandates cannot hold sub-investment-grade paper at all, so the buyer base thins out and the spread gaps rather than steps.
Discounting the same cash flows at 3.89% instead of 5.30% raises a perpetuity by this much. It is the number that turns a financing observation into a recommendation.
Why this model is circular, and what that means
The interest rate depends on the credit rating. The rating depends on interest coverage. Coverage depends on the interest expense, which depends on the rate. The model chases its own tail, and in Excel this is exactly what iterative calculation exists for — the original workbook carries an “interest rate difference must be zero” row purely to prove the loop settled.
Here it is solved to a fixed point directly. Worth knowing what a failure to settle means: it is not an arithmetic problem, it is coverage sitting exactly on a rung boundary, where a rounding difference flips the rating and the rate jumps. The agencies would be arguing about that company too.
- 1Guess a rate
- 2Interest = debt × rate
- 3Coverage = EBIT ÷ interest
- 4Rating = coverage on the ladder
- 5Rate = base + that rating’s spread
- 6Different from the guess? Go to 2.
Share your result ⚖️
Instagram and TikTok have no desktop share link, so copy the caption and paste it into the app.