###### Level I of the CFA® Exam – Topi ...

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Analysts may use either a Texas Instruments BA-II Plus or HP-12C (or the various editions of either calculator) when taking the CFA exams. Trained users of either calculator can perform all necessary tasks in relatively the same amount of time so there is no obvious best choice in terms of exam viability. In most cases, it probably makes sense to choose the calculator you’re the most comfortable with so you spend less of your valuable study time dedicated to learning calculation steps. Ideally, you should choose your calculator before you begin studying so you use the same calculator as you work through examples and practice tests. If you have one of each calculator but plan to use the BA-II Plus as your primary calculator then it may still be a good idea to try and borrow another BA-II Plus from a friend or co-worker to use as a backup in the unlikely event that you’ll need it.

If you’re unfamiliar with both calculators and have to choose which one to buy, there are a few factors to keep in mind. First of all, a new Texas Instruments BA-II Plus ($30) is a bit cheaper than a new HP-12C ($45-50). Secondly, the HP-12C uses Reverse Polish Notation (“RPN”), which means that operators follow their operands. In other words, instead of calculating the sum of three and four by entering **2+2=**, you would do so by inputting **2enter2+**. There are no parentheses buttons on an HP-12C calculator as the order of operations is implied by the order of inputs. Since most people are unfamiliar with RPN, the HP-12C may have a somewhat steeper learning curve than the BA-II Plus. Finally, some believe the HP-12C looks a bit sleeker than the Texas Instruments BA-II Plus, but calculator appearance may not be a priority when taking the exam.

In this blog post, we will focus on the HP-12C for those wanting to learn or refresh their memory on the basic steps involved in the most important calculations required for the CFA exams. For those familiar with the Texas Instruments BA-II Plus, a great drill would be to try to do the same calculations shown in this article with the BA-II Plus. If you are looking for more exam-style CFA questions, simply register an account at https://analystprep.com.

*Example: Marco is currently 47 years old and hopes to retire in 18 years with a $2 million nest egg. If he currently has $750,000 saved up, and assuming he can earn a 7% annual rate(compounded monthly) on his investments, how much will Marco need to put away at the end of each month to reach his goal?*

Since we need to find a monthly amount, there are a few adjustments that will need to be made.

First, we’ll enter the 18 years and adjust to monthly periods by using the 12x modifier on the n button.

**18g -> n**

Next, we’ll need to enter an adjusted interest rate, except this time we’ll divide the number by 12.

**7g -> i**

Finally, we have to enter in Marco’s current savings and his goal by retirement. The current savings should be entered as a negative number because that’s essentially how much is being invested or “spent” at time zero. We can change the sign by using the CHS button.

**750000CHSPV**

**2000000FV**

Finally, we find the missing piece of the equation by hitting the payment button.

**PMT = 1,472.89**

Marco will need to save at least $1,472.89 a month to hit his goal by retirement.

If instead, Marco was to invest his money at the beginning of each month, we can make a quick adjustment by using the **BEG** modifier on the 7 button to see how much he would need to save each month. (Payments can be reset to the end of each month by using the **END** modifier on the 8 button.)

**g -> 7**

**PMT = 1,464.35**

Because his money is compounding for just a bit longer, he needs to save a bit less money each month.

*Let’s assume that Marco was able to save up exactly $2 million by retirement and now wants to figure out how much money will be left over assuming he will live for another 20 years and will withdraw $100,000 at the beginning of each year. If Marco earned no return on his nest egg, he would have nothing left over in this scenario. However, Marco intends to leave the money invested but wants to reduce the risk of his portfolio. With his new portfolio, Marco estimates that he will earn approximately 5% a year. How much money will be left over after 20 years?*

This time, we don’t have to adjust to monthly amounts so the calculation should be more straightforward. Once again, because the present value is being invested or “spent”, it will be entered as a negative number. For this calculation, though, the payment amount will be positive because it represents how much Marco will receive at the beginning of each year.

**20n**

**5i**

**2000000CHSPV**

**100000PMT**

**g -> 7**

**FV = 1,834,670.23**

Because Marco is opting to remain invested through his retirement, he expects to have more than $1.8 million to leave to his beneficiaries.

*Let’s assume instead that Marco doesn’t want to leave any money behind and actually wants to take out a lump sum now to spend frivolously, leaving the remainder of his nest egg invested at 5%. How much “fun money” can he withdraw from his nest egg of exactly $2 million now if he still intends to withdraw $100,000 at the beginning of each year, but wants to have $0 left in his nest egg after 20 years?*

We first want to figure out how much he needs to invest now to still be able to withdraw $100,000 for the next 20 years.

**20n**

**5i**

**100000PMT**

**g -> 7**

**These inputs don’t change from the previous problem, but now we enter “0” for future value.**

**0FV**

**PV = -1,308,670.23**

Now we can just subtract the amount he needs to invest from the amount he currently has saved up to see how much money can be withdrawn now.

**2,000,000 – 1,308,670.23 = 691,467.91**

Assuming Marco’s estimates are correct, he can safely withdraw nearly $700,000.

*Let’s switch to a new fictional character. Paula wants to buy a fancy, new electric car, but the price tag is pretty hefty at $90,000. She is unable to get a loan from a bank because her income is too low so she asks her wealthy parents for a loan. While her wealthy parents want to do everything they can to make Paula happy, they didn’t get rich by making bad investments so they decide to charge their daughter 17.5% interest to compensate for the high risk. If Paula can afford payments of $1,500 at the end of each month, how many months will it take to fully pay off the loan?*

The interest rate will need to be adjusted to a monthly rate. Since Paula is receiving $90,000 in the form of a loan and paying out $1,500 a month, the present value will be entered as a positive amount and the payment will be negative.

**17.5g -> i**

**90000PV**

**1500CHSPMT**

**0FV**

**n = 144**

It will take Paula 144 months, or a full 12 years, to completely pay off the loan from her parents.

*Upon doing the math, Paula’s parents decide they would feel guilty making their daughter pay off a loan for 12 years. They decide 10 years would be a more reasonable amount of time. Without changing the loan amount of $90,000 or monthly payment amount of $1,500, they want to figure out the reduced interest rate to charge their daughter so that they loan can be fully paid in exactly 10 years. What is the interest rate they are looking for?*

**90000PV**

**1500CHSPMT**

**0FV**

These inputs remain the same from the previous problem, but now we’re going to lock in a 10-year payment period.

**10g -> n**

**i = 1.32**

**1.32 x 12 = 15.86**

Paula’s parents can charge their daughter interest of 1.32% a month, or a 15.86% interest rate.

*Bill has become quite wealthy by using the high income (from his position as the portfolio manager of an actively managed equity fund) to invest in stock and bond index funds. Despite his success, Bill is getting bored with his current portfolio, and wants to start branching out to more interesting investments. He is considering the purchase of an ad-based website for $20,000. Bill has a plan to revamp the website to drive more traffic to the site and boost ad revenue, but will need to hire more part-time employees to make the improvements. He has come up with a basic cash-flow model:*

Year |
Purchase/Sale |
Net Income |
Net Cashflow |

0 | ($20,000) | $0 | ($20,000) |

1 | ($10,000) | ($10,000) | |

2 | ($5,500) | ($5,500) | |

3 | $15,000 | $15,000 | |

4 | $15,000 | $15,000 | |

5 | $50,000 | $15,000 | $65,000 |

*What is the internal rate of return Bill can expect to earn on this investment?*

First, we’ll enter the initial investment in time zero by using the **CF**_{0 }modifier on the **PV** button.

**20000CHSg -> PV**

Now we’ll enter each year’s cash flow by using the** CF _{j }**modifier on the

**10000CHSg -> PMT**

**5500CHSg -> PMT**

**15000g -> PMT**

Since the expected cash flows in year 3 and 4 are the same, we can save time by using the **N**_{j }modifier on the **FV** button to repeat the previously entered cashflow for a second period.

**2g -> FV**

Now we’ll enter the final cash flow, which includes expected sales proceeds, and calculate the rate of return.

**65000g -> PMT**

**f -> FV = 28.51**

The website investment is expected to generate an internal rate of return of 28.51%

Due to the highly uncertain nature of the cash flows, Bill wants to use a discount rate of 25%. What is the NPV of the project?

Assuming the previously entered cashflows had not been cleared, we can calculate the NPV by simply inputting the discount rate.

**25i**

**f -> PV = 3,603.20**

The net present value of the website investment is $3,603.20 using a discount rate of 25%.

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