An infrastructure company's cost of debt rises with leverage. Compute its WACC at four debt levels and find where it is lowest.

WACC is 11.80% with no debt, 11.36% at 20%, 11.52% at 40% and 12.73% at 60%, so the lowest is at 20% debt. Relevering the 0.8 beta takes the cost of equity from 11.8% to 12.7%, 14.2% and 17.2%, while after-tax debt costs 6%, 7.5% and 9.75%. The tax shield wins at 20%; beyond that, dearer debt and dearer equity outrun it, and the firm is worth most, about Rs 2,641 crore, at the 20% point.

Two people buy the same flat; one pays cash, the other borrows 80% of the price. The second owner's return on the money they put in swings far more with every change in the flat's value. Leverage makes equity riskier, so the equity beta rises with debt: relevering Achalvi's 0.8 unlevered beta with the formula beta times (1 + (1 less tax) times debt over equity) gives 0.95 at 20% debt, 1.2 at 40% and 1.7 at 60%. With a 7% risk-free rate and a 6% premium the cost of equity goes from 11.8% to 12.7%, 14.2% and 17.2%. That is the half of the story candidates forget: they hold the cost of equity at 11.8% and conclude that debt is always cheaper.

Lay the four cases side by side. At 20% debt the after-tax cost of 6% is cheap enough to pull WACC down to 11.36% even though equity now costs 12.7%; at 40% the coupon jumps to 10% and equity to 14.2%, and WACC is back up to 11.52%; at 60% it is 12.73%, above the all-equity case. Firm value, EBIT after tax of Rs 300 crore capitalised at each WACC, peaks at Rs 2,641 crore at 20% debt against Rs 2,542 crore with no debt and Rs 2,357 crore at 60%. The turn happens because the lenders' step from 8% to 10% is a signal about default risk that the levered betaThe equity beta of a company after adjusting for its debt; it rises with leverage because debt makes equity returns more volatile. formula is also picking up on the equity side.

Give the number and its limits. On these inputs the board should sit near 20% debt, around Rs 528 crore, where WACC is lowest and the firm is worth most; the difference between 20% and 40% is small, 0.16 points of WACC, so the real decision is to stay below the point where lenders reprice. What the exercise leaves out matters as much. The lenders' quotes are the market's view of default risk at each level, so the curve is really a curve of credit ratings; a toll road with contracted revenue can carry more than 20% in practice because its cash flows are steadier than a 0.8 beta implies. The formula also assumes the structure is held constant, that the tax shield is always usable, and that there are no costs of financial distress beyond the coupon. The limit: four points do not make a curve, and the true minimum may sit anywhere between 20% and 40%; the answer is a region, not a number.