Chapter 4: Functions and Formulas

Spreadsheet-Based Decision Support Systems

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Overview

4.1 Introduction 4.2 Formulas and Function Categories 4.3 Logical and Information Functions 4.4 Text and Lookup & Reference Functions 4.5 Date & Time Functions 4.6 Mathematical and Trigonometry Functions 4.7 Statistical and Financial Functions 4.8 Conditional Formatting Formulas 4.9 Auditing 4.10 Summary

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Introduction

Various function names, arguments, and examples

Excel’s function dialog boxes

Formula Is option in conditional formatting

Auditing formulas and functions

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Formulas and Function Categories

Formulas– Simple values

– Basic operators

– Naming and referencing

– Functions

Function Categories– Logical – Information– Text – Lookup & Reference– Date & Time– Math & Trig– Statistical – Financial– Database (Ch 9)

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Finding and Using Functions

Insert > Functions from menu– fx icon in Standard toolbar

Insert Function menu has descriptions of each function with Help options

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Function Arguments

Almost every Function has at least one argument, or parameter

The Function Arguments window describes what each argument is and offers more details with the Help option

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Figure 4.4(a)

The SUM function sums the values in any given range of values– =SUM(number1, number2) or =SUM(range name)

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Figure 4.4(b)

The AVERAGE function finds the average of a given range– =AVERAGE(number1, number2) or =AVERAGE(range name)

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Figure 4.4(c)

The MIN and MAX functions find the minimum or maximum value in a given range of values– =MIN(number1, number2) or =MIN(range name)

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Logical Functions

TRUE and FALSE

IF and NOT

AND and OR

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Figure 4.7

The TRUE and FALSE functions simply display the words TRUE and FALSE respectively (no parameters)– =TRUE or =FALSE

The NOT function is used to display the opposite of any of the results of the other Logical functions– =NOT(cell_name)

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Figure 4.8

The IF function uses a specified condition to determine whether your data is true or false, and then returns a user-specified result in each case. – =IF(logical_test, value_if_true, value_if_false)

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Figure 4.9(a)

The AND function evaluates a list of conditions as True or False– =AND(condition1, condition2, …)

– All of the conditions must be true in order for TRUE to be displayed.

– If any of the conditions are violated, FALSE will be returned

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Figure 4.9(b)

The OR function also evaluates a list of conditions– =OR(condition1, condition2, …)

– Only one of the conditions needs to be true for TRUE to be the result

– All of the conditions would have to be violated in order to return FALSE

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Information Functions

There are several different Information functions

All of these functions give some basic descriptive information about any given data

One group of these functions we call the IsFunctions

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Figure 4.11

The ISEVEN and ISODD functions evaluate whether or not a number in a cell is an even or odd number, respectively.– =ISEVEN(cell_name) or =ISEVEN(number)

– =ISODD(cell_name) or =ISODD(number)

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Figure 4.12

The ISTEXT and ISNUMBER functions return TRUE or FALSE if a cell value is text or not, or a number or not, respectively.– =ISTEXT(cell_name) or =ISTEXT(value)

– =ISNUMBER(cell_name) or =ISNUMBER(value)

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Figure 4.13

The TYPE function evaluates the data type of a value– =TYPE(cell_name) or =TYPE(value)– a data type is a descriptive category of the different types of values possible

in Excel

Excel has designated a particular number to reference the categories of each data type. – 1 = numerical– 2 = text– 4 = logical value

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Text Functions

Text functions manipulate text values or analyze their characteristics

There are several Text Functions. We will discuss:– UPPER and LOWER

– CONCATENATE

– SUBSTITUTE.

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Figure 4.15

The UPPER and LOWER functions convert a cell, or range of cells, with text values into all uppercase or all lowercase text, respectively– =UPPER(range_name) or =LOWER(range_name)

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Figure 4.16

The CONCATENATE function joins fragments of a phrase or sentence together by combining text values of multiple cell– =CONCATENATE(cell1, cell2, …)

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Figure 4.17

The SUBSTITUTE function takes a cell with text and exchanges old text for new text. – =SUBSTITUTE(cell_name, old_text, new_text, instance)

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Lookup & Reference Functions

Lookup & Reference functions search for information within a given table of data and perform some actions on that data

There are several of these functions; for now, we describe:– VLOOKUP and HLOOKUP

– MATCH

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VLOOKUP and HLOOKUP

The VLOOKUP and HLOOKUP functions are helpful when searching for data in the spreadsheet

VLOOKUP searches for a value in the left-most column of a table, marks the row that contains that value, and then returns a value from that row for a specified column– =VLOOKUP(lookup_value, table_array, column_index_number,

range_lookup)

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VLOOKUP and HLOOKUP (cont)

HLOOKUP searches for a value in the top row of a table, marks the column that contains that value, and then returns a value from that column for a specified row– =HLOOKUP(lookup_value, table_array, row_index_number, range_lookup)

The range_lookup parameter measures the exactness for searching for the first parameter value. – True = find the closest match (default)

– False = find an exact match

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Figure 4.18

=VLOOKUP(lookup_value, table_array, column_index_number, range_lookup)

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Figure 4.19

=HLOOKUP(lookup_value, table_array, row_index_number, range_lookup)

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MATCH

The MATCH function searches a table of data and returns the location of a desired value. – =MATCH(lookup_value, table_array, match_type)

The match_type parameter, can be 0, 1, or –1. – 0 = the location of the first value it finds that is equal to the value for which we

are searching (default)

– 1 = the location of the largest value that is less than or equal to our specified value (given that the data is in ascending order)

– –1 = the location of the smallest value that is greater than or equal to our value (given that the data is in descending order

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Figure 4.20

Searching a column for closest matches

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Figure 4.21

Searching a row for an exact match

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Figure 4.23

The INDEX function, like the MATCH function, allows us to find an entry in a specified row and column of a range of cells.– =INDEX(range or range_name, row_number, column_number)

Example: Use the INDEX function to compute the distance between US cities.

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Figure 4.26

The OFFSET function references a cell that is a given number of rows and columns from a specified cell, or range of cells. – =OFFSET(reference_cell, rows_to_move, columns_to_move, [height],

[width])

Use a table of numbers to demonstrate the use of the OFFSET function.– Name the cell C2 the “RefCell” since we will reference this cell most often.

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Date & Time Functions

Excel’s system for calculating dates and times uses a serial number to enumerate all dates and times

– For dates, this number considers January 1, 1990 to be an initial starting point, which it sets to zero, and then counts each day thereafter as one unit

– For time, the initial starting point is at zero hours, zero minutes, and zero seconds counting toward the current time on a 24-hour scale. (It is reset to zero at midnight of each day.)

It is by using this numerical system that we are able to perform the functions in this category.

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Date & Time Functions (cont’d)

There are several functions in this category; we describe:– TODAY and NOW

– NETWORKDAYS, DAYS360, and YEARFRAC

– WEEKDAY and MONTH

– HOUR and MINUTE

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Two Functions

The TODAY and NOW functions display the current date and time, respectively (there are no parameters for these functions)– =TODAY()

– =NOW()

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Three More Functions

NETWORKDAYS finds the number of workdays between two dates

DAYS360 finds the total number of days between two dates

YEARFRAC finds the fraction of a year between two dates

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Figure 4.31

=NETWORKDAYS(start_date, end_date, holidays)

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Figure 4.32

=DAYS360(start_date, end_date, method)

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Figure 4.33

=YEARFRAC(start_date, end_date, basis)

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Four More Functions

The WEEKDAY function determines to which day of the week your date refers.

There are three possible numbering methods:– 1 = Sunday as day 1 and Saturday as day 7 (default)– 2 = Monday as day 1 and Sunday as day 7 – 3 = Monday as day 0 and Sunday as 6

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Four More Functions (cont)

The MONTH function determines to which month your date belongs. – The months are enumerated with January as 1 through December as 12.

The HOUR function takes the time and returns the number of the hour to which it belongs using a numbering system from 12:00 AM as 0 to 11:00 PM as 23.

The MINUTE function takes the time and returns a minute number from 0 to 59.

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Figure 4.35

=WEEKDAY(date, method) or =WEEKDAY(cell_name, method)

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Figure 4.36

=MONTH(date) or =MONTH(cell_name)

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Figure 4.37

=HOUR(time) or =HOUR(cell_name) =MINUTE(time) or =MINUTE(cell_name)

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Mathematical and Trigonometry Functions

Already used:– SUM

– AVERAGE

– MIN

– MAX

We will now describe:– SUMPRODUCT

– MMULT

– SQRT

– PI

– SIN, COS, and TAN

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SUMPRODUCT

The SUMPRODUCT function takes several arrays and finds the sum of

the product of each element in these arrays– =SUMPRODUCT(array1, array2, …)

This is equivalent to taking the product of several rows of values, storing the results in a column, and then taking the sum of that column of values

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Figure 4.38

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MMULT

The MMULT function is used to multiply two matrices, or ranges, of values. – =MMULT(array1, array2)

– =MMULT(range_name, range_name)

To be able to multiply two matrices, the number of columns of one matrix must equal the number of rows of the other matrix.

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Figure 4.40

First, highlight a range of cells with the dimension of number of rows of the first matrix by number of columns of the second matrix.

Then enter the MMULT equation and press SHIFT+CTL+ENTER.

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Statistical Functions

We describe in detail such statistical functions as MEAN and STDEV in Chapter 7, as well as such distribution functions as NORMDIST, BETADIST, CHIDIST, and EXPONDIST.

In Chapter 10, we will discuss the COUNT functions, COUNTIF and SUMIF, with databases functions.

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Financial Functions

There are several of these functions; we describe:– NPER

– PMT

– FV

– NPV

– XNPV

– RATE

– IRR

– SLN

– SYD

– DB

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NPER

The NPER function calculates the number of payments remaining. This function takes the rate, payment per period, and unpaid amount as parameters. The unpaid amount is entered as the present value of the payment. – =NPER(rate, period_payment, present_value, future_value, type)

The type parameter specifies if payments are made:– 0 = at the beginning of the period (default)

– 1 = at the end of the period

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PMT

The PMT function is used to calculate the monthly payment amount. The parameters for this function are the rate, number of payments left and unpaid amount, from which the monthly payments are calculated.

– =PMT(rate, Nper, present_value, future_value, type)

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Figure 4.42

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RATE and FV

The RATE function is used to find the interest rate. The parameters for this function are the number of periods, payment per period, present value or future value, and the type.– =RATE(nper, period_payment, present_value, future_value, type)

The FV function to calculates the future value with these known values as our parameters: – =FV(rate, nper, period_payment, present_value, type)

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Figure 4.43

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NPV and IRR

The NPV function calculates the net present value given the interest rate and payments each period. – =NPV(rate, payment1, payment2, …)

The IRR function calculates the internal rate of return. It takes the payments for all periods (including the initial investment) as a range of cells. – =IRR(payment_range, guess)

The guess parameter estimates the IRR– Default value is .10, or 10 percent

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Figure 4.44(a)

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Figure 4.44(b)

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XNPV

If the payment periods are irregular, that is if they occur on irregular intervals, you can still calculate the NPV using the XNPV function.

– =XNPV(rate, payments, dates)

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SLN, SYD, and DB

The SLN function calculates the straight-line depreciation of an asset. It takes the initial cost, salvage at the last period, and useful life as parameters – =SLN(initial_cost, salvage, life)

The SYD function calculates the sum of the year’s digits for a given period in the depreciation calculation. The parameters are the initial cost, salvage at the last period, useful life of the asset, and the period in which we are interested. – =SYD(initial_cost, salvage, life, period)

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SLN, SYD, and DB (cont)

The fixed declining balance function DB calculates the depreciation using the initial cost, salvage at the last period, useful life of the asset, and the period of interest as its parameters.

– =DB(initial_cost, salvage, life, period)

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Figure 4.45(a)

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Figure 4.45(b)

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Figure 4.45(c)

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Conditional Formatting Formulas

The Formula Is feature in Conditional Formatting allows us to use formulas to create the conditions checked before a format is placed in a cell.

The formulas used in Conditional Formatting are similar to those of the Logical category.

The Formulas Is option of Conditional Formatting allows us to format a cell, or range of cells, based not only on the value in the selected cells, but also on values in other cells.

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Figures 4.48 and 4.49

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Auditing

Auditing unveils all of the data cells involved in a function or reference. – Aids in data validation and verification.

– Select Tools > Auditing from the menu.

Auditing performs two primary actions: tracing precedents and tracing dependents.

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Summary

There are ten different categories of functions: Financial, Date and Time, Mathematics and Trigonometry, Statistical, Lookup and Reference, Database, Text, Logical, Information and Engineering.

The Formula Is option of Conditional Formatting allows you to specify conditions using logical comparisons of several cells.

Auditing is used to locate all of the data cells involved in a function or reference.

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