Lesson 2 of 9
The discount factor
Build a five-year factor table once and every cash flow after it is a multiplication. It also shows exactly where a valuation is sensitive.
By Javier Sanz
Founder of ValueScreener. Built Ninety Nine, a securities services provider, and sold it to a tier-one global bank; ran operations and internationalization at Alpaca, the brokerage API.
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In one minute
- A discount factor is the present value of one dollar arriving in a given year. Build the table once and reuse it.
- Factors fall faster than the eye expects: at 4.78 percent, year five keeps only 79 cents of a dollar.
- Reading the table tells you which year of a forecast your answer actually depends on.
Dividing each cash flow by one plus the rate to its own power is correct and slow. The faster form computes the divisions once, stores them as a column of factors, and turns every later valuation into a multiplication.
Five discount factors at 4.78 percent
- Year 10.9544
- Year 20.9108
- Year 30.8693
- Year 40.8296
- Year 50.7918
Building it
A factor for year n is one divided by (1 + r) to the power n. Nothing else. At 4.78 percent the first is 1 divided by 1.0478, which is 0.9544. The second is that divided by 1.0478 again, which is 0.9108, and so on down the column.
The table, in five divisions
- Write 1.0478 once. This is your only input.
- Year 1: 1 divided by 1.0478 equals 0.9544.
- Year 2: 0.9544 divided by 1.0478 equals 0.9108.
- Year 3: 0.9108 divided by 1.0478 equals 0.8693.
- Years 4 and 5: keep dividing. 0.8296, then 0.7918.
Each row is the row above divided by one plus the rate. That is the whole construction, and it means a wrong second row makes every row under it wrong, which is worth one check before you go on.
Reading a cash flow through it
Multiply each year's cash by its factor and add the column. The sum is the present value of the whole stream.
Where the sensitivity lives
The table answers a question a spreadsheet hides. Year one keeps 95 cents of each dollar and year five keeps 79. Push the same table out to year twenty at the same rate and the factor is 0.3930. A dollar promised in the twentieth year is worth 39 cents today, so the back half of a long forecast contributes far less than its share of the cash suggests.
That is why an argument about year eighteen of a forecast is usually an argument about very little, and why an argument about the terminal value is not. A terminal value is a factor applied to a number that stands for every year after the table stops.
Check yourself
At 4.78 percent, the year-three discount factor is 0.8693. What is the year-four factor?
- 0.8693 minus 0.0478
- 0.8693 divided by 1.0478, which is 0.8296
- 0.8693 multiplied by 1.0478
Show the answer
Answer: B.
Each factor is the one above divided by one plus the rate. Subtracting the rate is a different and wrong operation, and it drifts further from the truth every row.The five factors at 4.78 percent add to 4.3559. What does that number tell you directly?
- The total cash over five years
- The present value of one dollar a year for five years
- The rate of return on the stream
Show the answer
Answer: B.
Adding the factors values a level stream of one per year. Multiply the sum by the actual annual amount and you have the whole present value in one step.Why does a disagreement about year eighteen of a forecast usually matter less than one about the terminal value?
- Because forecasts are more accurate far out
- Because the factor for year eighteen is small, while a terminal value stands for every year after the table ends
- Because terminal values are not discounted
Show the answer
Answer: B.
The factor shrinks every year, so a single distant year contributes little. A terminal value is discounted too, but it represents an unbounded number of years, which is why it usually carries most of the answer.Sources
- Williams, The Theory of Investment Value, 1938: the present value of a stream of dated payments.
- US Department of the Treasury, Daily Treasury Par Yield Curve Rates, session of 11 September 2026: the 4.78 percent five-year par yield used to build the table.
What this leaves out
- One flat rate is used for all five years. Real yield curves are not flat, and the bond course prices a stream against a curve instead.
- Factors here assume cash arrives at the end of each year. Mid-year convention shifts every row and is a defensible alternative, not an error.
- Nothing here is advice about any security.