Debt service ratios (`ratios.debt_service`)¶

Answers the question "can the company service its debt?". Returns the interest cover on EBIT and on EBITDA, the net financial position to EBITDA, the debt service cover ratio (DSCR) of each period of a loan schedule and the loan life cover ratio (LLCR).

Formula¶

\[ \text{interest cover} = \frac{\text{EBIT}}{\text{interest}} \;\text{and}\; \frac{\text{EBITDA}}{\text{interest}} \qquad \frac{\text{NFP}}{\text{EBITDA}} \]

\[ \text{DSCR}_t = \frac{\text{CFADS}_t}{\text{debt service}_t} \qquad \text{LLCR} = \frac{\sum_{t=1}^{n} \text{CFADS}_t \,/\, (1 + r)^t + \text{reserve balance}}{\text{debt outstanding}} \]

where CFADS is the cash flow available for debt service, \(r\) the discount rate per period of the schedule (the cost of debt per period chosen by the analyst), the reserve balance the debt service reserve account at the valuation date, added undiscounted (zero when not given), \(n\) the number of periods up to the final maturity and the debt outstanding is measured at the start of the first period. Discounting is the one of tvm.present_value, at the end of each period.

Example¶

from decimal import Decimal

import fairmark as fm

r = fm.ratios.debt_service(
    balances="closing",
    ebitda_definition="reported EBITDA, no adjustments",
    interest_definition="gross interest expense",
    income_statement={"ebitda": 800, "ebit": 500, "interest": 100},
    closing={"net_financial_position": {"gross_debt": 2200, "cash": 300}},
    debt_schedule={
        "discount_rate": "0.06",
        "debt_outstanding": 1000,
        "periods": [{"cfads": 250, "debt_service": 200}] * 5,
    },
)
assert r.interest_cover_ebit["value"] == Decimal("5")  # 500 / 100
assert r.nfp_to_ebitda["value"] == Decimal("2.375")  # 1900 / 800
assert r.dscr[0]["value"] == Decimal("1.25")  # 250 / 200
# Level CFADS: LLCR = 250 × (1 − 1.06^−5) / 0.06 / 1000
assert abs(r.llcr["value"] - Decimal("1.05309094639142847003375")) < Decimal("1e-20")

# Without a debt schedule, DSCR and LLCR are not defined; the other ratios are computed.
s = fm.ratios.debt_service(
    balances="closing",
    ebitda_definition="reported EBITDA, no adjustments",
    interest_definition="gross interest expense",
    income_statement={"ebitda": 800, "ebit": 500, "interest": 100},
    closing={"net_financial_position": {"gross_debt": 2200, "cash": 300}},
)
assert s.llcr["not_defined"] == "no debt schedule given"
assert s.interest_cover_ebitda["value"] == Decimal("8")

Inputs¶

Field	Meaning	Default
`balances`	`closing`, or `average` of the opening and closing net financial position	required
`ebitda_definition`	How EBITDA was measured, in words, not empty; echoed in the conventions	required
`interest_definition`	How interest was measured (gross, or net of interest income), in words, not empty; echoed in the conventions	required
`income_statement`	`ebitda`, `ebit`, `interest` of the period, currency units	required
`closing`	`net_financial_position` with `gross_debt`, `cash` and `other_items`	required
`opening`	Same field at the start of the period	required with average balances, not used otherwise
`debt_schedule`	`discount_rate`: the cost of debt per period chosen by the analyst (decimal fraction); `debt_outstanding` at the start of the first period; optional `reserve_balance` (debt service reserve account at the valuation date); `periods`: a list of `{"cfads", "debt_service"}` up to the final maturity	optional: without it DSCR and LLCR are not defined

Outputs¶

Field	Meaning
`net_financial_position`	NFP used by the ratios, currency units
`interest_cover_ebit`	EBIT / interest, multiple
`interest_cover_ebitda`	EBITDA / interest, multiple
`nfp_to_ebitda`	NFP / EBITDA, multiple
`dscr`	CFADS / debt service of each period, multiple, in the order of the schedule; empty without a debt schedule
`pv_cfads`	Present value of the CFADS at the start of the first period, currency units; null without a debt schedule
`llcr`	(Present value of CFADS + reserve balance) / debt outstanding, multiple

Ratios are objects {"value": ..., "not_defined": ...}, as in every ratio group.

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

Convention	Options	Default
Balances	closing, average of opening and closing (net financial position)	required
EBITDA definition	as given by the analyst, non-empty	required
Interest definition	as given by the analyst (gross, or net of interest income), non-empty	required
Debt service	as given	fixed
LLCR discounting	end of each period, at `discount_rate` per period, the cost of debt chosen by the analyst	fixed
Reserve balance	added undiscounted to the LLCR numerator	none
Debt schedule	optional; without it DSCR and LLCR are not defined ("no debt schedule given")	none
Not defined	zero denominator; interest covers when interest or the numerator (EBIT or EBITDA) is zero or negative; NFP / EBITDA when EBITDA is zero or negative; DSCR when debt service is zero or negative; LLCR when debt outstanding is zero or negative	fixed

Errors¶

Code	When
`FM-E001`	Average balances without `opening`; an empty or blank `ebitda_definition` or `interest_definition`; a field is missing or unknown
`FM-E002`	A debt schedule is given with no periods
`FM-E003`	Discount rate at or below −100% per period
`FM-E008`	Arithmetic overflow (inputs far outside a realistic range)

Accuracy¶

Ratios are one decimal division each; discount factors are integer powers of \(1 + r\). Results are exact up to the 28 significant digits of the decimal type.

Verified against¶

Golden cases in tests/golden/ratios.debt_service/, whose expected values come from scripts/reference_ratios.py (Python decimal at 50 digits); the LLCR of a level CFADS equals the annuity closed form \(C\,(1 - (1 + r)^{-n}) / r\) divided by the debt outstanding. Further cases cover the reserve balance, a missing schedule and each not-meaningful sign.

Debt service ratios (ratios.debt_service)¶