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Texas Instruments Calculator Example: Solving for Unequal Cash Flows

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Cash Flow Worksheet 47

The time line reflects a sequence of cash flows with three sign

changes, indicating that one, two, or three IRR solutions can exist.

• When solving complex cash-flow problems, the calculator might not

find PB, DPB, IRR, and MOD, even if a solution exists. In this case, the

calculator displays Error 7 (iteration limit exceeded).

Example: Solving for Unequal Cash Flows

These examples show you how to enter and edit unequal cash-flow data

to calculate:

• Net present value (NPV)

• Net future value (NFV)

• Payback (PB)

• Discounted payback (DPB)

• Internal rate of return (IRR)

• Modified internal rate of return (MOD)

A company pays $7,000 for a new machine, plans a 20% annual return on

the investment, and expects these annual cash flows over the next six

years:

As the time line shows, the cash flows are a combination of equal and

unequal values. As an outflow, the initial cash flow (CFo) appears as a

negative value.

Year Cash Flow Number Cash Flow Estimate

Purchase CFo -$7,000

1C01 3,000

2–5 C02 5,000 each year

6C03 4,000

Contents

Main Important Information USA FCC Information Concerning Radio Frequency Interference Table of Contents 1 Overview of Calculator Operations..................................1 2 Time-Value-of-Money and Amortization Worksheets...21 3 Cash Flow Worksheet...................................................... 41 4 Bond Worksheet ............................................................. 53 5 Depreciation Worksheet ................................................ 59 Index.............................................................................. 105 6 Statistics Worksheet .......................................................65 7 Other Worksheets ........................................................... 71 Overview of Calculator Operations Turning On the Calculator Turning Off the Calculator Automatic Power Down (APD) Feature Selecting 2nd Functions Reading the Display # $Press " or # to display the previous or next variable in the Setting Calculator Formats Choosing the Number of Decimal Places Displayed Choosing the Angle Units Using Dates Choosing Calculation Methods Resetting Default Values Resetting the Calculator Pressing Performing a Hard Reset Clearing Calculator Entries and Memories Correcting Entry Errors Math Operations Examples of Math Operations Universal Power Parentheses Factorial Random Numbers Combinations n Cr n! nr)!r!( -------------------= -----------------------------= n Pr n! nr)!( Scientific Notation Memory Operations Clearing Memory Storing to Memory Recalling From Memory Memory Examples Calculations Using Constants Example: Multiply 3, 7, and 45 by 8 Keystrokes for Constant Calculations Last Answer Feature Example: Using the Last Answer in a Calculation Using Worksheets: Tools for Financial Solutions Accessing the TVM Worksheet Variables Accessing Prompted-Worksheet Variables Types of Worksheet Variables Enter-Only Variables Compute-Only Variables Automatic-Compute Variables Enter-or-Compute Variables in the TVM Worksheet Enter-or-Compute Variables in Prompted Worksheets Selecting Worksheet Settings Page Page Page TVM and Amortization Worksheet Variables Using the TVM and Amortization Variables Resetting the TVM and Amortization Worksheet Variables Clearing the Unused Variable Entering Positive and Negative Values for Outflows and Inflows Entering Values for I/Y, P/Y, and C/Y Specifying Payments Due With Annuities Updating P1 and P2 Different Values for BAL and FV Entering, Recalling, and Computing TVM Values Entering Cash Inflows and Outflows Generating an Amortization Schedule Generating an Amortization Schedule Manually Generating an Amortization Schedule Automatically Example: Computing Basic Loan Interest Answer: Examples: Computing Basic Loan Payments Computing Monthly Payments Computing Quarterly Payments Examples: Computing Value in Savings Computing Future Value Example: Answer: Computing Present Value Example: Computing Present Value in Annuities Cost Savings for a Present-Value Ordinary Annuity Cost Savings for a Present-Value Annuity Due in a Leasing Agreement Example: Computing Perpetual Annuities Perpetual ordinary annuity Example: Computing Present Value of Variable Cash Flows Page Example: Computing Present Value of a Lease With Residual Value Answer: Example: Computing Other Monthly Payments Example: Saving With Monthly Deposits Answer: Example: Computing Amount to Borrow and Down Payment Answer: Example: Computing Regular Deposits for a Specified Future Amount Answer: Example: Computing Payments and Generating an Amortization Schedule Computing Mortgage Payments Generating an Amortization Schedule Example: Computing Payment, Interest, and Loan Balance After a Specified Payment Computing the Monthly Payment Generating an Amortization Schedule for Interest and Balloon Payment Cash Flow Worksheet Cash Flow Worksheet Variables Resetting Variables Entering Cash Flows Inserting and Deleting Cash Flows Uneven and Grouped Cash Flows Uneven Cash Flows Grouped Cash Flows Entering Cash Flows Deleting Cash Flows Inserting Cash Flows Computing Cash Flows Computing NPV, NFV, PB, and DPB Computing IRR and MOD Example: Solving for Unequal Cash Flows Entering Cash-Flow Data Editing Cash-Flow Data Computing NPV, NFV, PB, and DPB Computing IRR and MOD Example: Value of a Lease with Uneven Payments Computing NPV Page Page Bond Worksheet Bond Worksheet Variables Resetting Bond Worksheet Variables Entering Dates Entering CPN Entering RV Setting the Day-Count Method Setting the Coupon Frequency Bond Worksheet Terminology Entering Bond Data and Computing Results Entering Known Bond Values Setting the Bond Day-Count Method and Coupon Frequency Computing the Bond Price (PRI) Computing the Bond Yield (YLD) Computing Accrued Interest (AI) Example: Computing Bond Price, Accrued Interest, and Modified Duration Computing Bond Price, Accrued Interest, and Modified Duration Depreciation Worksheet Depreciation Worksheet Variables Resetting the Depreciation Worksheet Variables Computing Values for DEP, RBV, and RDV Entering Values for DB and DBX Entering Values for LIF Entering Values for M01 Entering Data and Computing Results Selecting a Depreciation Method Entering Depreciation Data Computing Results for DEP, RBV, and RDV Generating a Depreciation Schedule Example: Computing Straight-Line Depreciation Page Page Statistics Worksheet Statistics Worksheet Variables Resetting Statistics Worksheet Variables Entering Data Points Analyzing One-Variable Statistics Analyzing Two-Variable Statistics Computing Values Automatically Regression Models Correlation Coefficient Entering Statistical Data Computing Statistical Results Selecting a Statistics Calculation Method Computing Results Computing Y' Computing X' Page Other Worksheets The calculator also includes these worksheets: Percent Change/Compound Interest Worksheet Percent Change/Compound Interest Worksheet Variables Resetting the Percent Change/Compound Interest Worksheet Variables Entering Values Computing Values Example: Computing Percent Change Example: Computing Compound Interest Example: Computing Cost-Sell-Markup Interest Conversion Worksheet Comparing the Nominal Interest Rate of Investments Resetting Variables Converting Variables Entering Values for Nom and EFF Converting Interest Rates Date Worksheet Date Worksheet Variables Resetting the Date Worksheet Variables Entering Dates Selecting the Day-Count Method Affects Calculations Computing Dates Example: Computing Days between Dates Profit Margin Worksheet Profit Margin Worksheet Variables Gross Profit Margin and Markup Clearing Profit Margin Worksheet Variables Computing Profit Margin Example: Computing Profit Margin Breakeven Worksheet Breakeven Worksheet Variables Resetting the Breakeven Worksheet Variables Computing Breakeven Example: Computing Breakeven Quantity Memory Worksheet Memory Worksheet Variables Clearing the Memory Worksheet Variables Using the Memory Worksheet Examples: Using the Memory Worksheet Page A Appendix Reference Information Formulas Page Page NFV 1i+() p n 1rrate+()1= ----------------------------------------------------- Page Page Page Page Page Profit Margin Breakeven Days between Dates Actual/actual day-count method Gross Profit Margin Selling Price Cost Selling Price ----------------------------------------------- 100= ------------------------ Y1YB() 4 ------------------------ Y2YB() 4 DBD Y2(Y1)360M2(M1)++ 30DT2(DT1)+= Error Messages Page Accuracy Information Rounding AOS (Algebraic Operating System) Calculations Algebraic Hierarchy Battery Information Replacing the Battery Battery Precautions Battery Disposal In Case of Difficulty Texas Instruments Support and Service For general information For technical support For Product (hardware) Service Texas Instruments (TI) Warranty Information Customers in the U.S. and Canada Only One-Year Limited Warranty for Commercial Electronic Product Australia & New Zealand Customers only All Other Customers Page Index Symbols Numerics A B C D E F G H I L M N O P Q R S T U V W X