# 1.5 Working with Discounts, Markup, and Markdown

## LEARNING OBJECTIVES

- Solve problems involving discounts, markup, and markdown.

Running a business requires you to integrate discounts, markup, and markdown. From discounts to markups and markdowns, all the numbers must fit together for you to earn profits in the long run. It is critical to understand how pricing decisions affect the various financial aspects of your business and to stay on top of your numbers. Merchandising does not involve difficult concepts, but to do a good job of it you need to keep track of many variables and observe how they relate to one another.

Up to this point, you have examined the various components of merchandising as separate topics. Your study of basic product pricing has included the following:

- Taking a list price and applying discounts to arrive at a product’s cost.
- Marking up a product by adding expenses and profits to the cost to arrive at a regular selling price.
- Marking down a product by applying a discount and arriving at a reducing selling price or sale price.
- Working with various percentages in both markup and markdown situations to either simplify calculations or present a clearer pricing picture.

## Reduced Profit

When you markdown the selling price of an item to a reduced selling price, what effect does this have on the costs, expenses, and profit? No matter what price you sell an item for, the cost and expenses do not change. The amount that you marked down the selling price reduces your profit because you will still have the same costs and expenses to cover. The **reduced profit** ([latex]P_{red}[/latex]) is the amount of profit earned when an item is sold at a reduced selling price. Because profit (reduced or not) is what is left over from the selling price after you deduct the costs and expenses:

[latex]\displaystyle{P_{red}=S_{red}-C-E}[/latex]

where

**[latex]P_{red}[/latex] is the reduced profit.**The reduced profit is the amount of profit earned when selling an item at a reduced selling price.**[latex]S_{red}[/latex] is the reduced selling price.**The sale price is the price of the product after reduction by the markdown.**[latex]C[/latex] is the cost of the item.**The cost is the amount of money that the business must pay to purchase or manufacture the product.**[latex]E[/latex] is the expenses.**Expenses are the financial outlays involved in selling the product.

How is the reduced profit related to the markdown amount? Suppose an item has a regular selling price of $100, costs of $30, and expenses of $20. Then the profit earned by selling the product at the regular selling price is $50. Now, suppose the item is marked down by $15. The reduced selling price is $75. The costs and expenses remain the same, $30 and $20 respectively. So the reduced profit earned by selling the product at the reduced selling price is $35. Note that this reduced profit is just the original $50 profit reduced by the markdown amount of $15. When you start marking down the selling price, the profit is reduced by an amount equal to the markdown amount.

[latex]\displaystyle{P_{red}=P-D}[/latex]

where

**[latex]P_{red}[/latex] is the reduced profit.**The reduced profit is the amount of profit earned when selling an item at a reduced selling price.**[latex]P[/latex] is the profit.**This is the profit when selling an item at the regular selling price.**[latex]D[/latex] is the amount of markdown.**This is the amount the regular selling price is reduced by to arrive at the reduced selling price.

From the above formula, you can see that as long as the markdown amount ([latex]D[/latex]) is **smaller** than the profit ([latex]P[/latex]), the reduced profit ([latex]P_{red}[/latex]) will be positive. Consequently, you would still make money when selling the item at the reduced selling price but not as much money if you sold the item at the regular selling price.

What happens when the markdown amount ([latex]D[/latex]) **equals** the profit ([latex]P[/latex])? Then the reduced selling price would equal the break-even price and the reduced profit would be 0. In other words, you do not make any money when selling the item at the break-even price but you also do not lose any money.

Is it possible to lose money on the sale of an item? Suppose an item has a regular selling price of $100, costs of $30, and expenses of $20. Then the profit earned by selling the product at the regular selling price is $50. Now, suppose the item is marked down by $65. The reduced selling price is $35. This sale price is less than the costs and expenses combined, so the item would be sold at a loss. In fact, using the formula above, the reduced profit is -$15, which indicates that every time the item is sold at the reduced selling price of $35, the business would lose $15.

When the markdown amount ([latex]D[/latex]) is **larger** than the profit ([latex]P[/latex]), the reduced profit ([latex]P_{red}[/latex]) will be negative. Consequently, you would lose money when selling the item at the reduced selling price.

### NOTES

- The sign (positive, negative, or zero) of the reduced profit is important. A positive reduced profit indicates that you are still making money (a profit) on the sale of the item. A zero reduced profit indicates that you are selling the item at the break-even price. A negative reduced profit indicates that you are losing money on the sale of the item, and the amount of the reduced profit indicates how much you are losing on each sale.
- You may think it is counter-intuitive to sell an item at a loss, but it is a common practice. For example, after season sales or discounted items are often sold at a loss in order to clear out inventory.

## EXAMPLE

A retailer purchases a small kitchen appliance for $100 with expenses of $45 for each appliance. The retailer wants a profit of $80 on each appliance sold. During a sale, the retailer offers a markdown of 35%. At the reduced selling price, what is the retailer’s profit or loss?

**Solution:**

**Step 1: ** The given information is

[latex]\begin{eqnarray*} C & = & \$100 \\ E & = & \$45 \\ P & = & \$80 \\ d & = & 35\% \end{eqnarray*}[/latex]

**Step 2:** Calculate the regular selling price.

[latex]\begin{eqnarray*} S& = & C+E+P \\ & = & 100+45+80 \\ & = & \$225 \end{eqnarray*}[/latex]

**Step 3:** Calculate the reduced selling price.

[latex]\begin{eqnarray*} S_{red} & = & S \times (1-d) \\ & = & 225 \times (1-0.35) \\ & = & 225 \times 0.65 \\ & = & \$146.25 \end{eqnarray*}[/latex]

**Step 4:** Calculate the reduced profit.

[latex]\begin{eqnarray*} P_{red} & = & S_{red}-C-E\\ & = & 146.25-100-45 \\ & = & \$1.25 \end{eqnarray*}[/latex]

At the reduced selling price, the retailer’s profit is $1.25.

## EXAMPLE

A retailer purchases shoes for $25 per pair and sells them for $47 per pair, which includes a profit of $5 per pair. During a sale, the shoes are marked down by 20%. Calculate the profit or loss at the reduced selling price.

**Solution:**

**Step 1: ** The given information is

[latex]\begin{eqnarray*} C & = & \$25 \\ S & = & \$47 \\ P & = & \$5 \\ d & = & 20\% \end{eqnarray*}[/latex]

**Step 2:** Calculate the expenses.

[latex]\begin{eqnarray*} S& = & C+E+P \\ 47 & = & 25+E+5 \\ 47-25-5 & = & E \\ $17 & = & E \end{eqnarray*}[/latex]

**Step 3:** Calculate the reduced selling price.

[latex]\begin{eqnarray*} S_{red} & = & S \times (1-d) \\ & = & 47 \times (1-0.2) \\ & = & 47 \times 0.8 \\ & = & \$37.60 \end{eqnarray*}[/latex]

**Step 4:** Calculate the reduced profit.

[latex]\begin{eqnarray*} P_{red} & = & S_{red}-C-E\\ & = & 37.60-25-17 \\ & = & -\$4.40 \end{eqnarray*}[/latex]

At the reduced selling price, the retailer loses $4.40 per pair.

## TRY IT

An item costs $90, the overhead expenses are 30% of cost, and the profit is 15% of cost. During a sale, the item is marked down by 25%. Calculate the profit or loss at the reduced selling price.

**Click to see Solution**

[latex]\begin{eqnarray*} S & = & C+E+P \\ & = & 90+0.3 \times 90+0.15 \times 90 \\ &= & $130.50 \end{eqnarray*}[/latex]

[latex]\begin{eqnarray*} S_{red} & = & S \times (1-d) \\ & =& 130.50 \times (1-0.25) \\ & = & 130.50 \times 0.75 \\ & = & $97.88 \end{eqnarray*}[/latex]

[latex]\begin{eqnarray*} P_{red} & = & S_{red}-C-E \\ & = & 97.88--90-27 \\ & = & -$19.12\end{eqnarray*}[/latex]

## Complete Merchandising Scenarios

Use the following steps to solve complete merchandising scenarios.

- It is critically important to correctly identify both the known and unknown merchandising variables that you are asked to calculate.
- For each of the unknown variables, identify the formulas that contain the unknown variables. You must solve one of these formulas to arrive at the answer. Based on the information provided, examine these formulas to determine which formula may be solvable. Write out this formula, identifying which components you know and which components remain unknown.
- Note the unknown variables among all the formulas you found in the pervious step. Are there common unknown variables among these formulas? Theses common variables are critical variables. Solving for these common unknown is the key to completing the question. Note that these unknown variables may not directly point to the information you were asked to calculate, and they do not resolve the merchandising scenario themselves. However, without these variables you cannot solve the scenario.
- Apply any of the merchandising formulas to calculate the unknown variables required to solve the formulas. Your goal is to identify all required variables and then solve for the original unknown variables identified in the first step.

### NOTE

Before proceeding, take a few moments to review the various concepts and formulas covered earlier in this chapter. A critical and difficult skill is now at hand. As evident in Steps 2 through 4 of the process described above, you must use your problem-solving skills to figure out which formulas to use and in what order. Here are some suggestions to help you on your way.

- Analyze the question systematically.
- If you are unsure of how the pieces of the puzzle fit together, try substituting your known variables into the various formulas. You are looking for
- Any solvable formulas with only one unknown variable,
*or* - Any pair of formulas with the same two unknowns, because you can solve this system using your algebraic skills of solving two linear equations with two unknowns.

- Any solvable formulas with only one unknown variable,
- Merchandising has multiple steps. Think through the process. When you solve one equation for an unknown variable, determine how knowing that variable affects your ability to solve another formula. There is usually a critical unknown variable. Once you determine the value of this variable, a domino effect allows you to solve any other remaining formulas.

## EXAMPLE

A skateboard shop stocks a Tony Hawk Birdhouse Premium Complete Skateboard. Each skateboard costs $45.46 and the store has overheads expenses of $25.17 on each skateboard. The shop wants to sell each skateboard for an operating profit of $10.55. During a sale, it offers a markdown rate of 10%. At the reduced selling price, calculate the store’s profit or loss.

**Solution:**

**Step 1: ** The given information is

[latex]\begin{eqnarray*} C & = & \$45.46 \\ E & = & \$25.17 \\ P & = & \$10.55 \\ d & = & 10\% \end{eqnarray*}[/latex]

**Step 2:** Calculate the regular selling price.

[latex]\begin{eqnarray*} S& = & C+E+P \\ & = & 45.46+25.17+10.55 \\ & = & \$81.18 \end{eqnarray*}[/latex]

**Step 3:** Calculate the reduced selling price.

[latex]\begin{eqnarray*} S_{red} & = & S \times (1-d) \\ & = & 81.18 \times (1-0.1) \\ & = & 81.18 \times 0.9 \\ & = & \$73.06 \end{eqnarray*}[/latex]

**Step 4:** Calculate the reduced profit.

[latex]\begin{eqnarray*} P_{red} & = & S_{red}-C-E\\ & = & 73.06-45.46-25.17 \\ & = & \$2.43 \end{eqnarray*}[/latex]

At the reduced selling price, the store’s profit is $2.43.

## EXAMPLE

A toy store sells an electronic toy for $150. The markup on the cost of the toy is 25%. The operating expenses are 15% of cost. During a sale, the toy is marked down by 10%.

- Calculate the cost of the toy.
- Calculate the profit if the toy is sold at the regular selling price.
- Calculate the reduced selling price.
- Calculate the profit or loss at the reduced selling price.

**Solution:**

**Step 1: ** The given information is

[latex]\begin{eqnarray*} S & = & \$150 \\ M & = & 0.25 \times C \\ E & = & 0.15 \times C \\ d & = & 10\% \end{eqnarray*}[/latex]

**Step 2:** Calculate the cost.

[latex]\begin{eqnarray*} S& = & C+M \\ 150 & = & C+0.25 \times C \\ 150 & = & (1+0.25) \times C \\ 150 & = & 1.25 \times C \\ \frac{150}{1.25} & = & C \\ \$120 & = & C \end{eqnarray*}[/latex]

The cost of the toy is $120.

**Step 3:** Calculate the expenses.

[latex]\begin{eqnarray*} E & = & 0.15 \times C \\ & = & 0.15 \times 120 \\ & = & \$18 \end{eqnarray*}[/latex]

**Step 4: ** Calculate the profit at the regular selling price.

[latex]\begin{eqnarray*} P& = & S-C-E\\ & = & 150-120-18 \\ & = & \$12 \end{eqnarray*}[/latex]

The profit at the regular selling price is $12.

**Step 5:** Calculate the reduced selling price.

[latex]\begin{eqnarray*} S_{red} & = & S \times (1-d) \\ & = & 150 \times (1-0.1) \\ & = & 150 \times 0.9 \\ & = & \$135 \end{eqnarray*}[/latex]

The reduced selling price is $135.

**Step 6:** Calculate the reduced profit.

[latex]\begin{eqnarray*} P_{red} & = & S_{red}-C-E\\ & = & 135-120-18 \\ & = & -\$3 \end{eqnarray*}[/latex]

At the reduced selling price, the store loses $3 per toy.

## EXAMPLE

A manufacturer makes laptop computers at a cost of $1800 per machine. The manufacturer’s operating profit is 20% on the selling price and the overhead expenses are 35% on the selling price. During a computer trade show, the company offered the computer at a discount of 17.5%.

- What is the regular selling price of the laptop?
- What is the profit or loss at the reduced selling price?
- What rate of markdown does the manufacturer have to offer to sell the laptop at the break-even price?

**Solution:**

**Step 1: ** The given information is

[latex]\begin{eqnarray*} C & = & \$1800 \\ P & = & 0.2 \times S \\ E & = & 0.35 \times S \\ d & = & 17.5\% \end{eqnarray*}[/latex]

**Step 2:** Calculate the regular selling price.

[latex]\begin{eqnarray*} S& = & C+E+P \\ S & = & 1800+0.35 \times S+0.2 \times S \\ S & = & 1800+0.55 \times S \\ S-0.55 \times S & = & 1800 \\ (1-0.55) \times S & = & 1800 \\ 0.45 \times S & = & 1800 \\ S & =& \frac{1800}{0.45} \\ S & = & \$4,000 \end{eqnarray*}[/latex]

The regular selling price of the laptop is $4,000.

**Step 3:** Calculate the expenses.

[latex]\begin{eqnarray*} E & = & 0.35 \times S \\ & = & 0.35 \times 4,000 \\ & = & \$1,400 \end{eqnarray*}[/latex]

**Step 4:** Calculate the reduced selling price.

[latex]\begin{eqnarray*} S_{red} & = & S \times (1-d) \\ & = & 4,000 \times (1-0.175) \\ & = & 4,000 \times 0.825 \\ & = & \$3,300 \end{eqnarray*}[/latex]

**Step 5:** Calculate the reduced profit.

[latex]\begin{eqnarray*} P_{red} & = & S_{red}-C-E\\ & = & 3,300-1,800-1,400 \\ & = & \$100 \end{eqnarray*}[/latex]

At the reduced selling price, the manufacturer makes a profit of $100 per laptop.

**Step 6:** Calculate the break-even price.

[latex]\begin{eqnarray*}BE & = & C+E \\ & = & 1,800+1,400 \\ & = & \$3,200 \end{eqnarray*}[/latex]

**Step 7: ** Calculate the rate of markdown at the break-even price.

[latex]\begin{eqnarray*}D & = & S-S_{red} \\ & = & 4,000-3,200 \\ & = & \$800 \end{eqnarray*}[/latex]

[latex]\begin{eqnarray*} d & = & \frac{D}{S} \times 100\% \\ & = & \frac{800}{4,000} \times 100\% \\ & = & 20\% \end{eqnarray*}[/latex]

At the break-even price, the rate of markdown is 20%.

### NOTE

In the previous example, the expenses are given as a percent of the regular selling price, which means the expenses are always based on the regular selling price and not the reduced selling price. Notice in the calculation of the reduced profit that the expenses are the expenses based on the regular selling price. The expenses are NOT recalculated based on the reduced selling price. Remember, the expenses are fixed and based on what you originally plan to sell the item for, and do not change even, if the item is placed on sale.

## EXAMPLE

A retailer sells an item for $110.50 each. The rate of markup on cost is 70%. The operating profit is 18% on cost. During a sale the item’s price is set so that the profit at the reduced selling price is $3.75.

- What is the cost of the item?
- What are the expenses?
- What is the reduced selling price?
- What is the rate of markdown for the reduced selling price?
- What is the profit or loss if the item is sold at cost?

**Solution:**

**Step 1: ** The given information is

[latex]\begin{eqnarray*} S & = & \$110.50 \\ M & = & 0.7 \times C \\ P & = & 0.18 \times C \\ P_{red} & = & 3.75 \end{eqnarray*}[/latex]

**Step 2:** Calculate the cost.

[latex]\begin{eqnarray*} S& = & C+M \\ 110.50 & = & C+0.7 \times C \\ 110.50 & = & (1+0.7) \times C \\ 110.50 & = & 1.7 \times C \\ \frac{110.50}{1.7} & = & C \\ \$65 & = & C \end{eqnarray*}[/latex]

The cost of the item is $65.

**Step 3:** Calculate the profit at the regular selling price.

[latex]\begin{eqnarray*} P & = & 0.18 \times C \\ & = & 0.18 \times 65 \\ & = & \$11.70 \end{eqnarray*}[/latex]

**Step 4:** Calculate the markup amount.

[latex]\begin{eqnarray*} M & = & 0.7 \times C \\ & = & 0.7 \times 65 \\ & = & \$45.50 \end{eqnarray*}[/latex]

**Step 5:** Calculate the expenses.

[latex]\begin{eqnarray*} M & = & E+P \\ 45.50 & = & E +11.70\\ 45.50-11.70& = & E \\ \$33.80 & = & E \end{eqnarray*}[/latex]

The expenses are $33.80.

**Step 6:** Calculate the reduced selling price.

[latex]\begin{eqnarray*} S_{red} & = & C+E+P_{red} \\ & = & 65+33.80+3.75 \\ & = & \$102.55 \end{eqnarray*}[/latex]

The reduced selling price is $102.55.

**Step 7:** Calculate the rate of markdown.

[latex]\begin{eqnarray*}D & = & S-S_{red} \\ & = & 110.50-102.55 \\ & = & \$7.95 \end{eqnarray*}[/latex]

[latex]\begin{eqnarray*} d & = & \frac{D}{S} \times 100\% \\ & = & \frac{7.95}{110.50} \times 100\% \\ & = & 7.19\% \end{eqnarray*}[/latex]

At the reduced selling price, the rate of markdown is 7.19%.

**Step 8:** Calculate the reduced profit when the reduced selling price is the cost ([latex]S_{red}=C=65[/latex]).

[latex]\begin{eqnarray*} P_{red} & = & S_{red}-C-E \\ & = & 65-65-33.80 \\ & = & -\$33.80 \end{eqnarray*}[/latex]

If the item is sold at cost, the loss is $33.80.

**EXAMPLE**

A retailer of electronic goods purchases TVs from a distributor after trade discounts of 15% and 7% on the list price of $700 per TV. The retailer then marks up the TVs by 60% on the selling price. The expenses are 25% of the selling price. During a sale, they offer a markdown of 20%.

- What is the regular selling price?
- What is the reduced selling price?
- What is the break-even price?

**Solution:**

**Step 1: ** The given information is

[latex]\begin{eqnarray*} L & = & \$700 \\ d_1 & = & 15\% \\ d_2 & = & 7\% \\ M & = & 0.6 \times S \\ E & = & 0.25 \times S \\ d & = & 20\% \end{eqnarray*}[/latex]

**Step 2:** Calculate the cost.

[latex]\begin{eqnarray*} C& = & L \times (1-d_1) \times (1-d_2) \\ & = & 700 \times (1-0.15) \times (1-0.07) \\ & = & 700 \times 0.85 \times 0.93 \\ & = & \$553.35 \end{eqnarray*}[/latex]

**Step 3:** Calculate the regular selling price.

[latex]\begin{eqnarray*} S & = & C+M \\ S & = & 553.35+0.6 \times S \\ S-0.6 \times S& = & 553.35 \\ (1-0.6) \times S & =& 553.35 \\ 0.4 \times S & = & 553.35 \\ S & = & \frac{553.35}{0.4} \\ S & = & \$1,383.38 \end{eqnarray*}[/latex]

The regular selling price is $1,383.38

**Step 4:** Calculate the reduced selling price.

[latex]\begin{eqnarray*} S_{red} & = & S \times (1-d) \\ & = & 1,383.38 \times (1-0.2) \\ & = & 1,383.38 \times 0.8 \\ & = & \$1,106.70 \end{eqnarray*}[/latex]

The reduced selling price is $1,106.70.

**Step 5:** Calculate the expenses.

[latex]\begin{eqnarray*} E & = & 0.25 \times S \\ & = & 0.25 \times 1,383.38 \\ & = & \$345.85 \end{eqnarray*}[/latex]

**Step 6:** Calculate the break-even price

[latex]\begin{eqnarray*}BE & = & C+E \\ & = & 553.35+345.85 \\ & = & \$899.20 \end{eqnarray*}[/latex]

The break-even price is $899.20.

## TRY IT

A retailer purchases an item for $180 less a discount of 20%. The markup on the item is 45% on cost and the operating expenses are 15% on cost.

- What is the regular selling price of the item?
- During a sale the item is marked down by 25%. What is the reduced selling price and profit or loss at the sale price?

**Click to see Solution**

1. Regular selling price.

[latex]\begin{eqnarray*} C & = & 180 \times (1-0.2) \\ & = & 180 \times 0.8 \\ & = & \$144 \\ \\ M & = & 0.45 \times C \\ & = & 0.45 \times 144 \\ & = & \$64.80 \\ \\ S & = & C+M \\ & = & 144+64.80 \\ & = & $208.80 \end{eqnarray*}[/latex]

2. Reduced selling price.

[latex]\begin{eqnarray*} S_{red} & = & S \times (1-d) \\ & = & 208.80 \times (1-0.25) \\ & = & \$81.60 \\ \\ E & = & 0.15 \times C \\ & = & 0.15 \times 144 \\ & = & \$21.60 \\ \\ P_{red} & = & S_{red}-C-E \\ & = & 81.60-144-21.60 \\ & = & -\$84\end{eqnarray*}[/latex]

## TRY IT

A distributor sells water cooling units for $1000 each. The operating profit is 18% of cost and the expenses are 22% of cost.

- What is the cost per cooling unit?
- During a sale, the units are sold at a price so that the profit is $45 per unit. What is the rate of markdown at the reduced selling price?
- If the units are marked down by 30%, what is the reduced profit or loss?

**Click to see Solution**

1. Cost.

[latex]\begin{eqnarray*} S & = & C+E+P \\ 1,000 & = & C+0.22 \times C+0.18 \times C \\1,000 & = & 1.4 \times C \\ \frac{1,000}{1.4} & = &C \\ \$714.29 & = & C \end{eqnarray*}[/latex]

2. Rate of markdown.

[latex]\begin{eqnarray*} E & = & 0.22 \times C \\ & = & 0.22 \times 714.29 \\ & = & \$157.14 \\ \\ S_{red} & = & C+E+P_{red} \\ & = & 714.29+157.14+45 \\ & = & \$916.43 \\ \\ D & = & S-S_{red} \\ & = & 1,000=916.43 \\ & = & \$83.57 \\ \\ d & = & \frac{D}{S} \times 100\% \\ & = & \frac{83.57}{1,000} \times 100\% \\ & = & 8.357\% \end{eqnarray*}[/latex]

3. Reduced profit or loss.

[latex]\begin{eqnarray*} S_{red} & = & S \times (1-d) \\ & = & 1,000 \times (1-0.3) \\ & = & \$700 \\ \\ P_{red} & = & S_{red}-C-E \\ & = & 700-714.29-157.14 \\ & = & -\$171.43\end{eqnarray*}[/latex]

**Exercises**

- Ziggy’s Skates purchases ice skates for $30 each pair and sells them at a regular price of $42 each pair.
- If the profit made is $5.25 per pair of ice skates, calculate the overhead expense per pair.
- If the discount offered during a Holiday Sale is 20%, calculate the reduced selling price and the profits or loss made on the sale of each pair.

**Click to see Answer**a. $6.75; b. $33.60 ,-$3.15

- Belanger Acoustics purchased acoustic guitars for $80 each and has marked them up by 20% on cost. The overhead expenses were 10% on cost.
- Calculate the regular selling price of each guitar and the profit made.
- If Belanger decides to offer a markdown of 5% what would be the reduced selling price and profit or loss they would make on the sale of each guitar?

**Click to see Answer**a. $96.00, $8.00; b. $91.20, $3.20

- Julia makes a 10% profit on the cost of T shirts, which she purchases at $15.00 each. The overhead expenses are 25% on cost. During a sale, she marked the T shirts down by 10%.
- What is the profit or loss on the sale of this item?
- What is the amount of markup on the sale price of the item?

**Click to see Answer**a. -$0.53; b. $3.22

- Guilherme was in the business of purchasing painting from Brazil and selling them in Toronto at his shop. On one shipment listed at $2,400, he received trade discounts of 10%, 8%, and 6%. The overhead expenses were 15% of his costs and he wanted to make an operating profit of 20% on cost.
- Calculate the regular selling price of the painting.
- Calculate the loss or profit he will make if he decides to markdown the selling prices by 15%.
- Calculate the maximum amount of markdown that he can offer so that he breaks even on the sale.

**Click to see Answer**a. $2521.76; b. 3.52%; c. 25.93%

- Juanita purchased designer purses for $242.88 each, less 12% and 8%. The markup is 35% on selling price and the operating profit is 15% on cost. During a sale , the designer purses were marked down to $260.00.
- What was the regular selling price?
- What was the rate of markdown?
- At the sale price, what was the profit of loss?

**Click to see Answer**a. $302.52; b. 14.06%; c. -$13.02

- The regular selling price of cell phones at a store is $125 each. During a sale, it was sold at a markdown of 45%. Calculate the profit or loss made on the sale of the cell phone if the break-even price is $75.

**Click to see Answer**-$6.25

- A retailer purchased shirts for $50 each, less 10%. The retailer has a markup of 20% on selling price and an operating profit of 10% on cost. During a sale, the shirts were marked down and sold at break-even price.
- What was the regular selling price of each shirt?
- What was the sale price?
- What was the rate of markdown offered during the sale?

**Click to see Answer**a. $56.25; b. $51.75; c. 8%

#### Attribution

“4.5: Merchandising” from Introduction to Business Math by Margaret Dancy is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted.

“6.4: Merchandising” from Business Math: A Step-by-Step Handbook (2021B) by J. Olivier and Lyryx Learning Inc. through a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License unless otherwise noted.