Series of Cash Flows

Series of Cash Flows | CFA Level I

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.

Today, we’re going to explore time value of money problems with multiple cash flows. We’ll cover cases with regular and uneven cash flows, using time value of money functions on your calculator.

Regular Cash Flows: Methods to Compute Future Value

So far, we’ve focused on single cash flow time value problems. But what if an investor makes regular investments of $100 per year? There are three methods to calculate the future value of these cash flows:

  1. Compute the future value of each cash flow separately and sum them up.
  2. Apply a general formula for regular cash flows.
  3. Use the time value of money (TVM) functions on your calculator.

Method 1 is straightforward but can be time-consuming for many cash flows. Method 2 is less intuitive and not recommended. Method 3 is the most efficient and versatile.

Using TVM Functions on Your Calculator

To use TVM functions, we recommend the Texas Instruments BA II Plus calculator. It has dedicated buttons for the following:

Timeline and Cash Flow Sign Conventions

When inputting cash flows into your calculator, remember the sign conventions:

  • Negative cash flow = money flowing out of the investor (above the timeline).
  • Positive cash flow = money flowing back to the investor (below the timeline).

Working Through an Example with TVM Functions

EXAMPLE

An investor places $1,000 in an investment account that grows at 6% per year. The account gives a guaranteed $30 dividend at the end of each year. How much is the expected amount left in the account after 5 years?

Here’s how to input values into the calculator:

  1. Clear TVM memory: Press “Second” then “Clear TVM.”
  2. Input N: Press “5” then “N.”
  3. Input IY: Press “6” then “IY.”
  4. Input PV: Press “1000,” then “Negative,” then “PV.”
  5. Input PMT: Press “30” then “PMT.”
  6. Compute FV: Press “Compute” then “FV.”

The result is $1,169.

Adjusting for Payments at the Beginning of Periods

If payments are made at the beginning of periods, set your calculator to “Begin” mode:

  1. Press “2ND,” “BGN,” “2ND,” and “SET.”

To switch back to “End” mode (default), repeat the sequence.

Uneven Cash Flows: Dealing with Irregular Payments

But what if the cash flows aren’t regular? For example, the investor contributes $200 in the second year instead of $100. In this case, you can’t use Methods 2 and 3 because they assume equal payments in every period. So, you’ll need to fall back on Method 1:

  1. Compute the future value of each cash flow individually.
  2. Sum up the results to get the total future value.

And that’s it! You’ve learned how to work with multiple cash flows using time value of money functions on your calculator. Keep practicing, and you’ll master these techniques in no time. See you in the next lesson, where we’ll discuss annuities!

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