0D. Introduction to Cash Flow (CF) Calculations for CFA Level 1 (with Examples)

Introduction

Hello and welcome back!

In the previous blog, we gained some experience in solving basic TVM questions. If you want to revise your TVM concepts or if you haven’t read our previous TVM blog, you can watch this video:- 

In this blog, we will talk about the Cash flow calculations.

Cash flows can be even or uneven, that is you could be getting the same cash flow every period or different/irregular cash flows in different periods.

Even cash flows are solved similar to the basic TVM calculations. Let’s see an example:-

Example 1

Let’s say we want to find out the present value of an investment that pays 1000$ annually at the end of every year for next 3 years. The rate of interest is 10%.

Let’s draw a timeline:-

In this example, we have multiple cash flows, starting from the end of year 1. Please note that in these types of calculations end of a period is same as the beginning of the next period. For example, end of year 1 is same as the beginning of year 2.

Now,

For this example,

PMT=1000; FV=0 (as we want to find the Present value of the entire stream of payments); N=3; I/Y = 10 and we need to find out PV

So, we will enter FV=0, PMT=1000, N=3, I/Y=10, CPTàPV to get a value of -2486.85.

Remember, the positive or negative sign signifies if the cash flow is an inflow or outflow. In this example, if you made an initial investment of 2486.85$, you will get 1000$ every year for 3 years.

However, if you borrowed 2486.85$ today, you will have to pay 1000$ every year for 3 years.

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

Example 2

Let’s say we want to find out the Future value of an investment that pays 1000$ annually at the end of every year for next 3 years. The rate of interest is 10%.

Let’s draw a timeline:-

Again, we have multiple even cash flows, starting from the end of year 1.

Now, for this example,

PMT=1000; PV=0 (as we want to find the Future value of the entire stream of payments); N=3; I/Y = 10 and we need to find out FV

So, we will enter PV=0, PMT=1000, N=3, I/Y=10, CPTàFV to get a value of - 3310$

If you are having issues with this, watch this video :-

Next, let’s talk about uneven cash flows.

Uneven cash flows can be handled by either handling each cash flow separately or by using the cash flow keys on the BA II plus calculator.

As we are handling variable cash flow amounts, don’t forget to draw a timeline to better visualize the inflow and outflow of money.

Also, remember to use different signs for inflow and outflow of cash. I recommend using positive sign for cash inflows and negative for cash outflows. If you follow a consistent sign system every time, chances of making a mistake are minimized.

Let’s look at some examples:-

Example 3

Let’s say we want to find out the present value of this stream of uneven cash flow. The rate of interest is 10%.

Let’s draw a timeline:-

Please observe a few things here: There is no cash inflow or outflow at the beginning of this project. After 1^st year, there is a cash outflow of a 1000$, which in simple terms means that you are investing/spending a 1000$. After this the Project starts making money and you earn 500$ after year 2, 400$ after year 3 and 300$ after year 4.

We are assuming the rate of return as 10%.

To find the PV of this stream of cash flows, we will handle each cash flow separately.

So,

For CF₁:  FV= -1000, I/Y=10, N=1, PMT=0, CPTàPV        PV= -909.09

For CF₂:  FV= 500, I/Y=10, N=2, PMT=0, CPTàPV           PV=413.22

For CF₃:  FV= 400, I/Y=10, N=3, PMT=0, CPTàPV           PV=300.53

For CF₄:  FV= 300, I/Y=10, N=4, PMT=0, CPTàPV           PV=204.9

So, Total PV = -909.09+413.22+300.53+204.9= 9.56

As the Total PV is positive, this implies cash inflow is greater than cash outflow and this is a profitable investment.

Let’s watch this video:-

Example 4

Let’s say we want to find out the future value of this stream of uneven cash flow. The rate of interest is 10%.

Let’s draw a timeline:-

I am sure you have noticed that these cash flows are exactly the same as in Example 3. The only difference is that we are now going to find out the Future Value at the end of 4^th year.

So,

For CF₁:  PV= -1000, I/Y=10, N=3, PMT=0, CPTàFV        FV= -1331

N is 3 here as this cash flow occurs at end of year 1 and we need to find FV at the end of 4^th year.

For CF₂:  PV= 500, I/Y=10, N=2, PMT=0, CPTàFV           FV=605

For CF₃:  PV= 400, I/Y=10, N=1, PMT=0, CPTàFV           FV=440

For CF₄:  FV=PV=300 as this cash flow occurs at the end of the 4^th year where we are finding the value.

          

So, Total FV = -1331+605+440+300 = 14

Again, as the total FV is positive, this implies cash inflow is greater than cash outflow and this is a profitable investment.

Remember, the decision about the profitability of any project should not be dependent upon the timing of analysis of cash flows, i.e. as long as you analyze all the cash flows at the same time period, you will get the same decision about the profitability of a project.

Is there another way we could have found the Future Value of this Project.

Indeed, if you remember FV = PV(1 + I/Y)^N

So, here FV= 9.56(1+0.1)⁴ 

= 9.56*1.1⁴

=13.996796

=14

Which is same as the FV we calculated here.

The point to note here is that there will be multiple ways to find out the value of a stream of cash flows at any particular time.

Let’s watch this video:- 

Example 5

Now, we will solve example 3 again, but this time we will use the cash flow keys on the BA II plus calculator.

The uneven cash flow stream is shown in the picture below. The rate of interest is 10%. 

Let’s draw a timeline:- 

First of all, we need to clear the values stored in the Cash Flow keys (if any). To do this Press CF à 2^ND àCE/C Key. As you should know by now, anytime we use the 2^ND key, we activate the secondary functions of the keys in the BA II Plus calculator. So, when we press CFà2^NDàCE/C keys, we activate the CLR WORK function which clears the cash flow registers.

It is important to note that before doing any TVM or Cash Flow calculations, we should clear the TVM register and the cash flow registers, respectively.

Now, let’s enter the cash flows.

CF0 = 0

C01 = -1000

C02 = 500

C03 = 400 and

C04 = 300

I/Y = 10

Finally Compute NPV to get 9.56.

I understand this might be new for some of you. Let’s watch this video to see how we can solve this question using a BA II Plus calculator.

I am sure you are now thinking if we can use the Cash Flow keys to get the Future Value of a series of uneven cash flows. Unfortunately, there is no key to do this. We need to find the Present Value and then utilize it to calculate Future Value.

So, for the previous example,

PV= 9.56, I/Y=10, N=4, PMT=0, CPTàFV        FV= -13.99 ≈ 14

This brings us to the end of this blog on Introduction to Cash Flow Calculations for CFA level 1 exam. As you can see, you 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 :-

The next step for you is to practice Cash Flow calculations as much as you can so that you can get comfortable with the ideas presented in this blog.

We will start discussing the Time of Value money Learning Outcome Statements (LOS) for CFA Level 1 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 terms. You can also subscribe to our YouTube Channel on this link