Perpetuity Value

Inspectable records

Ledger state

The current ledger marks this instrument verified clean within the source-bound verification corpus.

Area

Finance, Economics & Business

Tranche

tranche-2

Evidence ID

t2-032

Ledger rows

1

No ledger note is attached.

Review findings

The existing honest label correctly warns that the growing model breaks when g≥r, but it should also disclose the PMT timing convention, the end-of-period assumption for level payments, and the requirement that rate and growth use matching periodic decimal units.

Formula and scope findings

• The level perpetuity formula PV=PMT/r is standard only for equal payments made at the end of each period, with PMT representing each periodic payment and r>0.
• The growing perpetuity formula PV=PMT/(r-g) is standard when PMT is the first payment one period from valuation (PMT1). If PMT is the current payment (PMT0), the formula must be PV=PMT*(1+g)/(r-g). The spec does not define which meaning applies.
• Both rate and growth inputs must use the same compounding period and consistent units.

Unit assumptions

• PMT is a cash payment per period, expressed in currency units.
• rate and g are decimal periodic rates, so 5% is entered as 0.05, not 5.
• For these test vectors, level payments occur at the end of each period and growing PMT is the first payment one period from valuation.
• The rate and growth rate are nominally comparable only when they use the same period and compounding convention.

Boundary hardening

BREAK_CLAIMED · SELF_FLAGGED

The instrument has an undefined-result failure when g equals r: the growing-perpetuity denominator r-g becomes zero. It also must reject the broader invalid region g > r, where the infinite stream does not converge. Ambiguous rate units and cash-flow signs can produce materially different outputs if conventions are not specified.

Errata and corrections

No applied erratum is attached to this unique-name record.

Inspectable example

4 review vectors are recorded. One source-bound sample is shown below.

{
  "inputs": {
    "mode": "level",
    "PMT": 1000,
    "rate": 0.05
  },
  "expected_outputs": {
    "PV": 20000
  },
  "working": "PV=PMT/r=1000/0.05=1000/(5/100)=1000*20=20000."
}

Related workflows

No source-defined multi-instrument workflow membership is recorded.

Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

• VERIFIED_LEDGER.json · VERIFIED_CLEAN
• evidence-tranche2/tranche2-results.json
• BOUNDARY_HAZARD_CATALOG.json