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RPN Financial 12 manual · Chapter 9 of 16

Cash flows: NPV and IRR

Enter an uneven series of cash flows with CF0, CFj and Nj, then find the net present value and the internal rate of return.

9.1What cash flows are#

A project often has an initial cost and then payments that are not all the same. The cash-flow keys store up to 20 flows (the first and 19 more). Then fNPVPV (NPV) finds what they are worth today at your discount rate, and fIRRFV (IRR) finds the rate at which the project breaks even.

NPV=CF0+∑j=1NCFj(1+i)jNPV=CF_0+\sum_{j=1}^{N}\frac{CF_j}{(1+i)^{j}}
Net present value at a rate i per period.
NPV(IRR)=0NPV(\mathrm{IRR})=0
The internal rate of return is the rate at which the net present value is zero.

Cash coming in is positive and cash going out is negative.

9.2Enter the cash flows#

Key in the first flow (usually the cost, negative) and press gCF₀PV (CF₀). Key in each later flow and press gCFjPMT (CFj). Entering CF₀ clears any earlier flows.

0123−10,000CF₀+3,000CF₁+4,200CF₂+6,800CF₃
A project: pay 10,000 now and receive 3,000, 4,200 and 6,800 over three years.
Example 9.1

Count the flows

  1. Enter the flows, then recall n. The n register counts the flows after the first.

    10000CHSgCF₀PV3000gCFjPMT4200gCFjPMT6800gCFjPMTRCLn
Result of the example "Count the flows" The display shows: 3,000.00 / 4,200.00 / 6,800.00 / 3.00.
You should see3.00
Example 9.2

See a stored flow

  1. The flows are stored in R0, R1, R2 and so on. Recall R2.

    10000CHSgCF₀PV3000gCFjPMT4200gCFjPMT6800gCFjPMTRCL2
Result of the example "See a stored flow" The display shows: 3,000.00 / 4,200.00 / 6,800.00 / 4,200.00.
You should see4,200.00

9.3Net present value (NPV)#

Key in the discount rate per period and press i, then press fNPVPV (NPV). A positive NPV means the project earns more than the discount rate.

Example 9.3

NPV of the project at 10%

  1. Enter the flows. Key in 10 and press i, then f, NPV.

    10000CHSgCF₀PV3000gCFjPMT4200gCFjPMT6800gCFjPMT10ifNPVPV
Result of the example "NPV of the project at 10%" The display shows: 4,200.00 / 6,800.00 / 10.00 / 1,307.29.
You should seeA positive NPV of 1,307.29, so the project beats a 10% return.
Example 9.4

NPV with zero discount rate is just the sum

  1. A 0 rate adds the flows with no discounting.

    1000CHSgCF₀PV100gCFjPMT0ifNPVPV
Result of the example "NPV with zero discount rate is just the sum" The display shows: -1,000.00 / 100.00 / 0.00 / -900.00.
You should see-900.00

9.4Internal rate of return (IRR)#

After entering the flows, press fIRRFV (IRR). The answer is the rate per period, in percent, at which NPV is zero. It is stored in the i register. The flows must include at least one positive and one negative, or you see Error 7.

Example 9.5

IRR of the project

  1. Enter the flows and press f, IRR.

    10000CHSgCF₀PV3000gCFjPMT4200gCFjPMT6800gCFjPMTfIRRFV
Result of the example "IRR of the project" The display shows: 3,000.00 / 4,200.00 / 6,800.00 / 16.34.
You should seeThe project returns 16.34 percent a year.
Example 9.6

IRR with four flows

  1. 1000 out, then 500, 400, 300 and 100 back.

    1000CHSgCF₀PV500gCFjPMT400gCFjPMT300gCFjPMT100gCFjPMTfIRRFV
Result of the example "IRR with four flows" The display shows: 400.00 / 300.00 / 100.00 / 14.49.
You should see14.49
Example 9.7

Show more decimals

  1. Press f 4 afterwards for four decimals.

    1000CHSgCF₀PV500gCFjPMT400gCFjPMT300gCFjPMT100gCFjPMTfIRRFVf4
Result of the example "Show more decimals" The display shows: 400.0000 / 300.0000 / 100.0000 / 14.4888.
You should see14.4888
Example 9.8

IRR with no sign change is an error

  1. A flow of only positive amounts has no IRR.

    1000gCF₀PV500gCFjPMTfIRRFV
Result of the example "IRR with no sign change is an error" The display shows: Error 7 / 0.00 / 0.00 / 1,000.00 / 500.00.
You should seeError 7

9.5Repeated flows: Nj#

If the same flow repeats several times in a row, enter it once with gCFjPMT (CFj), then key in the number of repeats and press gNjFV (Nj). Nj applies to the last flow entered. The number must be a whole number from 1 to 99.

0123−1,000CF₀+300+300+300
CF₀ = −1,000, then CF₁ = 300 repeated 3 times.
Example 9.9

NPV with a repeated flow

  1. CF₀ −1000, CFj 300, Nj 3, then 10 i and NPV.

    1000CHSgCF₀PV300gCFjPMT3gNjFV10ifNPVPV
Result of the example "NPV with a repeated flow" The display shows: 300.00 / 3.00 / 10.00 / -253.94.
You should see-253.94

9.6Cash-flow limits and errors#

  • Up to 20 flows: CF₀ and 19 CFj. More gives Error 6.
  • Nj must be a whole number 1 to 99, and a flow must exist. Otherwise Error 6.
  • IRR needs both positive and negative flows (Error 7). If the calculation cannot settle on a rate, you see Error 3.
Example 9.10

Too many flows

  1. Enter CF₀ and then 20 more flows.

    1CHSgCF₀PV1gCFjPMT1gCFjPMT1gCFjPMT1gCFjPMT1gCFjPMT1gCFjPMT1gCFjPMT1gCFjPMT1gCFjPMT1gCFjPMT1gCFjPMT1gCFjPMT1gCFjPMT1gCFjPMT1gCFjPMT1gCFjPMT1gCFjPMT1gCFjPMT1gCFjPMT1gCFjPMT
Result of the example "Too many flows" The display shows: Error 6 / 1.00 / 1.00 / 1.00 / 1.00.
You should seeError 6

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