## Calculators in the CFA Exam

Although the CFA exam isn’t a number crunching exam, you will come across numerous questions that require the use of a calculator. Your two weapons of choice are the Texas Instrument BA II Plus and the Hewlett Packard 12C. Before buying your calculator, make sure to read the CFA Exam Calculator Policy that can be found here.

Also, if you are undecided between the two makes and you would like to try them, both brands have apps that you can go to your phone’s App Store and download. In terms of functionality the apps are identical to the physical calculators.

I will be using the BA II Plus for my explanations and examples (I will make a separate tutorial for Hewlett Packard lovers)

(1) Present Value/Future Value [Priority = High]

What is it?  Other than being able to quickly perform basic arithmetic operations on your calculator, I think this is probably one of the most important things you will need to be able to do. You will be given the amount of money in the bank account (PV), the prevailing interest rate and the period of time over which the interest will compound and from this you will need to compute the future value. You can be given any of the inputs and solve for the missing one.

If you have started with the basics and the concept of Time Value of Money is obscure to you, you might find this article helpful.

This is also applicable to fixed income where you have the market price of the bond, coupon payments and coupon payments frequency and you will need to compute the IRR of the bond. You can easily compute the present value of annuities or lease payments in Financial Reporting. Yes, simple Time Value of Money calculations are ubiquitous on the CFA exams so let’s get started.

Examples:

Q. A bond is trading at $102, it pays 5% coupon per annum and matures in 2 years. What is the bond’s yield? A. Mathematically this is what you would see if you applied the formula for calculating the yield: ${ Bond Price } = \frac { C f _ { 1 } } { ( 1 + y ) ^ { 1 } } + \frac { C f _ { 2 } + \text { FaceValue } } { ( 1 + y ) ^ { 2 } }$ If we look at the above formula for calculating the present value of a bond we can see that we are given everything except the y (for those who have studied corporate finance you can see that this is comparable to getting the IRR of a project), for the face value we can assume that it pays$100 at maturity.  This gives us the below formula:

$102 = \frac { 5 } { ( 1 + y ) ^ { 1 } } + \frac { 5 + 100 } { ( 1 + y ) ^ { 2 } }$

We will be using the grey buttons of our BA II Plus in the red box.

After ensuring that you have cleared the memory (2ND function + CE|C)

2 N button (you will see N = 2)

-102 PV (you will see PV = -102, make sure to put the negative sign here)

5 PMT (you will see PMT = 5, this was calculated as coupon rate * par or 5% * 100 = 5)

100 FV (you will see FV = 100)

Now that you have keyed in all the data, press the “CPT” key on the top left corner and press “I/Y”. If you keyed in everything correctly you will see that your yield is around 3.94%. If you press CPT and any of the inputs that you keyed in, you can verify what data has been entered. For example CPT PMT will still show you 5.

This was a very brief example but try playing around with the numbers, try changing the assumptions; for example you could easily verify that the price of the bond falls as you increase the Yield (I/Y) by gradually increasing the yield.

My example assumed that the coupon payment was 5% annual but if you were told instead that the coupon was 2.5% semi-annual, remember to also multiple the N * 2. At first, if you are not sure draw a diagram of all the future cash flows.

(2) NPV/IRR [Priority = Medium]

What is it?  Although there is an overlap with the previous topic, I thought this part deserved its own section. With regards to overlap I mean that we are still asking the calculator to compute present values, summing them or solving for IRRs. For some examples you can use the PMT button as shown above to get an answer to NPV and IRR questions. However, the limitation is that PMT only takes the same cash flows, i.e. if you are looking for the present value of something that pays $100 over 10 years at a fixed rate, let’s say 5% cost of capital, then you can just key in 10 N with 5 I/Y followed by 100 PMT and 0 FV then pressing CPT PV to get your answer of -$772.17.  What about a question to calculate the present value of a project that requires an investment of -$1000 at initiation or year 0, then pays$500 in year 1, $300 in year 2 and$400 in year 3. Your cost of capital is 3%.  This is where you cannot use PMT and you need to key in the cash flows for discounting.

Examples: I will use the example that I just introduced. Again this is a simplified example to illustrate the steps and you should definitely expect harder questions.

The below formula will yield the NPV for this project:

$NPV = - \text {Initial Investment} + \frac { C F _ { 1 } } { ( 1 + r ) ^ { 1 } } + \frac { C F _ { 2 } } { ( 1 + r ) ^ { 2 } } + \frac { C F _ { 3 } } { ( 1 + r ) ^ { 3 } }$

Plugging in the numbers we get:

$1,000 + \frac { 500 } { ( 1 + 0.05 ) ^ { 1 } } + \frac { 300 } { ( 1 + 0.05 ) ^ { 2 } } + \frac { 400 } { ( 1 + 0.05 ) ^ { 3 } } \cong 93.83$

Now let’s obtain this number on the calculator.

CF (this button just next to the yellow 2nd key), you should see CF(0) = 0, now just to be sure that we don’t have any data from previous exercises, please clear the memory by pressing 2ND function + CE|C. Once you have done this you can press the up and down arrow keys that are found on the top right next to the ON/OFF button to see what data is stored. You should see CF(0) = 0, C01 = 0, F01 =0. We are ready to start:

CF(0) = -1000 ENTER, you will see CF(0) = -1000. Press the down arrow to key in the next cash flow.

C01 = 500 ENTER you will see C01 = 500. If you press the down arrow key you will see F01 = 1. This indicates the frequency of the cash flows. For example if you want the same cash flow of 500 being paid 3 times from years 1 to 3 then you can enter 3. In our case we have only one payment so we will keep the default value of 1 and press the down arrow again.

Now you will see C02 and you will be able to enter the second cash flow of 300. Repeat this for the final cash flow of 400 and once you have entered all the cash flow data we can compute the NPV.

You should see C03 = 400 on your calculator. Now press the NPV button and you will see I = 0 on your calculator. Key in 5 and then press ENTER (important to note that 5 will be 5% so do not enter 0.05 otherwise you will enter 0.05%) now press the down arrow and you will see NPV = 0. Press the CPT key on the top left and you will see the NPV result of 93.83 and we are done. If you want to amend your rate you can press the up arrow which will display the “I”, enter a new rate and again press the down arrow and press CPT to calculate the NPV on the new updated rate.

(3) Storing Results [Priority = High]

What is it?  You can use the STO and RCL keys to store calculation results and quickly recall them for future use. Before I was aware of this feature I used to write down any interim calculation results on paper, then I used to key in those results in my calculator to perform calculations. This had some drawbacks as it was time consuming and prone to careless errors, not to mention the loss of accuracy due to rounding.

Example: for example let’s say 105.723 is your answer and you want to store this value for future use, press STO and then any number on your number key that you want to use to store this value. Let’s say I want the number “7” to store this value press the key order STO 7. Now try entering any number or clearing your work with CE|C. Now you can recall the previous number that we stored in memory by pressing RCL and “7”, magically 105.723 will appear on your calculator.

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