CFA Level 1 time value of money applications
Time value of money compares cash flows at the same date. Discount future cash flows to today, compound present cash flows forward, and match the rate, number of periods and payment timing before using an annuity formula.
The key ideas, at a glance
Single payment
Read the visual, then follow the worked example below. Use the stated case assumptions.
Illustrative worked case
amount
Year 1
1,000
amount
PV today 952.38
Year 2
1,000
amount
PV today 907.03
Year 3
1,000
amount
PV today 863.84
At 5%, the three end-of-year present values sum to 2,723.25. A payment today would require a different timeline.
| Concept | Rule or decision | Common mistake |
|---|---|---|
| Single payment | PV = FV / (1 + r)^n; FV = PV × (1 + r)^n. | Rate and period count must use the same time unit. |
| Ordinary annuity | Equal payments occur at the end of each period. | The first payment is one period away, not today. |
| Annuity due | Equal payments occur at the start of each period; shift an ordinary annuity one period earlier. | For matching conventions, multiply the ordinary-annuity PV by (1 + r). |
| Unequal cash flows | Discount each cash flow separately and add the values at the chosen date. | An annuity shortcut is inappropriate when amounts or timing differ. |
01Single payment
PV = FV / (1 + r)^n; FV = PV × (1 + r)^n.
Watch for: Rate and period count must use the same time unit.
02Ordinary annuity
Equal payments occur at the end of each period.
Watch for: The first payment is one period away, not today.
03Annuity due
Equal payments occur at the start of each period; shift an ordinary annuity one period earlier.
Watch for: For matching conventions, multiply the ordinary-annuity PV by (1 + r).
04Unequal cash flows
Discount each cash flow separately and add the values at the chosen date.
Watch for: An annuity shortcut is inappropriate when amounts or timing differ.
Selected 2026 study concepts. Match your preparation to your registered exam-year curriculum. These notes are not complete curriculum coverage.
Free PDF by email
CFA Level I: 20 practice MCQs
Enter your email on the PDF page to receive the printable pack, with answers and explanations. Selected level/pathway questions; see the topic mix before requesting.
No account or payment required for the PDFs. Includes the monthly newsletter; unsubscribe anytime.
Put the method to work
One worked example, from facts to answer
Given
You receive 1,000 at the end of each of the next three years. Annual discount rate is 5%.
Method
PV = 1,000 / 1.05 + 1,000 / 1.05² + 1,000 / 1.05³ = 2,723.25.
Answer and interpretation
The end-of-year payment stream is worth 2,723.25 today under the stated 5% rate. A payment today would change the timeline.
Original independent teaching example. Assumptions are stated above; this is not an official exam question or scoring key.
Apply the framework, step by step
Choose the right valuation date, cash-flow timing and compounding convention for a present-value or future-value problem. Read Quantitative Methods for the wider return, probability and statistical foundations.
Before you start: Compound interest, payment timing, annual versus periodic rates and consistent cash inflow/outflow signs.
METHOD 01
Single payment
PV = FV / (1 + r)^n; FV = PV × (1 + r)^n.
Pick the date at which all values will be compared. A future payment is discounted backward to that date; a payment already at that date needs no discounting. Compound forward when the requested value is at a later date. A timeline makes the direction and number of intervals explicit, especially when the question has an initial investment, several receipts and a terminal value.
Avoid this mistake: Rate and period count must use the same time unit.
METHOD 02
Ordinary annuity
Equal payments occur at the end of each period.
An ordinary annuity has equal payments at the ends of evenly spaced periods. The present-value annuity formula gives value one period before the first payment. If the first payment occurs at the end of year 4, the annuity’s initial valuation date is the end of year 3; discount that value a further three years to today. Counting payments is different from counting discounting intervals.
Avoid this mistake: The first payment is one period away, not today.
METHOD 03
Annuity due
Equal payments occur at the start of each period; shift an ordinary annuity one period earlier.
An annuity due moves otherwise identical payments one period earlier. Under a positive discount rate, earlier receipts have a larger present value. With matching conventions, multiply the ordinary-annuity present value by (1 + periodic rate). Calculator beginning/end settings reflect this timing distinction; they do not repair inconsistent rates, payment frequencies or sign conventions.
Avoid this mistake: For matching conventions, multiply the ordinary-annuity PV by (1 + r).
METHOD 04
Unequal cash flows
Discount each cash flow separately and add the values at the chosen date.
Unequal amounts or irregular dates require separate cash-flow discounting. Add only values that refer to the same date and currency. The discount rate should fit the cash flow’s timing and assumptions, and a nominal annual rate must be converted under its stated compounding convention. For net present value, include the initial outflow at time zero with the correct sign rather than discounting it again.
Avoid this mistake: An annuity shortcut is inappropriate when amounts or timing differ.
Apply it to a different case
- New facts
- Two payments of 500 arrive at the end of years 2 and 3. Annual discount rate is 5%; today is time zero.
- Working
- Value at end of year 1 = 500 / 1.05 + 500 / 1.05². Discount that value once more to today, or directly calculate 500 / 1.05² + 500 / 1.05³.
- Conclusion
- Both methods give approximately 885.43 today. Treating the first receipt as year 1 would value a different payment schedule.
Original teaching case under the stated assumptions, rather than an official exam question.
Questions about this method
- Where is an annuity’s present value located?
- For an ordinary annuity, it is one period before the first payment. If payments are deferred, first value the annuity at that date and then discount to the date the question requests.
- Why does an annuity due have a higher present value?
- With a positive discount rate, every payment is received one period earlier and therefore discounted for one fewer period. Under matching conventions its value is the ordinary-annuity value multiplied by (1 + periodic rate).
- When should I use individual discounted cash flows?
- Use them when amounts differ, dates are irregular, or the pattern does not fit a standard annuity. The method also provides a useful check on a calculator’s timing assumptions.
Sources and curriculum scope
Official outlines establish curriculum scope. The explanations and worked examples are independent teaching material; the sources do not verify or endorse them.
- 2026 CFA Level 1 curriculum outline
- Official Level 1 format and curriculum
- 2026 time value of money in finance
- 2027 CFA Level 1 curriculum outline
MiloPrep is an independent study resource, not affiliated with or endorsed by CFA Institute. CFA® and Chartered Financial Analyst® are trademarks owned by CFA Institute.