Hp 12c Solutions Handbook-2

93

Pricing Calculations

Markup and Margin CalculationsSales work often involves calculating the various relations between markup, margin, selling price and costs. Markup is defined as the difference between selling price and cost, divided by the cost. Margin is defined as the difference between selling price and cost, divided by selling price. In other words, markup is based on cost and margin is based on selling price.The following keystroke sequences are given to readily make these calculations on the HP-12C.

Example 1: If the cost of an item is $160 and the margin is 20%, what is the selling price? What is the markup?

CALCULATE GIVEN KEYSTROKESSelling Price Cost & Markup Key in cost, , key in markup (in %), .

Selling Price Cost & Margin Key in cost, 1 , key in margin

(in %), .

Cost Selling Price & Markup

Key in selling price, 1 , key in

markup (in %0, .

Cost Selling Price & Margin

Key in selling price, 1 , key in

margin (in %0, .

Markup Cost and Selling Price Key in cost, , key in selling price, .

Markup Margin Key in margin, 1

.

Margin Selling Price & Cost Key in selling price, , key in cost, .

Margin Markup Key in markup, 1

.

Keystrokes Display

160 160.00 Cost.

1 20 20.00 Margin (%).

200.00 Selling price.

20 20.00

1 25.00 Markup (%).

94

Example 2: If an item sells for $21.00 and has a markup of 50%, what is its cost? What is the margin?

The following HP 12C program may be helpful for repetitive calculations of selling price and costs as well as conversions between markup and margin.

Keystrokes Display

21 21.00 Selling price.

1 50 50.00 Markup (%).

14.00 Cost.

50 50.00

1 33.33 Margin (%).

KEYSTROKES DISPLAY

CLEAR 00-

01- 36

04 02-43, 33 04

03- 16

1 04- 1

05- 34

06- 25

07- 40

08- 10

09- 31

10- 43 36

11- 20

12- 43 36

13- 20

14-43, 33 00

REGISTERS

n: Unused i: UnusedPV: Unused PMT: Unused

95

1. Key in program.2. To calculate selling price, given the markup, key in the cost, press

, key in the markup and press 00 .

3. To calculate cost, given the markup, key in the selling price, press , key in the markup and press 00 .

4. To calculate selling price, given the margin, key in the cost, press , key in the margin and press 03 .

5. To calculate cost given the margin, key in the selling price, press , key in the margin and press 03 .

6. To calculate markup from the margin, key in the margin and press 03 .

7. To calculate margin from the markup, key in the markup and press 00 .

Example: Find the cost of an item selling for $38.00 with a margin of 30%. What is the markup on the item? If the markup is raised to 50%, what will the selling price be?

Calculations of List and Net prices With DiscountsIf it often useful to be able to quickly calculate list or net price when the other price and a series of discount rates are known. Alternatively, if the

FV: Unused R0-R.8: Unused

Keystrokes Display

38 38.00 Selling price.

30 03 30.00 Markup (%).

26.60 Cost.

30 03 42.86 Markup (%).

26.6 26.60 Cost.

50 00

39.90 New selling price.

96

list and new and several discounts are known it may be desirable to calculate a missing discount. The following series of keystrokes may be used:

1. Key in 1, press 1.

2. Key in the first discount (as a percentage) and press 1

.3. Repeat step 2 for each of the remaining known discount rates.

4. To calculate the list price, key in the net price and press 1 .

5. To calculate the net price, key in the list price and press 1 .

6. To calculate an unknown discount rate, immediately after doing step 3 (display should show 1.00), key in the net price, press and key in the list price.

7. Press 1 100 .

Example: The list price of an item is $3.28 and the net price is $1.45. Two of the discount rates are 48% and 5%. What is the third discount rate?

The following program for the HP 12C will be helpful in performing the calculations:

Keystrokes Display

1

11.00

48 1 1.00

5 1 1.00

1.45

3.28 10.49

100 10.51 3rd discount rate (%).

KEYSTROKES DISPLAY

CLEAR 00-

1 01- 1

02- 34

03- 25

97

1. Key in the program.

2. Key in 1 and press 1.

3. Key in the first discount rate (as a percentage) and press .

4. Repeat step 2 for each of the remaining discount rates.

5. To calculate the list price, key in the net price and press 1 .

6. To calculate the net price, key in the list price and press 1 .

7. To calculate the unknown discount rate, key in the net price, press , key in the list price and press 07 .

Example: Calculate the unknown discount rate for the previous example. If the list price is now raised to $3.75 what is the new net price?

04- 30

1 05-44 20 1

00 06-43, 33 00

1 07- 45 1

08- 20

09- 10

1 10- 1

11- 34

12- 30

13- 26

2 14- 2

15- 20

00 16-43, 33 00

REGISTERS

n: Unused i: UnusedPV: Unused PMT: UnusedFV: Unused R0: UnusedR1: R1D1xD2...D R2-R7: Unused

Keystrokes Display

98

1 1 1.00

48 0.52

5 0.95

1.45

3.28 07 10.51 3rd discount rate (%).

0.89 Include 3rd discount rate in calculation.

3.75 1 1.66 New net price.

hp calculators

HP 12C Percentage functions andcalculations

Percent computations

The HP12C percent computation

Practice with percentage calculations

hp calculators

HP 12C Percentage functions and calculations

hp calculators - 2 - HP 12C Percentage functions and calculations - Version 1.0

Percent computations

The percentage calculation gives the result of applying a rate, expressed as parts of a hundred (per cent), to a basevalue. A generic expression for a percentage computation is shown in Figure 1:

100abx ×

= Figure 1

where:a is the rate, expressed in parts of a hundred (percents);b is the base value;x expresses the percent of the base when the rate is applied (%).

The percent change expresses the percent difference between two generic values related to one of the values. A genericexpression for a percent change computation is shown in Figure 2:

( )bbax 100×−

=∆ Figure 2

where:a is the reference amount;b is the base value (b≠0);∆x expresses the percent change from b to a (∆%)

The percent of total expresses a percentage that relates two numbers. Usually one of them represents part of the other.A generic expression for a percent of total computation is shown in Figure 3:

baxT ×= 100 Figure 3

where:a is the part of the total;b is the total amount (b≠0);xT expresses the percentage a represents for the total b (%T)

The HP12C percent computations

The HP12C has three keys to compute percentages: b, à and Z. To compute either percentage, percent changeor percent of total given both a and b, simply key a and b in separated by \ and press the related percentage key.

On the HP12C, the base value used in percentages (first introduced value) is always kept, so it can be used in furthercalculations, like net amount. For example, the following sequence is a general sequence to compute net amount:

b \ a b ++or

-

hp calculators



Practice with percentage calculations

Example 1: Mr. O'Brien needs to compute an 11% tax fee over his employees extra activities. The amount to be paidfor the extra activities is $1,230. How much is 11% of $1,230?

Solution: The simplest keystroke sequence to compute the 11% of $1,230 is:

1230 \ 11 b

Figure 4

Answer: 11% of $1,230 is $135.30.

Example 2: Now that Mr. O'Brien has the 11% tax fee computed, what is the net amount after adding 11% to $1,230?Assume this is performed immediately after example 1.

Solution: Simply press + because both the base and the percentage (display) are still available.

Figure 5

Answer: The net amount is $1,365.30.

Example 3: Given that Mr. O'Brien’s total expenses are $15,890, what is the percentage that $1,365.30 represents inthis total? Assume this is performed immediately after example 2.

Solution: The simplest keystroke sequence to compute this percentage is:

15890 ~ Z

Figure 6

Answer: $1,365.30 represents 8.59% of $15,890.

Example 4: In order to convince a possible customer to buy a new stereo, the salesman offers him a 5.5% discount offthe price. Given that the stereo's price is $480, how much will the customer pay for it?

Solution: The keystroke sequence below can be used to compute the final price:

480 \ 5.5 b -

hp calculators



Figure 7

Answer: If he agrees with it, the customer will pay $453.60.

Example 5: The final balance of a savings account after six months is $12,325. Knowing that it started with $12,000,what is the percent change observed in this account?

Solution: The keystroke sequence to compute the percent change is:

12000 \ 12325 à

Figure 8

Answer: 2.71%. This means that $12,350 is 2.71% bigger than $12,000.

Example 6: A large company had sales of $123,000,000 last year. Given that one of its largest affiliates contributed tothis total with sales of $11,500,000, what is the percentage that represents its contribution to the total?

Solution: This is a classic percent of total computation, and the following keystroke sequence can be used tocompute it:

123000000 \ 115 00000 Z

Figure 9

Answer: $11,500,000 represents 9.35% of $123,000,000 (the total).

hp calculators

HP 12C Cost, Price and Margin Calculations

Cost, price and margin concepts

Cost, price and margin on the HP12C

Practice solving cost, price and margin problems

hp calculators

HP 12C Cost, Price, and Margin Calculations

hp calculators - 2 - HP 12C Cost, Price, and Margin Calculations - Version 1.0

Cost, price and margin concepts

Items that are bought and sold have a cost to the seller and a price to the buyer. The difference between the cost andthe price is the gross amount the seller makes on the sale. There are two ways of computing the percentage thisdifference represents. The term markup uses the cost as the basis for the percentage calculation while margin looks atthe price as the basis. The diagram in Figure 1 illustrates the relationship between cost and price.

Figure 1

The cost is the price minus a percent of the price called margin. The price can also be viewed as the cost plus apercentage of the cost called markup. The following expressions relate margin, price and cost with each other.

100(%) ×

−

=PRCCSTPRCMAR

−

=

100(%)1 MAR

CSTPRC

×

−=100(%) PRCMARPRCCST

Figure 2

How to calculate cost, price and margin on the HP12C

The table below summarizes the keystroke sequence for each of the calculations above.

Unknown Keystrokesmargin key in price, \, key in cost, àÞ

cost key in price, \, key in margin, b-

price key in cost, \, 1, \, key in margin, b-zFigure 3

Practice with solving interest rate conversion problems

Example 1: A television costs $195 and its price is $300. What is the margin obtained by the store that sells these TVsets?

Solution: The keystroke sequence to calculate the margin in this case is:

300 \ 195 à Þ

cost merchandise

margin

markup

price

% +

% -

hp calculators



Figure 4

Answer: The margin is 35% for a $195 cost and a $300 price.

Example 2: The store manager wants to sell more TV sets and wants to reduce the price. If she cannot reduce themargin below 28%, what is the lowest price allowed for this TV set? Assume the same $195 cost.

Solution: The keystroke sequence to calculate the lower price in this case is:

195 \ 1 \ 28 b - z

Figure 5

Answer: The lowest price for this TV set is $270.83 given a 28% margin and a $195 cost.

Example 3: Based on these figures, the store manager decides to sell the TV set for $284.99. What is the marginachieved with this price?

Solution: The following keystroke sequence calculates the margin with the new price:

284.99 \ 195 à Þ

Figure 6

Answer: With the new price, the margin is now 35%.

Example 4: A new stereo system has a sales price of $150.75. Given a 35% margin, what is its cost?

Solution: The keystroke sequence to calculate the cost with these figures is:

150.75 \ 35 b -

Figure 7

Answer: The cost is $97.99.

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Example 5: When calculating the price of a toaster, a 45% markup was used. What is the margin obtained with the saleof a toaster with this markup?

Solution: The following keystroke sequence calculates the margin given a 45% markup:

45 \ \ 1 ~ b + z

Figure 8

Answer: A margin of 31.03% is equivalent to a 45% markup.

hp calculators

HP 12C Cost, Price and Markup Calculations

Cost, price and markup concepts

How to calculate cost, price and markup on the HP12C

Practice solving cost, price and markup problems

hp calculators

HP 12C Cost, Price, and Markup Calculations

hp calculators - 2 - HP 12C Cost, Price, and Markup Calculations - Version 1.0

Cost, price and markup concepts

Items that are bought and sold have a cost to the seller and a price to the buyer. The difference between the cost andthe price is the gross amount the seller makes on the sale. There are two ways of computing the percentage thisdifference represents. The term markup uses the cost as the basis for the percentage calculation while margin looks atthe price as the basis. The diagram in Figure 1 illustrates the relationship between cost and price.

Figure 1

The cost is the price minus a percent of the price called margin. The price can also be viewed as the cost plus apercentage of the cost called markup. The following expressions relate margin, price and cost with each other.

100(%) ×

−

=CSTCSTPRCMU

×

+=100(%) CSTMUCSTPRC

+

=

100(%)1 MU

PRCCST

How to calculate cost, price and markup on the HP12C

The table below summarizes the keystroke sequence for each of the calculations above.

Unknown Keystrokemarkup key in cost, \, key in price, àprice key in cost, \, key in markup, b+

cost key in price, \, 1, \, key in markup, b+zFigure 2

Practice with solving interest rate conversion problems

Example 1: A television is sold for $300. Given that it costs $195, what is the markup?

Solution: The keystroke sequence to calculate the markup in this case is:

195 \ 300 à

Figure 3

cost merchandise

margin

mark-up

price

% +

% -

hp calculators



Answer: The markup is 53.85% for a $300 price given that is costs $195.

Example 2: The store manager wants to sell more TV sets and wants to reduce the price. If she cannot reduce themarkup below 40%, so what is the lowest price for this TV set? Assume the same $195 cost.

Solution: The keystroke sequence to calculate the lower price in this case is:

195 \ 40 b +

Figure 4

Answer: The lowest price for this TV set is $273 given a 40% markup and a $195 cost.

Example 3: Based on these figures, the store manager decides to sell the TV set for $289.99. What is the markup withthis price?

Solution: The following keystroke sequence calculates the markup with the new price:

195 \ 289.99à

Figure 5

Answer: With the new price, the applied markup is 48.71%.

Example 4: A new stereo system has a $150.75 sales price. Given a 53% markup for this stereo system, what must beits cost?

Solution: The keystroke sequence to calculate the cost with these figures is:

150.75 \ 1 \ 53 b + z

Figure 6

Answer: The cost of this stereo system is $98.53.

Example 5: When calculating the price of a toaster, a 32% margin is expected on each sale. What is the markup to beapplied to the cost of a toaster to obtain this margin?

hp calculators



Solution: The following keystroke sequence calculates the markup given a 32% margin:

32 \ \ 1 ~ b - z

Figure 7

Answer: A 47.06% markup is equivalent to a margin of 32%.

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Hp 12c Solutions Handbook-2