Capital Structure refers to the proportion of debt and equity being used to finance a firm's assets: Assets = (Debt + Equity) = Capital Structure

Capital structure affects the value of the firm. That is, the value of the firm might change with the amount of debt that is present. This would occur because the cost of financing with debt (AtRd) is normally lower than the cost of financing with equity (Rs), which means the WACC for the firm will be different at different blends of debt and equity financing (which means the value of the firm will be different at different blends of debt and equity financing)

You can see the effect in the WACC formula:

WACC = Wd(ATRd) + Ws(Rs)

If AT Rd = 6% and Rs = 12%:

At zero debt:

WACC = 0(.06) + 1.00(.12) = .12, or 12%

At 50/50 debt and equity WACC = .50(.06) + .50(.12) = .09, or 9%

Furthermore, as the amount of debt financing in a firm rises, AtRd and Rs themselves will rise, because of the increasing degree of riskiness present:

At zero debt:

WACC = 0(.06) + 1.00(.12) = .12, or 12%

At 50/50 debt and equity WACC = .50(.08) + .50(.14) = .11, or 11%

If the value of the firm varies with capital structure, then what we want to find is the optimal balance between debt and equity (if there is one) that produces the lowest WACC.

The debt level where WACC is the lowest is the same debt level where at which the firm's value is highest. You can see this effect in the PV formula: PV = FV / (1+r)^n

(as r decreases, PV increases)

The proportions of debt and equity present at this optimal point are called the Optimal Capital Structure for the firm

So why might the cost of debt & equity change as the proportions of each change on the balance sheet?

Spoiler Alert:

Answer: risk (as the proportions of debt and equity change, the riskiness of the firm's earnings changes)