Chapter 5 Summary
Key Concepts
 5.1 Net Present Value
 The characteristics of making decisions including decision types, monetary sources, and interest rates.
 Making decisions through net present value.
 5.2 Internal Rate of Return
 Using internal rate of return to choose whether to pursue one course of action.
Glossary of Terms
Cash Flow. A movement of money into or out of a particular project.
Cost of Capital. A weighted average of all of the debt and equity financing rates used to provide needed funds for a project.
Internal Rate of Return ([latex]IRR[/latex]). The annual rate of return on the investment being made such that the net present value of all cash flows in a particular project equals zero.
Net Present Value ([latex]NPV[/latex]). The difference in today’s dollars between all benefits and costs for any given project.
Formula & Symbol Hub
Symbols Used
 [latex]NPV[/latex] = net present value
 [latex]IRR[/latex] = internal rate of return
Formulas Used

Formula 5.1 – Net Present Value
[latex]NPV = \text{(Sum of}\;PV\;\text{of All Future Cash Flows)} − \text{(Initial Investment)}[/latex]
or
[latex]NPV = \text{(Sum of }\;PV\;\text{of Cash Inflows)} − \text{(Sum of}\;PV\;\text{of Cash Outflows)}[/latex]
Calculator

Cash Flow Worksheet
 Access the cash flow function by pressing [latex]CF[/latex] on the keypad.
 Always clear the memory using 2nd CLR WORK so that any previously entered data is deleted.
 Use the up arrow and down arrow to scroll through the various lines.
 Strictly adhere to the cash flow sign convention when using this function and press ENTER after keying in the data.
 To exit the window, press 2nd QUIT.
 The various lines are summarized below:
 [latex]CFo[/latex] = any cash flow today.
 [latex]CXX[/latex] = a particular cash flow, where [latex]XX[/latex] is one of a series of cash flow numbers starting with [latex]01[/latex]. You must key in cash flows in order from the first time segment to the last. You cannot skip a time segment, even if it has a value of zero, because each time segment is a placeholder on the timeline.
 [latex]FXX[/latex] = the frequency of a particular cash flow, where [latex]XX[/latex] is the cash flow number. It is how many times in a row the corresponding cash flow amount occurs. This allows you to enter recurring amounts together instead of keying them in separately. By default, the calculator sets this variable to [latex]1[/latex].

Net Present Value
 Use this function after you have entered all cash flows.
 Press [latex]NPV[/latex] on the keypad to access the function.
 Use the up arrow and down arrow to scroll through the window.
 To exit the window, press 2nd QUIT.
 This window has two lines:
 [latex]I[/latex] = the matching periodic interest rate for the interval of each time segment.
 [latex]NPV[/latex] = the net present value. Press [latex]CPT[/latex] to calculate this amount.

Internal Rate of Return
 Use this function after you have entered all cash flows.
 Press [latex]IRR[/latex] on the keypad to access the function.
 Press [latex]CPT[/latex] button to perform the calculation. The output is in percent format.
 To exit the window, press 2nd QUIT.
_{Cash Flows 1: Net Present Value (NPV) and IRR Calculations by Joshua Emmanuel [2:52] (transcript available).}
Attribution
“8.4 Chapter Summary” from Business and Financial Mathematics by Valerie Watts is licensed under a Creative Commons AttributionNonCommercialShareAlike 4.0 International License, except where otherwise noted.
“Chapter 15 Summary” from Business Math: A StepbyStep Handbook (2021B) by J. Olivier and Lyryx Learning Inc. through a Creative Commons AttributionNonCommercialShareAlike 4.0 International License unless otherwise noted.