Weighted average cost of capital (`coc.wacc`)¶

Returns the weighted average cost of capital (WACC) from the cost of equity, the pre-tax cost of debt, the tax rate of the tax shield and the target capital structure. The structure is given either as a debt-to-equity ratio D/E or as a debt weight D/(D + E). The result is the discount rate of dcf.fcff.

Formula¶

\[ WACC = \frac{E}{V}\, k_e + \frac{D}{V}\, k_d \,(1 - t), \qquad \frac{D}{V} = \frac{D/E}{1 + D/E}, \qquad \frac{E}{V} = 1 - \frac{D}{V} \]

where \(V = D + E\), \(k_e\) is the cost of equity (see coc.cost_of_equity), \(k_d\) the pre-tax cost of debt (see coc.cost_of_debt) and \(t\) the tax rate of the tax shield. All rates are annual effective rates, decimal fractions.

Example¶

from decimal import Decimal

import fairmark as fm

# Target debt weight 30%: 0.7 × 0.10 + 0.3 × 0.06 × (1 − 0.25)
r = fm.coc.wacc("0.10", "0.06", "0.25", debt_weight="0.3")
assert r.wacc == Decimal("0.0835")
assert r.equity_weight == Decimal("0.7")

# Target D/E 0.5, so weights 2/3 and 1/3: 2/3 × 0.0852 + 1/3 × 0.055 × (1 − 0.24)
by_ratio = fm.coc.wacc("0.0852", "0.055", "0.24", debt_to_equity="0.5")
assert by_ratio.wacc == Decimal("0.0707333333333333333333333333")
assert by_ratio.debt_weight == Decimal("0.3333333333333333333333333333")
assert by_ratio.after_tax_cost_of_debt == Decimal("0.0418")

Use the same target D/E here and when relevering the beta of the cost of equity, so that the two inputs describe the same capital structure.

Inputs¶

Field	Meaning	Default
`cost_of_equity`	Cost of equity, annual decimal fraction	required
`pre_tax_cost_of_debt`	Pre-tax cost of debt, annual decimal fraction	required
`tax_rate`	Tax rate of the tax shield, decimal fraction from 0 to below 1	required
`debt_to_equity`	Target D/E, decimal, not negative; give exactly one of `debt_to_equity` and `debt_weight`	none
`debt_weight`	Target D/(D + E), decimal fraction from 0 to below 1; give exactly one of `debt_to_equity` and `debt_weight`	none

Outputs¶

Field	Meaning
`wacc`	Weighted average cost of capital, annual decimal fraction
`equity_weight`	E / (D + E)
`debt_weight`	D / (D + E)
`debt_to_equity`	D/E implied by the weights; compare it with the D/E used to relever the beta
`after_tax_cost_of_debt`	\(k_d (1 - t)\), annual decimal fraction

The steps show the debt weight (derived from D/E when given that way), the equity weight, the after-tax cost of debt and the weighted sum.

Consistency with the beta¶

Use the same capital structure in the cost of equity and in the weights: relever the beta at the D/E implied by the WACC weights (returned as debt_to_equity). Target weights assume a constant D/V, which matches Harris-Pringle; Hamada assumes a constant amount of debt. Mixing a Hamada beta with target weights is a common, tolerated approximation; state it when it matters.

Conventions (explicit, reported in `explain.conventions`)¶

Convention	Options	Default
Rates	annual effective, decimal fractions	fixed
Weights	target capital structure, as D/E or D/(D + E)	none: one must be given
Tax rate of the tax shield	input, no tax-specific logic (IRAP included or not in the rate passed)	none: must be given

Errors¶

Code	When
`FM-E001`	Both or neither of `debt_to_equity` and `debt_weight` are given, D/E is negative, the debt weight is outside 0 to below 1, D/E is so large that the equity weight rounds to zero, the tax rate is outside 0 to below 1, or a field is missing or unknown
`FM-E008`	Arithmetic overflow (inputs far outside a realistic range)

Accuracy¶

The formula is rational: results are exact up to the 28 significant digits of the decimal type. Weights derived from D/E that are not finite decimals (such as ⅓) are rounded at the 28^th significant digit.

Verified against¶

Golden cases in tests/golden/coc.wacc/, whose expected values are closed-form computations written out in each file.

Weighted average cost of capital (coc.wacc)¶