17 Sample Markup Problems

Ted Mitchell

#1 Cost of Product as Percent of Price (revenue per unit)

• You have purchased an apple for V = $2 and have a selling price P= $5 per apple.

• What is the cost of the apple as a percent of the selling price?

• Answer;• Cost as Percent of price = V/P = 2/5 = 40%

#2 Selling price (revenue per unit) as Percent of Cost

• You have purchased an apple for V = $2 and have a selling price P= $5 per apple.

• What is the selling price of the apple to the cost of the apple?

• Answer• Cost as Percent of price = P/V = 5/2 = 250%

3 Markup Problem

• A boy buys an apple for V = $2 and sells it for P = $5. What is his dollar markup or unit contribution (M) to Fixed costs and Profits?

• P - V = M• $5 - $2 = M• $3 = M = Unit per Unit Sold

4 Markup Problem

• A boy buys an apple for V = $2 and sells it for P = $5. What is his Markup on Price (Mp)?

• (P - V) / P = Mp• ($5 - $2) / $5 = Mp• $3/$5 = 0.6 = 60% =Mp

5 Discount Off List

• A store pays an apple distributor V = $2 per dollars per apple and sells it the suggested list price P = $5. What is the store’s Discount Off List or Markup (Mp)?

• (P - V) / P = Mp• ($5 - $2) / $5 = Mp• $3/$5 = 0.6 = 60% = Discount off list price

6 Commission Rate

A store gives their salesmen a 60% commission on the sale of an apple. The selling price is $5 per apple and the cost of each apple to the store is $2. How many dollars does the salesperson earn every time he sells an apple?• (P - V) / P = Mp• ($5 - $2) / $5 = 60% commission• Salesmen’s profit = P x Mp = $5 x 60% = $3

7 Discount Off List to Cost

• An apple distributor gives a store a 60% discount off the suggested list price of P = $5 per apple (i.e., Mp = 60%). What is the store’s cost per apple (V)?

• (P - V) / P = Mp• (5 - V) / 5 = 0.6• 5 - V = 0.6(5) = 2• 2 = V or the cost per apple = $2

8 Given Markup on Price and Cost

• A boy buys an apple for V = $2 and sells it with a markup on price of 60% (i.e., Mp = 60%). What is the selling price of the apple?

• (P - V) / P = Mp• (P - 2) / P= 0.6• P - 2 = 0.6P • P -0.6P = 2 • P = 2/.4 = 5 or the price per apple = $5

Many students simply memorize

• Cost based pricing equation to set a selling price using markup and variable cost is

• Price = (variable cost per unit)/(1-Mp)

• P = V/(1 - Mp)• P = $2/(1-60%)• P = $2/(1-0.6)• P = $2/0.4 = $5

9 Markup on Cost

• A boy buys an apple for V = $2 and sells it for P = $5. What is the Markup on Cost (Mv)?

• (P - V) / V = Mv• (5 - 2) / 2= Mv• 3/2 = 1.50 = 150% = Mv

• Markup on cost = Mv = 150%

10 Convert Markup on Cost to Markup on Price

• You are told that a product has a markup on cost of 25% What is the product’s markup on price?

• (1/Mp) - (1/Mv) = 1• 1/Mp – 1/0.25 = 1• 1/Mp = 1 + 1/0.25• 1/Mp = 1 + 4 = 5• Mp = 1/5 = 0.20 or 20%

11 Convert Markup on Cost to Markup on Price

• You are told that a product has a markup on cost of 25% What is the product’s markup on price?

• Make 25% into a fraction• Mp = 25% = 25/100• “add the top part to the bottom part”

25/(25+100)• And solve for Mp = 25/125 • Mp = 25/125 = 0.20 or 20%

12 Chain Markdowns & Markups

• You marked down your selling price of $10 in the store by 10% two weeks ago, followed by a 20% markdown last week. This week you marked the price up by 15%. What is your current price?

• Current price = $10 x (1 - markdown #1) x (1 - markdown #2) x (1 + markup)

• Current price = $10 x (1-10%) x (1-20%) x (1+15%)

• Current price = $10 x 0.9 x 0.8 x 1.15 = $8.28

13 Chain Markdowns & Markups• You marked down your original selling price of $10 in the store by

10% two weeks ago, followed by a 20% markdown last week. What is the size of the total percentage markdown or discount over the two events?

• Current price = $10 x (1-markdown #1) x (1-markdown #2)

• Current price = $10 x (1-10%) x (1-20%)• Current price = $10 x 0.9 x 0.8 = $7.20• Total Markdown % =

(Current price – Original Price)/(Original price)• Total Markdown = ($10 -7.20)/$10 = -$2.80/$10• Total Markdown or Discount = -2.80/10 = -0.28 or -28%

14 Chain Markdowns & Markups

• You marked down your original selling price of $10 in the store by 10% two weeks ago, followed by a 20% markdown last week. What is the size of the total percentage markdown or discount?

• To solve directly• Total discount =

Discount 1 + Discount 2 + (Discount 1 x Discount 2)• Total discount = D1 + D2 + (D1 x D2)• Total discount = (-0.10) + (-0.20) + (-0.10 x -0.20)• Total discount = -0.30 + 0.02 = -0.28 or -28%

15 Markups in a Channel of Distribution

• A retailer sells wagons at a list price $800 each and receives a 40% markup on price.

• His distributor gets a 20% markup on the price he sells the wagon for to the retailer

• The manufacturer get a 30% markup on the price he sells the wagon for to the distributor

• What is the dollar cost that the manufacturer pays to make each wagon?

• Manufacturer’s cost to make each wagon=$800 x (1-0.4) x (1-0.2) x (1-0.3) = $268.80

16 More Markups in a channel of distribution

• The manufacturer builds wagons for $228.80 each and sells them to a distributor with a markup on price of 60%.

• The distributor sells the wagons to a retailer.• The retailer sells the wagons to the final

consumer for $800 each and receives a 30% discount off the $800 suggested retail price.

• What dollar profit does the distributor make on each sale?

17 Markups in a Channel of Distribution

• A retailer sells wagons at a list price $800 each and receives a 40% markup on price.Pays the distributor 0.6 of $800 = $480

• His distributor gets a 20% markup on the price he sells the wagon for to the retailerThe distributor keeps 20% of the price he’s paid0.2 x $480 = $96and pays the manufacturer $480 – $96 = $384

• The manufacturer get a 30% markup on the price he sells the wagon for to the distributor

• What is the dollar profit that the manufacturer makes on the sale of each wagon?

• Manufacturer’s profit per sale is 30% of the $384 price he is paid0.3 x $384 = $115.20His cost per wagon = $384 -$115.20 = $268.80

• Markup problems are simple but you have think about them carefully

• If you rush, you can get them wrong.

• Any Questions on Markup?