This applies to any calculator that has the time value of money (TMV) and net present value (NPV) function. **Net Present Value Formula**

NPV = Σ ( pmt_k ÷ (1 + rate/100)^k for k = 0 to n )

pmt_k: payment for each period k

rate: the periodic rate**Breaking Cash Flow Groups**

A lot of financial calculators (Texas Instruments BA II Plus, BA II Plus Professional, HP 10 bII+, HP 17bii+) allow for a cash flow to have a frequency greater than 99 (to most likely higher limit of 999). However, the popular HP 12C and older financial calculators allows a frequency limit of 99.

This comes into play when finding the net present value of payments of a pension and retirement plans.

For example:

Evaluate a pension factor of the following payment structure:

Initial Cash Flow: 0

Cash Flow Set 1: 1 for 120 flows

Cash Flow Set 2: 0.9 for 180 flows

Cash Flow Set 3: 0.8 for 180 flows

Periodic Rate: 0.45%

Cash Flow Setup:

CF0 = 0

CF1 = 1; FRQ1 = 120

CF2 = 0.9; FRQ2 = 180

CF3 = 0.8; FRQ3 = 180

Calculated NPV = 182.88

Here is the same problem with breaking large groups into smaller ones. Let's say 99 is the frequency limit. Hence: 120 = 99 + 21 and 180 = 99 + 81. So here it is with the large cash flow frequencies split. This can be used with the HP 12C.

Periodic Rate: 0.45%

Cash Flow Setup:

CF0 = 0

CF1 = 1; FRQ1 = 99

CF2 = 1; FRQ2 = 21

CF3 = 0.9; FRQ3 = 99

CF4 = 0.9; FRQ4 = 81

CF5 = 0.8; FRQ5 = 99

CF6 = 0.8; FRQ6 = 81

Calculated NPV = 182.88**Net Future Value (NFV) and Net Utility Stream (NUS)**

Some advanced financial calculators have the net future value (NFV) and net utility stream (NUS) functions. But this section will show how to calculate NFV and NUS using the NPV and TVM functions.

Steps:

1. Enter the cash flows and periodic interest rate.

2. Calculate NPV. Store this amount in memory as needed.

3. Set up the TVM variables as such:

For calculating NFV:

P/YR (payments per year) = 1

N = total number of cash flows

I = periodic interest rate

PV = -NPV (enter the NPV then press the change sign)

PMT = 0

Compute FV. (that is the NFV)

For calculating NUS:

P/YR (payments per year) = 1

N = total number of cash flows

I = periodic interest rate

PV = -NPV (enter the NPV then press the change sign)

FV = 0

Compute PMT (that is the NUS).

Let's go through a couple of examples:

Example 1:

Periodic Rate: 5%

Initial Cash Flow: -1000 (Flow 0)

Cash Flow 1: 100

Cash Flow 2: 250

Cash Flow 3: 500

Cash Flow 4: 750

Cash Flow 5: 500

NPV = 762.70

Computing NFV:

P/YR = 1

N = 5

I = 5

PV = -762.70

PMT = 0

Compute FV: 973.43 (NFV = 973.43)

Computing NUS:

P/YR = 1

N = 5

I = 5

PV = -762.70

FV = 0

Compute PMT: 176.16 (NUS = 176.16)

Example 2:

Periodic Rate: 4.75%

Initial Cash Flow: -1000 (Flow 0)

Cash Flow 1: 200

Cash Flow 2: -500

Cash Flow 3: 500

Cash Flow 4: -100

Cash Flow 5: 800

Cash Flow 6: 1000

NPV = 478.51

Computing NFV:

P/YR = 1

N = 6

I = 4.75

PV = -478.51

PMT = 0

Compute FV: 632.14 (NFV = 632.14)

Computing NUS:

P/YR = 1

N = 6

I = 4.75

PV = -478.51

FV = 0

Compute PMT: 93.52 (NUS = 93.52)

Hopefully this helps. Have a great day and I will talk to you next time!

Eddie

This blog is property of Edward Shore. 2014

A blog is that is all about mathematics and calculators, two of my passions in life.

## Thursday, March 27, 2014

### Finance Calculators: Tips and Tricks with the Cash Flow Operation

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