Present Value & Fair Value Measurement
Two foundational measurement bases in accounting:
- Present Value (PV) — discount future cash flows back to today’s dollars.
- Fair Value — the price that would be received in an orderly market transaction today.
ACC 926 Module 3 — “Data, Decisions, Measurement”. ADMN 201 mentions Net Present Value in the financing chapter; this is the underlying mechanic.
Time Value of Money — Why It Exists
A dollar today is worth more than a dollar tomorrow because:
- It can be invested to earn a return.
- Inflation erodes future purchasing power.
- Future cash flows carry uncertainty.
Discounting strips out these factors so cash flows occurring at different times can be compared on a single basis (today).
flowchart LR F[Future Cash Flow<br/>FV at time n] -->|Discount at rate i| P[Present Value<br/>PV today] P -->|Compound at rate i| F2[Future Cash Flow<br/>FV at time n]
(diagram saved)
Lump Sum (Single Amount) Formulas
PV = FV × (1 / (1 + i)^n)
FV = PV × (1 + i)^n
Where i = periodic interest rate, n = number of periods.
Example
$50,000 needed in 25 years at 3%:
PV = 50,000 / (1.03)^25 = 50,000 / 2.0938 = 23,880
You need $23,880 today.
Annuity Formulas (Series of Equal Payments)
Ordinary Annuity (payments at end of period)
PV_annuity = Pmt × [(1 − (1 + i)^−n) / i]
FV_annuity = Pmt × [((1 + i)^n − 1) / i]
Annuity Due (payments at start of period)
Multiply the ordinary annuity result by (1 + i).
Example
$10,000 per year for 5 years at 10%:
PV = 10,000 × [(1 − 1.10^−5) / 0.10] = 10,000 × 3.7908 = 37,908
Uneven Cash Flows
PV each cash flow individually, then sum.
| Year | Cash flow | Factor at 10% | PV |
|---|---|---|---|
| 1 | 5,000 | 0.90909 | 4,545.45 |
| 2 | 2,000 | 0.82645 | 1,652.90 |
| 3 | 3,000 | 0.75132 | 2,253.96 |
| Total | 8,452.31 |
Where PV Shows Up in Accounting
| Topic | PV use |
|---|---|
| Bonds | Issue price = PV of principal + PV of coupon annuity |
| Notes Receivable / Payable | Recorded at PV when stated rate ≠ market rate |
| Leases (IFRS 16) | Lessee recognizes right-of-use asset + lease liability at PV of lease payments |
| Pensions | Defined benefit obligation = PV of promised payments |
| Asset Retirement Obligations | PV of future decommissioning costs |
| Impairment (IFRS Rational Entity Model) | Value-in-use = PV of future cash flows |
IFRS 13 — Fair Value Hierarchy
When fair value is required, IFRS 13 ranks inputs by reliability:
| Level | Input type | Example |
|---|---|---|
| Level 1 | Quoted prices in active markets for identical assets | Stock listed on TSX |
| Level 2 | Observable inputs other than Level 1 (similar assets, observable rates) | Corporate bond priced from yield curve |
| Level 3 | Unobservable inputs (entity’s own assumptions, model-based) | Private company equity, complex derivative |
Level 1 is preferred; entities only fall to Level 2 or 3 when Level 1 inputs aren’t available. Level 3 measurements require the most disclosure because they’re the most subjective.
Valuation Techniques
- Income Models — DCF / discounted cash flow
- Market Models — Comparable transactions, multiples (e.g., EV/EBITDA)
- Cost Models — Replacement cost
Cross-Course Connections
- LongTermFinancing — ADMN 201 introduces NPV in capital budgeting; this is the calculation engine
- InvestmentVehicles — bond pricing relies on PV
- PresentValue-LongTermFinancing — connection page bridging the two
- Investments — fair value categories (FV-NI, FV-OCI) all derive from IFRS 13
- IFRSvsASPE — IFRS 13 hierarchy doesn’t apply formally under ASPE
Key Points
- PV = FV / (1 + i)^n for lump sums
- PV_annuity = Pmt × [(1 − (1+i)^−n) / i] for ordinary annuity
- Annuity due = ordinary annuity × (1 + i)
- Uneven cash flows: PV each separately, then sum
- IFRS 13 Levels 1/2/3 rank fair value input observability; Level 1 best, Level 3 most disclosure
- PV used wherever future cash flows must be brought to today: bonds, leases, pensions, impairment, ARO