Core Economic Concepts (Time Value of Money & Net Present Value)
The Big Question
Imagine someone offers you $1000 today or $1000 five years from now.
Which would you choose?
Now imagine the offer changes:
$1000 today, or $1400 in five years
Which option is better now?
The answer depends on something economists call the Time Value of Money (TVM). Money available today can be invested, earn interest, and grow over time, meaning future money is not directly comparable without adjustment
Learning Outcomes
- Define the Time Value of Money (TVM) in their own words
- Understand how discounting converts future cash flows into present values
- Calculate Present Value (PV) using the standard discounting equation
- Define and interpret Net Present Value (NPV)
- Apply NPV to determine whether an investment should be accepted or rejected
What is the Time Value of Money?
Time Value of Money Finance – TVM Formulas & Calculations – Annuities, Present Value, Future Value [1]
Summary of Formulas
The following formulas are typically lumped into a method called Discounted Cash Flow ( DCF ).
The Future Value formula calculates how much a present investment will grow after earning interest over time.
Where:
- FV = Future Value
- PV = Present Value
- r = interest rate per period
- n = number of periods
The Present Value formula determines what a future amount of money is worth today.
Where:
- PV = Present Value
- FV = Future Value
- r = discount rate
- n = number of periods
An annuity is a series of equal payments made at regular time intervals.
Where:
- FV = Future Value
- PMT = payment each period
- r = interest rate
- n = number of periods
This formula determines the current value of a stream of equal future payments.
Where:
- PV = Present Value
- PMT = periodic payment
- r = discount rate
- n = number of periods
When interest is compounded multiple times per year.
Where:
- PV = present value
- r = annual interest rate
- m = compounding periods per year
- t = years
Net Present Value (NPV)
Real projects involve multiple cash flows, not just one thus we will take what we learned above and apply it to more complex problems.
Net Present Value calculates the total present value of all future cash flows minus the initial cost.
Where:
- NPV = Net Present Value
- Ct = cash flow at time t
- r = discount rate
- t = time period
There is a standard table for making decisions based off these numbers:
| NPV | Decision |
|---|---|
| NPV > 0 | Accept project |
| NPV = 0 | Break-even |
| NPV < 0 | Reject project |
Please Watch the following video and read the article: “Net Present Value Explained” [2]
This concept is best reinforced with an example:
Payback Period
The payback period is the amount of time required to recover the initial investment from a project’s cash flows. There is a key simplification with this approach, it doesn’t account for the TVM unlike NPV. This is typically used for simple measuring of risk, and is commonly used for small projects or quick decisions.
Please watch this video and read this article : “Payback Period: Definition, Formula, and Calculation”
For even cashflows:
For uneven cashflows (Advanced):
Final Review & Discussion
Think about the key concepts we explored today. These tools are commonly used in engineering and business to evaluate investments and make informed decisions about projects.
In the comment section below, briefly respond to the following prompts:
- What concept from this module made the most sense to you? Why?
- Was there anything that confused you at first but became clearer as you worked through the examples or activities?
- Did you have any misconceptions about how money grows or how projects are evaluated? What changed in your understanding?
References
[1] @leveragedshort, “Time Value of Money Finance – TVM Formulas & Calculations – Annuities, Present Value, Future Value,” YouTube. Oct. 21, 2014. Accessed: Feb. 09, 2026. [Video]. Available: https://www.youtube.com/watch?v=m3azU7gYHc0
[2] W. Team, “Net Present Value (NPV),” WallStreetMojo, 2025. Accessed: Feb. 09, 2026. [Online]. Available: https://www.wallstreetmojo.com/net-present-value-npv-formula/
[3] J. Kagan, “Payback Period: Definition, Formula, and Calculation,” Investopedia, Nov. 26, 2003. Accessed: Feb. 09, 2026. [Online]. Available: https://www.investopedia.com/terms/p/paybackperiod.asp
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