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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