0C. Introduction to Time Value of Money (TVM) Calculations for CFA Level 1 (with Examples)

Hi, in this post, we will talk about the TVM calculations.

Time Value of Money or TVM calculations are one of the most fundamental calculations that you need to know for the CFA exam.

Before we discuss how to do the TVM calculations, check your BA II Plus calculator to ensure that :- 

a.) the no. of digits after decimal is at least 6, and,

b.) the P/Y value is set to 1. 

If you don’t know how to do this, please watch our video CFA Calculator: Introduction and Settings :-

Now, ensure that you are familiar with the following keys on your BA II Plus calculator:-

• PV key which is used for Present value or Current Value or Value at time 0

• FV key which is used for Future value or Value at time t

• N which signifies Number of compounding periods

• I/Y key which is used for Interest rate per compounding period

• PMT key which is used for Per period payments or Annuity payments, or constant periodic cash flow

• CPT key which signifies Compute or calculate

Remember FV = PV(1 + I/Y)^N

Drawing a time line

The next thing I will talk about is the significance of drawing a time line, a chronological order of events in any Quantitative calculation for CFA exam. Before you start solving any TVM calculation; I would strongly recommend drawing a time line of events. This is nothing but a linear representation of various data that is provided in the question.

This is important because most of the times you are trying to compare investments at a specific point in time. If you compare investments at time 0, you are comparing present value; while if you compare investments at time t, you are comparing future value.

The easiest way to understand this is through examples. So let’s solve a few examples:-

Example 1

Let’s say we want to find the value of an Investment of a 1000$, 3 years from now. What other piece of information we need?

We definitely need the Interest rate, because we need to know at what rate our investment can earn money for us. Let’s say the Interest rate is 10%.

What else?

We also need to know the frequency of compounding, i.e. how frequently will we earn interest on our interest.

Let’s say we are compounding annually.

Also, Remember FV = PV(1 + I/Y)^N

So,

After 1^st year the value of our investment will be PV(1+I/Y) = 1000(1+ 0.1) = 1000 *1.1 = 1100

After 2^nd year the value of our investment will be PV(1+I/Y)²  = 1000(1+ 0.1)²  = 1000 *1.21 = 1210

After 3^rd year the value of our investment will be PV(1+I/Y)³  = 1000(1+ 0.1)³  = 1000 *1.331 = 1331

Let’s draw a graph of the values we obtain here:-

As you can see, our investment of 1000$ became 1100$ after a year, 1210 after 2 years and 1331 after 3 years. We are progressively earning more Interest every year, because we are earning interest on interest, i.e. compound interest.

If you are having difficulties understanding this, you should revise Compound Interest concepts.

So, how do we do this in BA II Plus calculator?

For this example :-

PV=1000;  N =3; I/Y=10; PMT=0; and we need to find out FV

If you have any issues solving this, watch this video :-

As you can see, using the BA II Plus calculator makes these calculations very simple.

Example 2

Let’s say we want to find the value of an Investment of a 1000$, 3 years from now, compounded semi-annually. The rate of interest is 10%.

Let’s draw a timeline:-

As we are compounding semi-annually,

PV=1000;  N =6; I/Y=5; PMT=0; and we need to find out FV

If you have any issues solving this, watch this video :-

Example 3

Let’s say we want to find the present value of an Investment which yields 1331$, 3 years from now. The rate of interest is 10% compounded annually.

Let’s draw a timeline:-

As we are compounding annually,

FV=1331;  N =3; I/Y=10; PMT=0; and we need to find out PV

If you have any issues solving this, watch this video :-

Example 4

Let’s say we want to find out in how many years will an initial investment of 1000$, yield 1331$ if the rate of interest is 10% compounded annually.

Let’s draw a timeline:-

As we are compounding annually,

FV=1331;  PV = 1000; I/Y=10; PMT=0; and we need to find out N

Did you get an error when using the values above? WHY?

Let’s watch this video

Example 5

Let’s say we want to find out at what Interest rate will an initial investment of 1000$, yield 1331$ in 3 years, if the interest is compounded annually.

Let’s draw a timeline:-

As we are compounding annually,

FV=1331;  N =3; PV=-1000; PMT=0; and we need to find out I/Y

Let’s watch this video

As you can see, we can find out any missing information as long as we are provided with rest of the values.

You can watch a video explaining the points discussed in this blog here :-

If you have reached this far in this blog, congratulations! You can now start practicing TVM calculations on your own.

We will discuss Cash Flow calculations in the next blog.

For more CFA tips watch the posts in this blog. You will also find a number of CFA topics discussed on this blog in simple