Definition
Present Value (PV)
Today's value of a sum to be received in the future, calculated by discounting the future amount back to the present using a required rate of return: PV = FV / (1 + r)^n. Present value is the mirror image of future value; discounting moves money backward in time the same way compounding moves it forward. A higher discount rate or a longer time until receipt both produce a lower present value, because the future dollars are discounted more heavily.
$10,000 invested today at 6% annually grows to $13,382 in five years. Run the same math in reverse: $13,382 to be received five years from now, discounted at 6%, has a present value of $10,000. To an investor whose required return is 6%, the two amounts are equivalent.
The direction of the relationships trips students up: a HIGHER discount rate produces a LOWER present value, and a LONGER wait produces a LOWER present value. Both are inverse relationships. Also often mixed up: discounting (used for present value) moves money backward in time, while compounding (used for future value) moves it forward; the formulas are reciprocals of each other, not interchangeable.
How is Present Value (PV) tested on the exam?
- Calculating the present value of a single future sum given a discount rate and time period
- Identifying the inverse relationship between the discount rate and present value
- Identifying the inverse relationship between time to receipt and present value
- Comparing a payment offered today against a larger payment offered in the future at a given required return
- Recognizing the discount rate as the investor's required rate of return in present value calculations
Calculation example
Calculation Example
PV = FV / (1 + r)^n - Identify the future value needed: $50,000
- Identify the rate: 7% per year
- Identify the number of periods: 10 years
- Compute the discount factor: (1.07)^10 = 1.9672
- Divide: $50,000 / 1.9672 = $25,417
Discounting is a shrink ray pointed at future money: the higher the rate and the longer the wait, the smaller the dollars look by the time they land in today's terms. Future value zooms money up going forward; present value shrinks it coming back.
Practice questions
Test your understanding with the questions below. Pick an answer to reveal the explanation.
A client is offered a choice: receive $10,000 today or $13,382 five years from now. The client's required rate of return is 8%. Which choice has the greater value to this client?
A is correct. Discount the future payment at the client's 8% required return: PV = $13,382 / (1.08)^5 = $13,382 / 1.4693 = about $9,108. Since $9,108 is less than $10,000, the payment today is worth more to this client.
B compares nominal dollar amounts and ignores the time value of money entirely. C states a rule that doesn't exist; discounting typically penalizes later payments, not favors them. D would be true only at a discount rate of exactly 6% (where $13,382 in five years equals $10,000 today); at 8%, the future payment is worth less.
The Series 65 exam tests whether you can compare cash flows arriving at different times by bringing them to the same point in time. The nominal-dollar comparison in option B is the classic trap.
In time value of money calculations, present value (PV) represents:
A is correct. Present value is today's value of a future sum, found by discounting the future cash flow back to the present at a required rate of return.
B describes future value, the opposite direction of travel. C ignores discounting altogether, which is the entire point of present value analysis. D describes cost basis, a tax concept unrelated to time value of money.
Present value versus future value direction questions are quick points on the Series 65 exam if you keep the two straight: discounting travels backward to today, compounding travels forward.
A client needs $50,000 in 10 years and expects to earn 7% annually. Approximately how much must the client invest today to reach that goal?
B is correct. PV = $50,000 / (1.07)^10 = $50,000 / 1.9672 = approximately $25,417.
A applies simple-interest thinking, stripping 7% per year for 10 years (70%) off the target. C discounts only one year ($50,000 / 1.07) instead of ten. D multiplies instead of divides ($50,000 x 1.9672), compounding the money forward when the question calls for discounting it backward.
Present value calculations on the Series 65 exam most often go wrong in the direction of travel: multiplying by the growth factor instead of dividing by it. Checking that your answer is SMALLER than the future amount catches that error instantly.
All of the following statements about present value are accurate EXCEPT
D is correct (the EXCEPT answer). The discount rate is a critical input that directly drives the result: raising it lowers the present value, and lowering it raises the present value.
A is accurate: rate and present value move inversely. B is accurate: more periods of discounting shrink the present value further. C is accurate: discounting future cash flows to today is the definition of the calculation.
The inverse relationships (rate up means PV down, time up means PV down) are the most frequently tested present value facts on the Series 65 exam, often without requiring any actual math.
Which of the following statements about present value are accurate?
1. Increasing the discount rate decreases the present value of a future sum
2. Extending the time until receipt decreases the present value of a future sum
3. A dollar today is worth more than a dollar received in the future
4. Present value is calculated as PV = FV x (1 + r)^n
B is correct. Statements 1, 2, and 3 are accurate.
Statement 1 is TRUE: a higher discount rate discounts future dollars more heavily, lowering their present value. Statement 2 is TRUE: more periods of discounting also lower the present value. Statement 3 is TRUE: this is the core time value of money principle, and it holds because a dollar today can be invested to earn a return. Statement 4 is FALSE: multiplying by (1 + r)^n is the FUTURE value formula; present value divides by that factor (PV = FV / (1 + r)^n).
Statement 4 is the classic formula-direction trap. The Series 65 exam expects you to know that compounding multiplies and discounting divides, and mixing them up reverses every answer downstream.
Where does Present Value (PV) appear on the Series 65 exam?
This term is tested in the following Series 65 exam topics: