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Fairmark

Cost of debt (coc.cost_of_debt)

salvo8519/fairmark

Cost of debt (`coc.cost_of_debt`)¶

Returns the pre-tax and the after-tax cost of debt. The pre-tax rate is either given directly (for example the rate on the company's current borrowing) or built as a risk-free rate plus a credit spread. The after-tax rate applies the tax shield at a tax rate given explicitly.

Formula¶

\[ k_d = r_f + s \quad\text{(when built from a spread)} \qquad k_d^{\text{after tax}} = k_d \,(1 - t) \]

where \(r_f\) is the risk-free rate, \(s\) the credit spread 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

# Risk-free rate 3% plus a spread of 2.5%, tax shield at 24%.
r = fm.coc.cost_of_debt("0.24", risk_free_rate="0.03", credit_spread="0.025")
assert r.pre_tax_cost_of_debt == Decimal("0.055")
assert r.after_tax_cost_of_debt == Decimal("0.0418")  # 0.055 × (1 − 0.24)
print(r.conventions[-1])  # tax rate of the tax shield 0.24

# The same pre-tax rate given directly.
direct = fm.coc.cost_of_debt("0.24", pre_tax_cost_of_debt="0.055")
assert direct.after_tax_cost_of_debt == Decimal("0.0418")

Inputs¶

Field	Meaning	Default
`tax_rate`	Tax rate of the tax shield, decimal fraction from 0 to below 1	required
`pre_tax_cost_of_debt`	Pre-tax cost of debt, annual decimal fraction; give either this, or `risk_free_rate` and `credit_spread`	none
`risk_free_rate`	Risk-free rate, annual decimal fraction, with `credit_spread`	none
`credit_spread`	Credit spread over the risk-free rate, annual decimal fraction, with `risk_free_rate`	none

The tax rate is the one the analyst considers deductible for the tax shield; the engine applies no tax-specific logic (for Italian companies, whether IRAP is included is decided in the rate passed). The rate is echoed in explain.conventions.

Outputs¶

Field	Meaning
`pre_tax_cost_of_debt`	Pre-tax cost of debt, annual decimal fraction
`after_tax_cost_of_debt`	\(k_d (1 - t)\), annual decimal fraction

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

Convention	Options	Default
Rates	annual effective, decimal fractions	fixed
Pre-tax cost of debt	given, or risk-free rate plus credit spread	none: one must be given
Tax rate of the tax shield	input	none: must be given

Errors¶

Code	When
`FM-E001`	Neither or both ways of giving the pre-tax rate are used, only one of `risk_free_rate` and `credit_spread` is given, 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 formulas use only additions and multiplications: results are exact up to the 28 significant digits of the decimal type.

Verified against¶

Golden case in tests/golden/coc.cost_of_debt/, whose expected values are closed-form computations written out in the file.