What is a discount factor?
A discount factor is a number between 0 and 1 that represents the present value of one dollar (or one unit of currency) received in the future. It answers the question: how much is $1 received in n years worth in today's money, given a discount rate r?
The core idea is the time value of money — a dollar today is worth more than a dollar tomorrow because today's dollar can be invested to grow. The discount rate (r) quantifies how much more valuable present cash is relative to future cash. The higher the discount rate, the more steeply future cash flows are reduced.
- Discount factor is always between 0 and 1 when r > 0
- Discount factor = 1.0 when r = 0 (no time preference)
- Discount factor falls as either r or n increases
- It is also called the present value factor or PV factor
Discount factor formula
n = number of periods
To get the present value of a future cash flow, multiply by the discount factor:
Example: receive $1,000 in 3 years, discount rate 8%:
The discount factor of 0.7938 tells you that every $1 received in Year 3 at an 8% rate is worth only $0.79 today — a 20.6% reduction due to the time value of money.
Step-by-step calculation
Discount factor table — 7 periods × 5 rates
This reference table shows the discount factor for periods 1–7 across five commonly used discount rates. Notice how factors fall sharply at higher rates and longer time horizons:
Key observation from the table: at 15% discount rate, a Year 7 cash flow has a factor of only 0.3759 — meaning $1 received in 7 years is worth less than 38 cents today. This is why high discount rates make long-dated projects very difficult to justify in DCF analysis.
Rate sensitivity — how the discount rate changes present value
For the same cash flow ($5,000 in Year 5), here is how the discount factor and resulting present value change across different rates:
The same $5,000 cash flow in Year 5 is worth $4,529 at a 2% rate but only $2,009 at 20% — less than half. This is why the choice of discount rate in NPV and DCF analysis is so consequential: a wrong rate assumption can make a value-destroying project look attractive, or make a good project look marginal.
Worked examples
$1,000 in 1 year at 5%
r = 0.05 · n = 1
✅ $1,000 in 1 yr at 5% = $952.38 today
$8,000 in 4 years at 7%
r = 0.07 · n = 4
🔵 $8K in 4 yr at 7% = $6,103 today
Project A (yr 1) vs B (yr 5) at 9%
Same $10,000 payment, different timing
🟡 Year-1 payment worth $2,675 more
Startup at 25% WACC, Year 3
$50,000 projected cash flow in Year 3
🟡 High rate cuts value by almost half
Discount factor in DCF analysis — multi-year example
In a discounted cash flow (DCF) model, you calculate a separate discount factor for each year and multiply it by that year's projected cash flow. The sum of all present values equals the NPV.
Example: project with 5-year cash flows at a 10% discount rate:
The NPV of +$10,271 means this project creates value above the 10% required return — it should be accepted. The cumulative PV column also shows the discounted payback occurs during Year 4, when the cumulative PV turns positive.
Common mistakes to avoid
- Mismatching rate and period units. An annual rate cannot be used with monthly periods without conversion. Monthly rate ≈ Annual rate ÷ 12 (approximate). Always confirm that r and n use the same time unit.
- Forgetting to convert percentage to decimal. 8% must be entered as 0.08 in the formula. Using 8 instead of 0.08 produces a nonsensically small factor and a wildly wrong PV.
- Confusing the discount factor with present value. The discount factor (e.g. 0.7938) is a multiplier — not a dollar amount. Present value = future cash flow × discount factor. Skipping the multiplication is a common error in exam questions.
- Applying the wrong discount rate. Use the rate that reflects the risk of the specific cash flow. WACC for project-level DCF. Risk-free rate for certain government cash flows. Using a too-low rate overstates present value; too-high understates it.
- Year 0 always has a factor of 1.0. Cash flows occurring today (n=0) are already in present-value terms. The discount factor for n=0 is always 1 ÷ (1+r)⁰ = 1, regardless of r.
Frequently asked questions
What is the formula for discount factor?
Discount factor = 1 ÷ (1 + r)^n, where r is the discount rate per period as a decimal and n is the number of periods. To find present value: PV = Future cash flow × Discount factor.
Is discount factor the same as present value factor?
Yes — the terms are used interchangeably in finance and accounting. Both describe the multiplier that converts a future cash flow into its present value equivalent. Some textbooks also call it a PV interest factor (PVIF).
Why does the discount factor decrease over time?
Because future cash flows become less valuable in present terms as the waiting time increases. Mathematically, (1 + r)^n grows larger as n increases, so 1 divided by that number gets smaller. Intuitively, money received further in the future has more time for uncertainty and opportunity cost to accumulate.
Can the discount factor be greater than 1?
Only if the discount rate is negative — which can theoretically occur in environments where nominal interest rates are negative. In that case, future cash flows are worth more than present cash. Under all normal positive discount rate assumptions, the factor is between 0 and 1.
How is discount factor used in NPV?
In NPV analysis, you calculate a separate discount factor for each period: Year 1 factor = 1÷(1+r)¹, Year 2 = 1÷(1+r)², and so on. Each cash flow is multiplied by its period's factor to get its present value. NPV = sum of all present values (including the Year 0 investment at face value).