NFV of uneven cash flows compounded semi-annually

@itsrobwhite

There are two ways you can do this on a BA II Plus Professional.

Before going through them, it is important to note that these cannot be done with the basic version of the BA II Plus, which does not have an NFV feature. This is definitely one of the key advantages of the professional version. Personally, I recommend paying extra for the additional features if possible.

Let’s use the example of Practice Problem 19 from the Time Value of Money reading. An investor makes the following deposits:

Year 1: $4,000
Year 2: $8,000
Year 3: $7,000
Year 4: $10,000

With an interest rate of 4% compounded semiannually, the NFV of these cash flows is $30,446.91.

Method 1

Input the following cash flows into the CF feature:
C01: 0
F01:1
C02: 4,000
F02: 1
C03: 0
F03: 1
C04: 8,000
F04: 1
C05: 0
F05: 1
C06: 7,000
F06: 1
C07: 0
F07: 1
C08: 10,000
F08: 1

Then open the NPV feature and input the semiannual rate of 4%/2 = 2% as the interest rate (I). Go down to NFV (it’s right after NPV) and hit CPT, you’ll get 30,446.90606

This method treats every period as 6 months rather than one year, so deposits are only made every other period.

Method 2

Input the following cash flows into the CF feature:
C01: 4,000
F01:1
C02: 8,000
F02: 1
C03: 7,000
F03: 1
C04: 10,000
F04: 1

Then open the ICONV feature, which you do by hitting [2ND] [2], and enter the following:

NOM: 4 (This is the nominal rate)
C/Y: 2 (This is the number of compounding periods per year)

Hit CPT EFF and you will get an effective annual rate of 4.04

Finally, open the NPV feature and input 4.04 os the interest rate (I). This will also compute 30,446.90696 as the NFV.

Which Method is Better?

Since either method will get you the same answer, it’s really a matter of personal preference. However, I recommend Method 2 because it is more intuitive to think about four annual cash flows rather than 8 semiannual payments – including cash flows of 0 every other period. More importantly, it requires a lot fewer keystrokes in the CF feature. This matters if, like me, you are lazy or if, also like me, your likelihood of committing a calculator error increases exponentially if you are required to enter more cash flows, some of which have a value of zero. 

In short, Method 2 takes less time and carries a lower risk of getting the wrong answer simply because you used the wrong inputs in your calculator. These are important considerations when you are writing a CFA exam.

Don’t Forget

This has been written above, but bears repeating – You can’t use either method with the basic BA II Plus, so be sure to use a BA II Plus Professional.

This should be possible on both calculators. Treat each semi-annual period as a unit of ‘n’, i.e. if the question states a 3 year period then n = 6, i = semi-annual interest, enter the rest of the info and calculate as normal.

method 2 is better..thanks

woooooooooooooooooooooooooooooooooooow, thank u so much for this