The present value interest factor (PVIF) is the multiplier used to convert one future amount into value at an earlier date. It is also called a present value factor or present worth factor. In some property-valuation contexts, the same factor is called a reversion or reversionary factor when it discounts expected sale or reversion proceeds.
Key Takeaways
- PVIF is (1/(1+r)^n) for a constant effective periodic rate.
- Present value equals the future cash flow multiplied by its PVIF.
- At a positive rate, PVIF is below one and declines as rate or time increases.
- Rate and period units must match.
- A reversion factor used for one future property payment is the same present-worth-of-one calculation.
- PVIF applies to one future amount; PVIFA applies to a finite stream of equal payments.
- A factor table does not determine the correct discount rate, timing, or cash flow.
- Rounded factors can create material errors when cash flows are large or distant.
For effective periodic discount rate (r) and (n) matching periods:
$$
PVIF_{r,n}=\frac{1}{(1+r)^n}
$$
The present value of future value (FV_n) is:
$$
PV=FV_n\times PVIF_{r,n}
$$
PVIF is dimensionless. The resulting present value uses the same currency units as the future cash flow.
Worked Example: Discounting One Payment
Assume 1,000 is expected in five years and the appropriate annual discount rate is 6%:
$$
PVIF_{6\%,5}=\frac{1}{(1.06)^5}=0.747258
$$
Apply the factor:
$$
PV=1{,}000(0.747258)=747.26
$$
Under those assumptions, each unit payable in year five is worth about 0.7473 at the valuation date. The factor does not establish that the 1,000 payment is certain or that 747.26 is an observable market price.
Sensitivity to Rate and Time
| Annual rate | PVIF, 1 year | PVIF, 5 years | PVIF, 10 years |
|---|
| 3% | 0.9709 | 0.8626 | 0.7441 |
| 6% | 0.9434 | 0.7473 | 0.5584 |
| 10% | 0.9091 | 0.6209 | 0.3855 |
At 6%, a unit due in ten years has a factor of 0.5584, compared with 0.9434 for a unit due in one year. At ten years, raising the rate from 3% to 10% lowers the factor from 0.7441 to 0.3855.
The table demonstrates sensitivity; it does not identify which rate is correct. The rate must be supported for the cash flow and measurement purpose.
PVIF as the Reciprocal of FVIF
The future value interest factor is:
$$
FVIF_{r,n}=(1+r)^n
$$
For matching inputs:
$$
PVIF_{r,n}=\frac{1}{FVIF_{r,n}}
$$
Multiplying a present amount by FVIF moves it forward. Multiplying the resulting future amount by PVIF moves it back, subject to consistent rates, periods, and rounding.
Reversion and Reversionary Factor
Property valuation may separate periodic income during a holding period from a lump-sum reversion, such as expected sale proceeds at the end. The future reversion can be discounted with the present value of one factor:
$$
PV_{reversion}=R_n\times\frac{1}{(1+r)^n}
$$
where (R_n) is the expected net reversion at time (n).
Assume expected net sale proceeds of 500,000 after five years and a supported annual discount rate of 8%:
$$
PVIF_{8\%,5}=\frac{1}{(1.08)^5}\approx0.680583
$$
$$
PV_{reversion}=\frac{500{,}000}{(1.08)^5}\approx340{,}291.60
$$
The expected sale amount should be net of the costs and obligations included in the valuation framework. Market value, rent changes, capital spending, taxes, selling costs, vacancy, and property condition can all change the actual reversion.
One Factor per Cash-Flow Date
For multiple future cash flows, calculate a factor for each date:
$$
PV=\sum_{t=1}^{T}CF_t\times PVIF_{r_t,t}
$$
Using the five-year factor for every cash flow would incorrectly treat earlier payments as if they occurred in year five. A yield curve may also require a different spot rate for each maturity.
PVIF vs. PVIFA
| Factor | Formula | Use |
|---|
| PVIF | (1/(1+r)^n) | One future amount at period (n) |
| PVIFA | ([1-(1+r)^{-n}]/r) | Equal end-of-period payments from periods 1 through (n) |
PVIFA is the sum of individual PVIFs for the annuity dates:
$$
PVIFA_{r,n}=\sum_{t=1}^{n}\frac{1}{(1+r)^t}
$$
Using PVIF for an entire payment stream omits payments. Using PVIFA for one terminal amount treats that amount as though it recurs each period.
Different Compounding Conventions
If (j) is a nominal annual rate compounded (m) times per year for (t) years:
$$
PVIF=\frac{1}{\left(1+\frac{j}{m}\right)^{mt}}
$$
For a continuously compounded rate (c):
$$
PVIF=e^{-ct}
$$
Do not choose a formula by label alone. Confirm whether the input is nominal, periodic, effective, or continuous.
Variable Rates and Discount Curves
If the effective rate changes by period, one cumulative factor is:
$$
PVIF_T=\prod_{t=1}^{T}\frac{1}{1+r_t}
$$
Fixed-income and derivative models may instead use discount factors bootstrapped from a market curve. Those factors can reflect day counts, collateral conventions, interpolation, and instrument-specific market practices not captured by a textbook annual formula.
How to Use a Present Value Factor
- Set the valuation date and cash-flow date.
- Count the periods using the required timing convention.
- Identify whether the rate is periodic, nominal, effective, or continuous.
- Match rate units with period units.
- Confirm that the rate fits the cash flow’s currency, risk, and purpose.
- Calculate rather than interpolate when exact inputs are available.
- Apply a separate factor to each distinct cash-flow date.
- Keep enough precision until the final amount is calculated.
- Label a property reversion factor as the PVIF applied to the terminal payment.
- Test rate and timing sensitivity when the factor materially affects value.
Common Mistakes and Limitations
- Treating PVIF as a rate: It is a multiplier derived from rate and time.
- Entering 6 instead of 0.06: The formula uses a decimal rate.
- Mixing annual rates and monthly periods: Units must match.
- Using one factor for a cash-flow stream: Each date needs its own PVIF or an appropriate annuity factor.
- Confusing PVIF with PVIFA: One values a single amount; the other values recurring payments.
- Ignoring reversion costs: Expected sale proceeds may need adjustments before discounting.
- Rounding too early: Small factor errors scale with the cash-flow amount.
- Assuming a table supplies the right rate: Rate selection requires separate support.
- Treating factor-based value as market price: Risk, liquidity, taxes, and transaction terms remain relevant.
Public Source Checks
- The California State Board of Equalization’s income-approach lesson describes a reversion factor as the present worth of one used to value a single future reversion payment.
- The Federal Reserve Bank of St. Louis FRED Blog explains the present-value factor and how rate changes affect a future payment’s current value.
- New York University professor Aswath Damodaran’s present-value primer explains discounting, compounding, and present-value mechanics for different cash-flow patterns.
FAQs
What does a PVIF of 0.75 mean?
It means one unit received on the stated future date has a modeled present value of 0.75 units under the specified rate and timing assumptions.
Is a reversionary factor different from PVIF?
Not when it refers to the present-worth-of-one factor applied to one future reversion payment. Property valuation may use the specialized label to identify the terminal proceeds being discounted.
Why is PVIF below one?
At a positive discount rate and positive number of periods, the denominator exceeds one. Zero or negative rates can produce different relationships.
Can PVIF be used for several payments?
Yes, but each payment date needs its own factor. For equal recurring end-of-period payments, PVIFA provides the sum of those factors.
This article is educational only and does not provide individualized investment, property, valuation, accounting, tax, actuarial, or legal advice.