# Present Value of a Single Cash Flow | CFA Level 1

PREREQUISITE LESSON

This lesson is a prerequisite for the course. While you won’t be directly tested on its content in the exam, it’s assumed you’ve gained this knowledge or skill during your university studies. We strongly recommend reviewing this lesson, as its content may be essential for understanding subsequent parts of the curriculum.

Previously, we covered the future value of a single cash flow. Now, it’s time to switch gears and dive into the present value (PV) of a single cash flow. We’ll also examine how various compounding frequencies impact our calculations. Buckle up and let’s get started!

## Cracking the Present Value Formula

To find the present value, we simply rearrange the future value formula. Here’s the magical formula you’ve been waiting for:

PV = FV / (1 + r)^n

Where:

Let’s use this formula to solve our previous \$1,000 goal example:

EXAMPLE

How much should you deposit today to have \$1,000 in 2 years, given a 5% fixed interest rate?

Plug in the future value (\$1,000), discount rate (5%), and time periods (2) into the PV formula:
PV = \$1000 / (1+0.05)^2 = \$907

You need to deposit \$907 today to achieve your goal.

## Using the Present Value Formula in Real-Life Scenarios

Now that we have the formula, let’s apply it to a few examples involving different compounding frequencies and scenarios.

EXAMPLE

Semi-annual compounding: \$905.95 (deposit today to have \$1,000 in 2 years, with a 5% annual interest rate compounded semi-annually)

EXAMPLE

## Conclusion

By rearranging the future value formula, we’ve uncovered the present value formula that can help us determine how much we need to deposit today for various goals. Remember to adjust the interest rate (r) and the number of periods (n) based on the compounding frequency.

## ✨ Visual Learning Unleashed! ✨ [Premium]

Elevate your learning with our captivating animation video—exclusive to Premium members! Watch this lesson in much more detail with vivid visuals that enhance understanding and make lessons truly come alive. 🎬