Buying and Selling
Francis Joseph H. Campena, Ph.D.
Mathematics Department
De La Salle University Manila
October 24, 2016
Francis Joseph H. Campena, Ph.D. (DLSU)
Buying and Selling
October 24, 2016
1 / 15
Outline
1
Mark-On, Mark-Up, Mark-Down, Gross Margin
2
Single Trade Discount and Discount Series
3
Profit Loss and Break Even
4
Commission
Francis Joseph H. Campena, Ph.D. (DLSU)
Buying and Selling
October 24, 2016
2 / 15
Mark-On, Mark-Up, Mark-Down, Gross Margin
Mo : Mark-on Price-The original price of the product
Mu : Mark-up Percentage-The amount of increase in the original
price of the product
Md : Mark-down Percentage-The amount of degrease in the original
price of the product
Mu
r : Mark-up rate- r =
Mo
Md
r : Mark-down rate- r =
Mo
S: Selling Price S = Mo + Mu or S = Mo − Md
Mg : Gross margin-it is another way of looking at how a selling price
of an item is affected by and add-on amount. Mg = S − Mo
Mg
r : Gross Margin rate- r =
S
Francis Joseph H. Campena, Ph.D. (DLSU)
Buying and Selling
October 24, 2016
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Single Trade Discount and Discount Series
Definition
Single Trade Discount: A single trade discount is a discount that is given
to a customer (usually a wholesaler) when the customer buys a product.
The discount is expressed simply as a single discount of a given percentage.
D = r × Mo ; S = Mo − D
Discount Series or Chain Discounts : A chain of discounts is usually
offered by retail stores to give an illusion of a larger discount that they
really are. This is just a sequence of discounts applied to a product being
purchased.
S = Mo (1 − r1 )(1 − r2 ) · · · (1 − rk ), D = Mo − S
where, D : Discount; Mo : Mark-on Price; r , r1 , . . . , rk : Discount rates; S :
Selling Price
Francis Joseph H. Campena, Ph.D. (DLSU)
Buying and Selling
October 24, 2016
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Single Trade Discount and Discount Series
A refrigerator with a Php12,990 mark-on price is on sale at 20% off. If you
buy it now, how much will you save?
ANS.
D = (0.2)(Php12, 990) = Php2, 598
A stereo unit has list price of $1000. It goes on sale at a discount of 30%.
However, too few buyers are interested and so the manager gives an
additional 20% off. What is the final price of the stereo?
ANS.
S = $1000(1 − 0.3)(1 − 0.2) = $560.
Francis Joseph H. Campena, Ph.D. (DLSU)
Buying and Selling
October 24, 2016
5 / 15
EXERCISES
1. An evening gown lists for Php15,000 and is offered at a discount rate
for 30%. Since it does not sell for quite some time, the store manager
offers a second discount for 40% off the discounted price. However, it
does not work also and does not sell. In desperation, the store offers
another 50% off on top of the the previous discounts. What was the
final price of the gown?
2. A branded shirt cost Php1,500 and is marked 20% off. How much was
the discount? What is the selling price of the shirt?
3. A rice cooker was sold for Php450 during a holiday sale. It was marked
at 70% off. How much was the mark-on price of the rice cooker?
4. The organizer of a conference ordered 250 pieces of bags for the
conference kit priced at Php150 per bag. However, since the order was
in bulk, they were given a 35%-20%-10% discount series. How much
was the bill of the organizer for the said purchase?
Francis Joseph H. Campena, Ph.D. (DLSU)
Buying and Selling
October 24, 2016
6 / 15
Single Trade Discount and Discount Series
Suppose a series of discounts r1 , r2 , r3 , . . . , rk were given, the equivalent
single discount rate r is computed as
r = (1 − r1 )(1 − r2 ) · · · (1 − rk )
The organizer of a conference ordered 250 pieces of bags for the
conference kit priced at Php150 per bag. However, since the order was in
bulk, they were given a 35%-20%-10% discount series. What single
discount rate is equivalent to the given series of discounts?
Francis Joseph H. Campena, Ph.D. (DLSU)
Buying and Selling
October 24, 2016
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Profit Loss and Break Even
Fixed Cost: Expenses necessary to keep the business open. This cost
is not dependent sales volume. Usually includes salaries of emplyes,
rent basic utilities and other necessary expenses.
Variable Cost: includes expenses in producing each product or item.
Total Cost or Total Expenses: the sum of fixed cost and variable cost.
Revenue: the income that the business has from its normal business
activities. In a simple business activity of selling one product the
revenue is the price per item times the quantity of products sold.
Profit : the amount remaining from the revenue after all expenses
have been deducted.
Loss : if expenses are greater than the revenue the difference of these
amount is called a loss.
Break Even Point: the point where neither profit nor a loss is made.
Francis Joseph H. Campena, Ph.D. (DLSU)
Buying and Selling
October 24, 2016
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Profit Loss and Break Even
Total Cost Function
TC (x) = vx + FC (x)
where FC (x) represents the fixed cost, v represents the variable cost
per unit and x represents the number of units produced.
Total Revenue Function
TR(x) = px
where p is the price per unit of product or item and x is the number
of units sold.
Profit Funtion
P(x) = TR(x) − TC (x).
Francis Joseph H. Campena, Ph.D. (DLSU)
Buying and Selling
October 24, 2016
9 / 15
Example
Assume that the fixed cost necessary to run a coffee shop on a monthly
basis is Php30,000. In addition, a cup of coffee which is for sale at Php40
cost the shop Php10 for bulk coffee, filter and water expenses.
1
What is the break-even quantity?
2
How much profit is obtained when 3,000 cups of coffee are sold?when
4,500 cups are sold?
3
How many cups must be sold to earn a profit of Php12,000?
Francis Joseph H. Campena, Ph.D. (DLSU)
Buying and Selling
October 24, 2016
10 / 15
Exercises
1
A manufacturer of a certain commodity sells his product at Php10
per unit, selling all he produces. The fixed cost is Php5,000 and the
variable cost is Php5 per unit.
At what level of production will the manufacturer have a profit of
Php1,000?
at what level of production will he have a break-even?
Francis Joseph H. Campena, Ph.D. (DLSU)
Buying and Selling
October 24, 2016
11 / 15
Example
A retailer purchased a printer for Php3,500. Operating expenses incurred
were 5% based on cost. If the retailer wanted a 10% net profit based on
cost, determine the following:
selling price
net profit
break-even price
Francis Joseph H. Campena, Ph.D. (DLSU)
Buying and Selling
October 24, 2016
12 / 15
Example
The unit price of a certain commodity is given by p = 24 − 4x for x units
sold and the cost in producing the commodity consists of a fixed vost of
Php16 and a variable cost of Php4 per unit. Price, cost and quantity are
expressed in thousands.
What are the total revenue, total cost and profit functions?
What sales volume will the manufacturer have a break even?
What is the highest possible revenue for this commodity?
Francis Joseph H. Campena, Ph.D. (DLSU)
Buying and Selling
October 24, 2016
13 / 15
EXERCISES
In each item, TR(x) represents the total revenue and TC (x) represents
the total cost function. If x is the number of unit produced and also the
number of units sold, determine the break-even quantity/quantities.
1. TR(x) = 10x ; TC (x) = 2x + 8000
2. TR(x) = 156x ; TC (x) = 86x + 10, 500
3. TR(x) = 2x ; TC (x) = 0.01x 2 + 0.50x
Francis Joseph H. Campena, Ph.D. (DLSU)
Buying and Selling
October 24, 2016
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Salaries and Wages
content...
Francis Joseph H. Campena, Ph.D. (DLSU)
Buying and Selling
October 24, 2016
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Commission
Francis Joseph H. Campena, Ph.D. (DLSU)
Buying and Selling
October 24, 2016
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