Using Spreadsheets to Solve Problems
1.8 The IF Function
With relational operators and Boolean logical functions we have been able to determine if data
meets a set of criteria by returning the Boolean Logical values TRUE or FALSE. What if instead
of determining if a value is TRUE or FALSE, we wish to type a status message (e.g., “Yes” or
“No”) or perform one calculation versus another? The Excel IF function has the ability to
logically analyze information, and the flexibility to return answers other than TRUE and
FALSE.
SIMPLE IF FUNCTIONS
THE IF FUNCTION SYNTAX
The logical IF function takes a Boolean value as its first argument. This can either be the result
of a Boolean function, relational expression, or a reference to a cell containing a Boolean value.
The function tests whether the value is TRUE or FALSE. If the value is TRUE, the computer
performs the action specified by its second argument. If the comparison is FALSE the computer
performs the action specified by its third argument. The syntax of an IF function is:
IF (logical_test, value_if_true, value_ if_ false)
The use of the IF function corresponds to the use of the word “if” in everyday English. In the
sentence “if it is raining today, I will stay inside; otherwise, I will go outside” the logical test is
whether or not it is raining, the value if true is staying inside, and the value if false is going
outside.
As an example, consider the spreadsheet in Figure 1. The spreadsheet lists the names of several
employees, their monthly wage (column C), and their benefit eligibility (column B). Since it is
not clear what a TRUE or FALSE value in column B indicates (i.e., does the TRUE in cell C4
mean John is eligible for benefits, or is it TRUE that he is he is ineligible for benefits?), it is
desirable to list whether or not an employee is eligible for benefits in a more user-friendly way.
One of the simplest examples of the use of the IF function is to take a TRUE or FALSE value
and return an associated text label.
A
1 Medical Premium
2
3
4
5
6
Name
Erlich, John
Carson, Betty
Thomas, Justin
B
$
C
D
E
F
Medical
Premium
300
0
300
Total
Compensation
$
1,800
$
750
$
2,500
300
Benefit
Eligibility
TRUE
FALSE
TRUE
Benefit
Status
Wage
1500
eligible
750 ineligible
2200
eligible
Figure 1
Ifs & Nested Ifs 1.8
CSE1111
Page 99
Using Spreadsheets to Solve Problems
Assume that the TRUE value in column B indicates that an employee is eligible for benefits. In
column D the IF function can be used to display the text “eligible” or “ineligible” based on the
value in column B. To use the IF function in cell D4, consider each of the three arguments: the
logical test, the value if true, and the value if false.



The first argument is the logical test. The logical test is the value that the decision of the
IF function is based on. Whatever is placed in this argument must ultimately reduce to a
single TRUE or FALSE value. The formula being written needs to determine whether or
not John is eligible for benefits. This is indicated by a Boolean value in cell B, so the
logical test will be to reference the value in cell B4.
The second argument is the value to be displayed if the logical test is evaluated to be
TRUE; in this case it will be the text label “eligible”.
The third argument is the value to be displayed if the logical test is evaluated to be
FALSE; in this case it will be the text label “ineligible”.
The resulting formula will then be:
=IF(B4,“eligible”,“ineligible”)
Notice that the logical test simply references the cell, since the cell already has a TRUE/FALSE
value. It is not necessary to write B4=TRUE for this argument. Also note the value_if_true and
the value_if_false arguments are enclosed in quotes. This is because the resulting values to be
displayed are text. If the quotes are omitted the computer will look for a range named eligible
and either returns the value from that range or gives a #NAME! error if the range name does
not exist.
A SIMPLE EXAMPLE
While displaying whether or not an employee is eligible for benefits is nice, frequently
translating a Boolean value to a text label is not enough. What if we needed to calculate values,
not just display text, based on whether or not certain criteria are met? One example might be
calculating an employee’s total compensation including medical benefits, where the company
pays the premium for benefit eligible employees. This would require $300 be added to the
salary if the employee was eligible for the benefit.
To begin to answer this question, consider the simpler problem of determining the benefit
value each employee should receive: What formula will be needed in cell D4 that can be copied
down the column to determine medical benefit value (cost of premium) for this employee? The
benefit value is $300 if the employee is eligible for benefits (as listed in cell B1).

To solve this problem, first determine if John receives benefits by looking in the
corresponding cell in column B. The TRUE value indicates that he does receive benefits
(logical test). Based on the problem statement, if he receives benefits the medical premium
is $300 (result if TRUE). If he does not receive benefits there is no premium. i.e., the
premium is $0 (result if FALSE).
Ifs & Nested Ifs 1.8
CSE1111
Page 100
Using Spreadsheets to Solve Problems

To decide between different results based on some criterion, use an IF function. To better
understand the logical structure of this problem, consider writing out the IF function with
English text without values inserted (this is called “pseudo code”):
If(eligible for benefits, $300, otherwise $0).
Translated into Excel syntax this would be: =If(B4,B1,0).

Now consider whether each cell reference should be relative or absolute. The formula
needed in cell D5 is =IF(B5,B1,0). The value needed for the logical_test changes relatively
(B4 to B5). However, the benefit amount remains $300 (as given in cell B1), so this
reference should have an absolute row. The value if there is no benefit is just the constant
$0, which does not change. The final formula is:
=If(B4,B$1,0).
To calculate total compensation, the medical premium value can be added to the monthly
salary with the formula =C4+E4. A somewhat more complex question would be to calculate
this total compensation directly, without first calculating the premium value in a separate cell.
To do this, the formula =C4+IF(B4,B$1,0) could be used. Another possible way of writing
this formula is =IF(B4,B$1+C4,C4), placing the addition inside of the IF statement for both
the values_if_true and the value_if_false arguments.
What not to do:
What would happen if we instead wrote the formula =If(B4=TRUE,B1,0)? This syntax works
equally as well. Frequently however, students try to use quotes around “TRUE” resulting the
formula. =If(B4=“TRUE”,B1,0). “TRUE” with quotes is a label, while TRUE without quotes is
a value. As with numbers, a label used instead of a value (such as “FALSE” instead of FALSE)
can lead to incorrect results. Be careful never to use quotes with Boolean values.
Furthermore, the expressions B4=TRUE and B4 are logically equivalent if B4 contains a
Boolean value. To see why, consider the possible values of cell B4. If cell B4 contains TRUE,
then the result of the relational expression B4=TRUE is true. In this case, the expression B4
is TRUE as well. Now, if B4 contains FALSE, the result of the relational expression B4=TRUE
is FALSE. The result of the expression B4 is FALSE in this case as well. In either case (B4
contains TRUE or contains FALSE), the two expressions are equivalent. Therefore it is not
necessary to write B4=TRUE.
NESTING RELATIONAL EXPRESSIONS FOR A LOGICAL TEST
Let’s change the original example to the spreadsheet seen in Figure 2. Now assume the
employer will pay 50% of the medical premium for employees who qualify for medical benefits
and to qualify for benefits, employees must earn at least $1000 per month. Write an Excel
formula in cell C4 that can be copied down the column to determine the company’s
contribution to the medical premium of each employee.
Ifs & Nested Ifs 1.8
CSE1111
Page 101
Using Spreadsheets to Solve Problems
A
1 Medical Premium
2 % Paid by company
3
4
5
6
Name
Erlich, John
Carson, Betty
Thomas, Justin
B
C
300
50% Medical
Premium by
Company
Wage
1500
150
750
0
2200
150
D
$
Total
Compensation
$
1,650
$
750
$
2,350
Figure 2


Logically, first determine if John receives benefits by comparing his wage to the $1000
minimum set by the company. Does John receive this $1000 minimum? If John does
qualify, calculate the medical premium paid by the company as 50% of $300. If John does
not qualify the benefit is $0.
To evaluate a condition and decide between different solutions, use the IF function. In
pseudo code: If(a person qualifies for benefits by earning more than $1000, then company
pays 50% of the premium, otherwise $0)
o Notice that there are no TRUE/FALSE values already listed on the worksheet that
describe whether or not an employee qualified for benefits. This calculation will need
to be nested within the IF function’s logical_test. To compare two values in Excel
(John’s salary vs. $1000), a relational expression can be used. The relational
expression B4>=1000 will evaluate to the TRUE/FALSE value needed for the logical
test argument.
o Also note that the value if true, 50% of $300, is also not listed. Again the expression
will need to be nested within the value_if_true argument, in this case B1*B2.
Translated into Excel syntax the formula is =IF(B4>=1000,B1*B2,0).

Is the formula copied? Yes. To determine if any modifications are needed, consider how
each of the values changes when the formula is copied down the column. Does the monthly
salary change from B4 to B5? Yes. Does B1 become B2? No, the value of the benefits is
fixed. Similarly the value of the percentage paid the company in cell B2 is fixed. Hence the
final version of the formula should be =If(B4>=1000,B$1*B$2,0)
NESTING BOOLEAN LOGICAL FUNCTIONS FOR A LOGICAL TEST
What if this problem were again changed to require an employee to have a salary between
$1000 and $2000 (inclusive) in order to qualify for medical benefits? Changing the criteria
will require the logical test (first argument) of the IF function to be modified accordingly.
Here both the criteria, that a value is greater than or equal to 1000 and that the value is less
than or equal to 2000, need to be true for the statement to be true. Since both criteria must
be true for the statement to be true, an AND function will be needed. If solving just for this
criterion the following expression could be used: AND(B4>=1000,B4<=2000). Nesting this
within the formula results in the following:
=If(And(B4>=1000,B4<=2000),B$1*B$2,0)
Ifs & Nested Ifs 1.8
CSE1111
Page 102
Using Spreadsheets to Solve Problems
NESTING IF FUNCTIONS
Thus far we have used IF functions to evaluate a single logical test and decide between one of
two outcomes based on that test. These outcomes may be inserting text into the spreadsheet,
displaying a value, or even the result of a nested formula. Frequently problems arise that have
more than two outcomes. For example, a ticket for a movie is one price for children, another for
adults, and a third for senior citizens. How can that type of problem be solved in Excel?
We have already seen how nesting can be used to test for complex criteria or to calculate values
where arguments of functions are themselves nested formulas/functions. Nesting can also be
used with an IF function to decide between more than two different results. What if the
calculation in the value_if_false argument contained another IF function? If the computer
reaches this point, because the logical test in the first IF is FALSE, the computer will calculate
the value of this 2nd IF and use the result as the FALSE (3rd argument) of the 1st IF. Let’s take a
deeper look into how this might work.
A PROBLEM WITH 3 POSSIBLE OUTCOMES:
Again consider of valuing of an employee’s medical benefits, but this time the criteria will be
that the employer will pay no benefits to those earning less than $1000, 50% of the premium
for those earning at least $1000 but less than $2000, and the full premium for those receiving
wages of $2000 or more. In order to decide the value of the company’s benefit contribution it
will be necessary to first determine which criterion applies. To understand this problem a little
better (step 1), a decision tree has been created in Figure 3 which visually represents the logic
in this problem.
Company
Contribution $0
TRUE
Does this
person
earn less
than
$1000
Company
Contribution
FALSE
Does this
person earn at
least $1000 but
less than $2000
TRUE
FALSE
50%
Company
Contribution
100%
Figure 3
A diamond represents a decision with two possible outcomes: TRUE or FALSE. Each outcome
is either a specific value, such as $0, or leads to another diamond where the next decision is
made. In Excel, each of the diamonds can be implemented using an IF function, so the
value_if_true and/or the value_if_false can simply be another IF function. Up to 7 levels of
nesting can be used in this manner.
Ifs & Nested Ifs 1.8
CSE1111
Page 103
Using Spreadsheets to Solve Problems
In this decision tree the first diamond tests to see if John’s wages are less than $1000. If they
are then $0 is returned. If John’s wages are not less than $1000 the next diamond will test
whether or not John’s wages are at least $1000 but less than $2000. If this is TRUE then a
calculation of 50% of the premium cost will be returned; otherwise the entire cost of the
premium will be returned.
This will be translated into Excel syntax (step 2) based on the worksheet in Figure 4.
A
1 Medical Premium
2
3
4
5
6
Name
Erlich, John
Carson, Betty
Thomas, Justin
B
$
C
D
E
300
Medical
Premium paid
Wage
by company
1500
150
750
0
2200
300
Total
Compensation
$
1,650
$
750
$
2,500
Category
Management
Hourly
Hourly
Figure 4
Given the complexity, let’s first translate the decision tree into Excel psuedo code using an IF
function:
If(John’s wage<1000, $0 for premium, otherwise if (John’s wage is at least $1000 but
less than $2000, 50% premium, otherwise 100% premium)).
Next, translate this into the proper Excel syntax. Be sure the formula contains an identical
number of openning and closing parentheses in the correct places:
=If(B4<1000,0,If(B4<2000,B1*0.5,B1))
Finally, for step 3 add relative/absolute cell referencing to copy this formula down the column:
=IF(B4<1000,0,IF(B4<2000,B$1*0.5,B$1)).
This can also be written as IF(B4<1000,0,If(B4<2000,0.5,1))* B$1.
Look at the second IF logical test. One may ask why the logical_test doesn’t evaluate that both
John’s wage is at least $1000 and that his wage is less than $2000 (i.e., AND(B4>=1000,
B4<2000)). To see why it is okay to assume that B4 is greater than or equal to 1000, consider
how the function works: First the computer will evaluate the first IF, testing to see if B4<1000.
If it is less (TRUE) then the computer will return the answer $0 and the calculation is complete.
If the logical test is FALSE (B4 is not less than $1000) Excel will continue evaluating the
expression by going to the second IF statement. Thus the value could not possibly be less than
$1000 if the second IF is evaluated, so it need not be tested.
In some problems, it will matter which case is analyzed first. In this problem each category is
mutually exclusive. A wage can only fall into one category (either <$1000, >=$2000 or in
between). Therefore the order of the nesting is not important. The formula could have just as
easily been written as follows: =IF(B4>=2000,B$1,IF(B4<1000,0,0.5*B$1)). One could
Ifs & Nested Ifs 1.8
CSE1111
Page 104
Using Spreadsheets to Solve Problems
also test the “between 1000 and 2000” criteria first, although this would require the more
complex logical test using a Boolean function and is not recommended:
=IF(And(B4>=1000,B4<2000), 0.5*B$1, IF(B4<1000,0,B$1)).
A case where the order would matter is if we set the criteria for the company’s contribution to
medical premiums as follows:


The company does not pay benefits for management (column E – Category).
The company will pay full premiums for hourly employees who earn over $1000 and
50% for those who earn $1000 or less.
Here we do not have mutually exclusive categories. A person can earn over $1000 and still not
qualify, as in the case of management. So the first logical test must be to determine which
employment category an employee is in, and only if they are not in management apply the
second set of criteria based on wages. This formula can be written as follows:
= IF(E4= “management”,0,IF(B4<=1000,.5*B$1,B$1))
Ifs & Nested Ifs 1.8
CSE1111
Page 105
Using Spreadsheets to Solve Problems
EXAMPLE 1.8-1 SIMPLE IF’S – BUYING A USB DRIVE
A
B
C
D
1
2
Simple If's - USB Flash Drive Analysis
3
4
Hurdle Amount:
5
6
7
8
9
10
11
12
13
Item
Sandisk Cruzer Micro
A-DATA PD10 Rotating Lid
PQI Cool Drive U339 USB 2.0
PQI Cool Drive U339 4GB USB 2.0
Apacer Handy Steno AH320
Sandisk Cruzer Micro U3 4GB
Kingston DataTraveler
ACP-EP Memory 2 GB USB 2.0
Price
$ 29.99
$ 10.99
$ 12.99
$ 32.99
$ 10.99
$ 49.99
$ 34.00
$ 20.00
Less then
hurdle price
TRUE
TRUE
TRUE
FALSE
TRUE
FALSE
FALSE
TRUE
$
E
F
Amount
Spent
$
29.99
$
10.99
$
12.99
$
$
10.99
$
$
$
20.00
Alernative
Purchase Criteria
$
59.98
$
32.97
$
38.97
$
65.98
$
32.97
$
$
68.00
$
40.00
30.00
Buy or Do
not Buy
buy
buy
buy
do not buy
buy
do not buy
do not buy
buy
1. Write an Excel formula in cell C6 that can be copied down the column to determine if this
USB drive is less than the maximum amount (hurdle) you are willing to spend on a USB
drive.
2. Write an Excel formula in cell D6 that can be copied down the column to indicate whether or
not you will buy this USB drive. The formula should return the text “buy” if you will
purchase it (i.e., it costs less than the hurdle amount), and “do not buy” if you will not.
3. Write an Excel formula in cell E6 to determine how much money you would spend, if any, on
this USB drive. You will buy a drive if it costs less than the hurdle amount. Make sure you
can copy the formula down the column.
4. Alternatively, consider a different buying (and budget) plan as follows:

If the cost of the USB drive is less than $20, you will purchase 3 of that drive.

If the cost of the USB drive is at least $20 but less than or equal to $35, you will
purchase 2 of that drive.

If the cost of the USB drive is over $35 you not purchase that drive.
Write an Excel formula in cell F6 that can be copied down the column to determine how much
money you will spend, if any, on the purchase of these USB drives using this new buying plan.
Ifs & Nested Ifs 1.8
CSE1111
Page 106
Using Spreadsheets to Solve Problems
EXAMPLE 1.8-2– TRAVEL PRICES
1
2
3
4
5
6
7
A
Commission
<$1000
$1000 or more
B
$
Markup
Luxury trips
Other trips
50
5%
15%
10%
Comm!
Trip!
You manage a travel agency in Columbus and have been asked to provide an easy to read table
breaking down the pricing of some of your popular travel packages. Travel packages are priced
based on their wholesale price plus a markup. The markup is determined by the luxury rating.
In addition profit made by the markup, your agency also receives a commission from the
airline.
1. Write an Excel formula in cell Trip!D3 that can be copied down the column to determine
(True/False) if this trip costs less than the average offering on this list.
2. Write an Excel formula in cell Trip!E3 that can be copied down the column to determine
(True/False) if this trip is a luxury trip. Trips in categories A and B are considered to be
luxury trips.
3. Write an Excel formula in cell Trip!F3 that can be copied down the column to determine the
Retail Price of this trip. The markup for luxury trip packages is 15% of the wholesale price.
The markup for non-luxury trip packages is 10% of the wholesale price (as given on sheet
comm!). The Retail Price is the wholesale price plus the markup.
4. In addition to the price markup, travel agents also receive a commission from the airline.
This commission is a flat fee of $50 per trip from trips costing less than $1000 (based on
retail price of trip) or 5% of the wholesale price for trips with a retail price of $1000 or more
(as given on sheet comm!). Write an Excel formula in cell Trip!G3 (using cell references
wherever possible) to calculate the commission value. Write the formula so it can be copied
down the column.
5. Write an Excel formula in cell Trip!H3 that can be copied down the column to determine the
profit category of this trip. Trips with commissions of $50 or less commission are in the
“low” category, trips with a commission over $50 but less than $100 are in the “medium”
category, and trips with a commission of $100 or more are in the “high” category.
6. Write an Excel formula in cell D12 to determine the number of trip packages that cost less
than the average wholesale price of the trips on this list.
Ifs & Nested Ifs 1.8
CSE1111
Page 107
Using Spreadsheets to Solve Problems
EXAMPLE 1.8-3– CHAPTER REVIEW – DISCOUNT PRICING
A
Sales!
1
2
3
4
5
6
7
8
B
C
D
E
F
G
H
I
J
senior
sales
total
sale
senior
sale
discount discount discount sales
Grand
Sale# amount$ discount category value
value
used
value
tax
Total
1 $ 28.99
TRUE
F
$
4.35 $
$
4.35 $ 24.64 $ $ 24.64
2 $ 137.50 FALSE
F
$
$ 13.75 $ 13.75 $ 123.75 $ $ 123.75
3 $ 21.00 FALSE
O
$
$
$
$ 21.00 $ 2.52 $ 23.52
4 $ 499.99 FALSE
O
$
$ 75.00 $ 75.00 $ 424.99 $ 51.00 $ 475.99
5 $ 89.98 FALSE
O
$
$
$
$ 89.98 $ 10.80 $ 100.78
6 $ 234.50
TRUE
O
$ 35.18 $ 35.18 $ 35.18 $ 199.33 $ 23.92 $ 223.24
7 $ 32.54 FALSE
F
$
$
$
$ 32.54 $ $ 32.54
Data!
1
2
3
4
5
6
7
8
9
10
11
A
Description
food
other
B
C
Category % of total
F
0%
O
12%
As the owner of a small convenience store you have
Discounts
started to keep track of store sales. For each sale, you
Senior Discount
12%
will record the discounts which apply to each sale.
Sales Discount
Your pricing is such that sales are discounted based
<$100
0%
> $100 but < $200
10%
on the sales amount, as given on the Data! worksheet.
$200 or more
15%
The only exception to this is where a senior discount
is applied (for those eligible customers over the age of 65). Seniors will receive the greater of
either the sales discount or the senior discount.
1. Write an Excel formula in cell Sales!E2 that can be copied down the column to determine
the value of the senior discount. Only seniors are eligible for this discount. Senior status is
indicated in column C on sheet Sales!. The senior discount percentage in given on sheet
Data!. Non-seniors receive no discount. (Note the ‘-‘ display is the currency format for the
value $0).
2. Write an Excel formula in cell Sales!F2 that can be copied down the column to determine
the value of the sales discount. As indicated on sheet Data!, sales of less than $100 receive
no discount, sales of at least $100 but less than $200 receive a 10% discount, and sales of
$200 or more receive a 15% discount of the sale amount.
3. Write an Excel formula in cell Sales!G2 that can be copied down the column to determine
the discount amount used. The discounted value used will be the greater of the two
discounts (senior discount or sales discount). (**challenge – try to do this without an IF).
4. Write an Excel formula in cell Sales!H2 that can be copied down the column to determine
total sale value after the discount.
Ifs & Nested Ifs 1.8
CSE1111
Page 108
Using Spreadsheets to Solve Problems
5. Write an Excel formula in cell Sales!I2 that can be copied down the column to determine
the sales tax on this item. Sales tax rates are listed by category on sheet Data!. Categories
for each sale are listed in column D.
6. Write an Excel formula in cell Sales!J2 that can be copied down the column to determine
the value of the sale including tax rounded to the nearest cent.
Ifs & Nested Ifs 1.8
CSE1111
Page 109