This is “Multiple Cash Flows”, section 7.1 from the book Finance for Managers (v. 0.1).
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Jamie was up late watching infomercials, and saw that she could purchase the latest wonder product for either $43, or three easy monthly installments (the first payment is immediate) of $15. If she earns 4% APR compounded monthly in her savings account, which option should she pick?
The trick to comparing cash flows usually is to PV them all to the same point in time. When they have been discounted to the same time, then they can be added, subtracted, or compared without worry. Discounting all of the cash flows for an investment to the present, adding inflows and subtracting outflows, is called finding the net present value (NPV)Discounting all of the cash flows for an investment to the present, adding inflows and subtracting outflows.. When deciding among investments, we typically wish to choose the one with the highest (or, in some cases, least negative) NPV.
The NPV of paying $43 immediately is obviously−$43. To find the NPV of the installment plan, we should look at the timeline.
Figure 7.1 NPV Example Timeline
4% APR compounded monthly gives a monthly interest rate of 0.3333%. (More discussion of example)
Many financial calculators have an NPV solving functionality to handle multiple cash flows. Please check the appendix for differences between the models, but the standard process is:
In our example problem, the initial cash flow (CF0) is −$15. Both of the next two cash flows are −$15, so we can either enter them separately (C01: −15; F01: 1; C02: −15; F02: 1) or tell the calculator to repeat the entry (C01: −15; F01: 2). Both methods will give the proper answer. Here are the precise keystrokes for the latter method:<CF> <2ND> <CLR WORK> −15 <ENTER> <DOWN ARROW> −15 <ENTER> <DOWN ARROW> 2 <ENTER> <NPV> 0.3333 <ENTER> <DOWN ARROW> <CPT>
Remember that interest rate should be entered as a percentage (0.3333 in this case, not 0.003333).
The corresponding spreadsheet function is:=NPV(periodic rate, cash flows from period 1 to n) + net of initial cash flows
Note that the spreadsheet function expects cash flows to start in the first period: any initial cash flows need to be netted and added to the result. Like the financial calculator, positive values should be used for cash inflows, and negative values for outflows.
Figure 7.2 NPV in a Spreadsheet