Classic Financial II manual · Chapter 8 of 16

Cash flows, NPV and IRR

Enter uneven cash flows with frequencies, then find the net present value and the internal rate of return.

8.1Enter a series of cash flows#

Press CF to open the cash-flow worksheet. CF0 is the starting cash flow (usually negative: the money you invest). Press ↓ for C01, the first later cash flow, and then F01, how many times in a row it happens (1 if you skip it). Each new C line appears when you enter the one before. Up to 32 cash flows can be entered.

Invest 100 now, receive 60 in each of the next two years.

The cash-flow worksheet opens at CF0. The display shows: CF0= 0.00. — The cash-flow worksheet opens at CF0.

Example 8.1

Enter an investment and two returns

CF0 is -100, C01 is 60, skip F01 and enter 60 for C02.
CF100+/-ENTER↓60ENTER↓↓60ENTER

Example 8.2

Use a frequency

CF0 = -7,000, then 3,000 once, then 5,000 four times.
CF7000+/-ENTER↓3000ENTER↓↓5000ENTER↓4ENTER

8.2Find the net present value (NPV)#

NPV adds up the cash flows after discounting each at the interest rate you give. A positive value means the investment earns more than that rate.

NPV = CF_0 + \sum_{t=1}^{n}\frac{CF_t}{(1+r)^t}

Net present value.

Press NPV, type the rate per period in I and press ENTER, move ↓ to NPV and press CPT.

Example 8.3

NPV at 10%

Enter the cash flows, open NPV, enter 10 for the rate, then compute.
CF100+/-ENTER↓60ENTER↓↓60ENTERNPV10ENTER↓CPT

Example 8.4

NPV with repeated cash flows

The series with a repeated flow, at 20%.
CF7000+/-ENTER↓3000ENTER↓↓5000ENTER↓4ENTERNPV20ENTER↓CPT

8.3Find the internal rate of return (IRR)#

IRR is the rate at which the NPV is exactly zero. Enter the cash flows, press IRR and then CPT.

0 = CF_0 + \sum_{t=1}^{n}\frac{CF_t}{(1+\text{IRR})^t}

IRR solves for the rate that makes NPV zero.

Example 8.5

IRR of an investment

With the same cash flows, open IRR and compute.
CF100+/-ENTER↓60ENTER↓↓60ENTERIRRCPT

Example 8.6

IRR with more digits

Show nine decimals first.
CF100+/-ENTER↓60ENTER↓↓60ENTERIRRCPT2NDFORMAT.9ENTER2NDQUITCPTIRR

Example 8.7

IRR when there is no sign change

All cash flows positive: no solution.
CF100ENTER↓60ENTERIRRCPT

8.4Delete or insert a cash flow#

Move to a C line and press 2NDDEL↑ (DEL) to remove that cash flow, or 2NDINS↓ (INS) to insert a blank one before it. 2NDCLR WORKCE/C clears the whole worksheet.

Example 8.8

Delete a cash flow

Enter the series, go back to C02 and delete it. The next line is C01 again.
CF7000+/-ENTER↓3000ENTER↓↓5000ENTER↓4ENTER↑↑↑2NDDEL↑

Example 8.9

Insert a cash flow

Insert a blank flow before C01; it appears as 0.
CF7000+/-ENTER↓3000ENTER↓↓5000ENTER↓4ENTER↑↑↑2NDINS↓

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