Single Trade Discount and Discount Series || Business Math

Summary

This script delves into the concept of trade discounts, explaining key terms like suggested retail price, trade discount, net price, and discount rate. It outlines formulas for calculating trade discount and net price, and illustrates these with examples involving various discount rates. The script further explores trade discount series, showcasing how multiple discounts are applied sequentially and how to calculate the single equivalent rate, concluding with the net price and trade discount for different scenarios.

Takeaways

• 📚 The script introduces the concept of trade discounts, explaining it as the amount of discount a wholesaler or retailer receives off the list price of an item.
• 🔢 It defines 'Net Price' as the price paid by a retailer after applying the trade discount to the list price.
• 📉 The 'Discount Rate' is the percentage of the list price that is given as a discount to the retailer.
• 📝 The formula for calculating the trade discount is presented as Trade Discount (TD) = Discount Rate (DR) * List Price (LP).
• ➖ The net price is calculated by subtracting the trade discount from the list price, symbolized as Net Price (NP) = LP - TD.
• 💡 An example is given to illustrate the calculation of trade discount and net price for an item listed at 10,000 pesos with a 20% discount rate.
• 🛒 The script discusses the concept of trade discount series, where multiple discounts are applied successively to the list price.
• 🔄 The reasons for using trade discount series include encouraging volume purchases, promoting special or seasonal items, and enticing new clients.
• 🧮 The formula for calculating the net price with a series of discounts is provided, involving multiple applications of 1 minus the discount rate.
• 📉 The single rate equivalent (SRE) of a series of discounts is calculated by multiplying the inverse of each individual discount rate.
• 📱 An example of a new cell phone model subject to multiple discounts is used to demonstrate the calculation of the single rate equivalent and net price.

Q & A

What is the definition of 'suggested retail price' or 'catalog price'?

The suggested retail price or catalog price refers to the price at which a manufacturer suggests an item should be sold to customers.

What does 'trade discount' mean in the context of the transcript?

Trade discount is the amount of discount that a wholesaler or retailer receives off the list price, which is the difference between the list price and the net price.

How is the 'trade discount' calculated according to the transcript?

The trade discount is calculated as the product of the discount rate and the list price, represented as TD = DR * LP, where TD is the trade discount, DR is the discount rate, and LP is the list price.

What is the formula for determining the 'net price' as mentioned in the transcript?

The net price is determined by subtracting the trade discount from the list price, which can be represented as NP = LP - TD, where NP is the net price, LP is the list price, and TD is the trade discount.

What is the significance of the 'discount rate' in trade discount calculations?

The discount rate is the percentage rate applied to the list price to determine the trade discount, and it represents the amount to be paid by the retailer to the manufacturer.

Can you provide an example from the transcript where the net price is calculated after a 20% discount on a 10,000 peso item?

Yes, in the example, a 10,000 peso item with a 20% discount results in a trade discount of 2,000 pesos (10,000 * 0.20), and the net price is 8,000 pesos (10,000 - 2,000).

How does the transcript explain the concept of 'trade discount series'?

A trade discount series, as explained in the transcript, is when a manufacturer offers two or more trade discount percentages that apply to the same item price, encouraging volume purchases, promoting special or seasonal items, and enticing new clients.

What is the formula for calculating the 'net price' when there is a series of trade discounts?

The formula for calculating the net price with a series of discounts is NP = LP * (1 - DR1) * (1 - DR2) * ... * (1 - DRn), where NP is the net price, LP is the list price, and DR1, DR2, ..., DRn are the discount rates.

How is the 'single trade discount equivalent' determined when there are multiple discount rates?

The single trade discount equivalent is determined by the formula SRE = 1 - (1 - DR1) * (1 - DR2) * ... * (1 - DRn), where SRE is the single equivalent rate, and DR1, DR2, ..., DRn are the individual discount rates.

What is the significance of calculating the 'single trade discount equivalent'?

Calculating the single trade discount equivalent helps to understand the overall discount rate that is equivalent to a series of discounts, which can simplify the comparison and understanding of the total discount being offered.

Outlines

00:00

📚 Introduction to Trade Discounts

The script begins with an introduction to trade discounts, explaining key terms such as suggested retail price, trade discount, net price, and discount rate. It defines trade discount as the amount of discount a wholesaler or retailer receives from the list price. The script then introduces formulas for calculating trade discount (td = dr * lp) and net price (np = lp - td), where 'td' is trade discount, 'dr' is discount rate, and 'lp' is list price. An example is provided to illustrate the calculation of trade discount and net price for an item listed at 10,000 pesos with a 20% discount rate.

05:02

🔢 Calculating Net Price and Trade Discount

This paragraph delves deeper into the calculation of net price and trade discount, using an example where a factory sells goods at a retail price with a given discount rate. The process involves converting the discount rate to a decimal, applying it to the retail price to find the net price, and then determining the trade discount by subtracting the net price from the list price. The example provided involves a 20,000 peso item with a 15% discount rate, resulting in a net price of 17,000 pesos and a trade discount of 3,000 pesos.

10:07

📉 Understanding Trade Discount Series

The script explains the concept of trade discount series, which involves applying multiple discount rates sequentially to the list price of an item. It outlines the reasons for using discount series, such as encouraging volume purchases, promoting special or seasonal items, and enticing new clients. The paragraph also provides a formula for calculating the net price in a series of discounts and the single equivalent rate of discount. An example is given where a refrigerator is sold with a list price of 25,000 pesos and trade discounts of 30%, 20%, and 10%, resulting in a net price of 12,600 pesos and a total trade discount of 12,400 pesos.

15:07

📱 Applying Trade Discount Series to a Cell Phone Example

This paragraph applies the concept of trade discount series to a new model of cell phone priced at 40,500 pesos with three different discount rates: 15%, 20%, and 5%. The script guides through the process of calculating the net price and the single equivalent discount rate for the series. The calculation shows that the single equivalent discount rate is 49.6%, and the net price after applying all discounts is 26,163 pesos. Additionally, the total trade discount for the cell phone is calculated to be 14,337 pesos.

20:11

📈 Summarizing Trade Discount Calculations

The final paragraph summarizes the formulas and processes discussed in the script for calculating net prices and trade discounts, both for single discounts and discount series. It reiterates the importance of understanding discount rates and their impact on the final price of goods. The summary serves as a recap of the key points and formulas introduced throughout the script, ensuring a clear understanding of trade discount calculations.

Keywords

💡Suggested Retail Price (SRP)

The Suggested Retail Price, often abbreviated as SRP, is the price at which a manufacturer recommends that an item be sold to customers. In the context of the video, SRP serves as the starting point for calculating trade discounts. It is a key term as it sets the baseline for all subsequent discount calculations, as seen when the video discusses how trade discounts are applied to the SRP to determine the net price.

💡Trade Discount

A trade discount refers to the amount of discount that a wholesaler or retailer receives on the list price of an item. The video explains that this discount represents the difference between the list price and the net price. It is central to the theme as the video delves into how trade discounts are calculated and applied, using formulas and examples to illustrate the process.

💡Net Price

The net price is the actual price at which a wholesaler or retailer purchases an item after all trade discounts have been applied. It is crucial in the video's narrative as it represents the final cost that businesses pay for goods, which is calculated by subtracting the trade discount from the list price, as demonstrated in the examples provided.

💡Discount Rate

The discount rate is the percentage or proportion of the list price that is offered as a discount to retailers or wholesalers. It is a fundamental concept in the video, used to calculate the trade discount, which is then applied to determine the net price. The video provides a formula where the trade discount is the product of the discount rate and the list price.

💡List Price

The list price is the original price of an item as set by the manufacturer before any discounts are applied. It is a critical term in the video's discussion of trade discounts, as it is the reference point for calculating the trade discount and subsequently the net price. The list price is used in formulas and examples throughout the video to demonstrate discount calculations.

💡Trade Discount Series

A trade discount series refers to a sequence of multiple discount rates that are applied successively to the list price of an item. This concept is important in the video as it shows how manufacturers can offer a tiered discount structure to encourage volume purchases or promote specific items. The video provides an example where a refrigerator is subject to a series of discounts, and the net price is calculated by applying each discount rate in sequence.

💡Single Equivalent Rate (SER)

The single equivalent rate, or SER, is the overall discount rate that is equivalent to a series of trade discounts. It is a significant concept in the video as it helps to simplify the understanding of the total discount being offered when multiple discounts are applied. The video explains how to calculate the SER using a formula that involves the product of (1 minus each individual discount rate).

💡Chain Discount

A chain discount, also known as a series discount, is when additional discounts are deducted one after another from the list price. This term is relevant in the video's discussion of trade discount series, where it explains that the single equivalent rate of discount is not simply the sum of individual discounts. The video uses the concept of chain discount to illustrate how the total discount can be calculated when multiple discount rates are applied consecutively.

💡Volume Purchases

Volume purchases refer to the buying of goods in large quantities, often to qualify for discounts. This concept is mentioned in the video as one of the reasons for using trade discount series, where manufacturers offer discounts to encourage retailers to buy in bulk. The video implies that volume purchases can lead to significant cost savings for retailers due to the application of trade discounts.

💡Seasonal Items

Seasonal items are products that are typically in higher demand during certain times of the year. The video mentions promoting seasonal items as a reason for using trade discount series. By offering discounts on these items, manufacturers can incentivize retailers to stock up and sell more of these products during their peak selling seasons, thus moving inventory effectively.

Highlights

Definition of terms related to trade discounts, including suggested retail price, catalog price, trade discount, net price, and discount rate.

Explanation of the trade discount formula: TD = DR * LP, where TD is trade discount, DR is discount rate, and LP is list price.

Derivation of the net price formula: NP = LP - TD, and its alternative expression NP = LP * (1 - DR).

Example calculation of trade discount and net price for an item listed at 10,000 pesos with a 20% discount rate.

Method to determine the trade discount and net price when the retail price and discount rate are known but not the net price.

Example involving a 20,000 pesos item with a 15% discount rate to find the amount paid by a store and the trade discount.

Process to find the discount rate when the net price and trade discount are known, using the formula DR = (TD / LP).

Explanation of trade discount series and their use in encouraging volume purchases, promoting special items, and enticing new clients.

Calculation of net price and trade discount for an item with a series of discounts (30%, 20%, and 10%).

Determination of the single trade discount rate equivalent to a series of discounts using the formula SRE = 1 - (product of (1 - DRi)).

Example of a new cell phone model with a list price of 40,500 pesos subject to a series of discounts and the calculation of the single rate equivalent.

Method to calculate the net price for an item given its list price and the single trade discount rate equivalent.

Calculation of the total trade discount for the cell phone example by subtracting the net price from the list price.

Summary of formulas used for net price in a series of discounts and for calculating the single discount rate equivalent.

Importance of understanding trade discount series for businesses to strategically price products and manage discounts.

Practical application of trade discount calculations in retail and wholesale businesses to determine final prices and savings.

Transcripts

good day our topic will be trade

discussed so the alpha

will be the following so we have

definition of terms

as well as derivation of formula and the

stated

samples

okay so let's have suggested retail

price catalog price this price

mean all the same thing so meaning to

say the price which the manufacturer

suggests an item to be sold

to the customers

well the trade is gone it is the amount

of discount that the wholesaler or

retailer receives of

the list price so this is the difference

between the list price

and the net price

so let's have next which is net price

so the net price is actually the price

of an apache

or retainer piece for the list price

minus the trade

disk

next our definition of term is actually

the discount rate

so it is the amount of item to be paid

by the retailer to the manufacturer

so let's talk about the formula that we

will use for this trade discount so

let's have first the trade discount

so the trade discount is equal to the

product of discount rate and the list

price

so if we will put this in symbol so td

is equal to dr

times lp where in td is the trade

discount

dr is the discount rate and lp is the

list price

next on our formula is the net price so

we have

okay so net price is actually the list

price minus trade discount

okay we are in symbol np is equal to lp

minus td

such that np is the net price lp is the

list price and td is the trade discount

or i can rewrite this one as np

is equal to lp minus dr times lp

take note that the trade discount is

equal to the discount rate times the

list price

and powering the common buffer which is

after the lp

so i have the net price is equal to this

price times 1

minus er okay

let's have our example an item listed at

10 000 pesos

is subject to a discount of 20 percent

so what is the amount of discount

and the net price so let's have our step

number one but before that

let's identify first the given since our

given is ten thousand so that is

considered as the list price

and twenty percent as our discount print

so let's have step number one so we

would like to find the trade discount

take note that the trade discount is

equal to list price times discount three

then we will plug

in the numbers so this price is equal to

ten thousand

and our discount rate is twenty percent

but take note we will convert twenty

percent into decimal first

so we have ten thousand times point

twenty or the final answer for

three discount is equal to twenty

thousand

so this is your trade discount or

simply ask the discount next we want to

find out the net price

so we will move on to the second step so

that is why

find the net price so to find for the

net price that is after the list price

minus the trade discount take note that

our list price is equal to ten thousand

while our trade discount

or simply as the discount is equal to

two thousand

so we have net price is equal to eight

thousand pesos so therefore the discount

is two thousand pesos

and the net price is eight thousand

pesos

that's our second example the mpd

factory sold 20 000 pesos

water flows to the kog store the given

amount represents the retail price

of the votes for which the npd factory

has offered a 15 percent

rate this discount what is the apple

amount trade of kyj store

and what is the late discount now in

order to solve this problem let's

identify first the

given since the list price is equal to

20 000 pesos

discount rate is 15 we do not know yet

the net price as well as the trade

discount

since we do not know the trade discount

yet

let's look for the net price but they

told that we can use the formula

net price is equal to this price times 1

minus discount rate

since we do not know the rate discount

so since the list price is equal to 20

000

and the discount rate is feels 15

so i can simply plug in the numbers so i

have twenty thousand

times one minus fifteen percent

or twenty thousand times eighty five

percent

then i'll convert eighty five percent to

decimal

so i have 20 000 times 0.85

or the net price is equal to 17 000

pesos

since i know not the net price then i

can determine now the trade is gone

so that is my second step so the trade

discount is equal to this price

minus the net price take note that the

list price is equal to twenty

thousand minus seventeen thousand

so the trade discount is equal to three

thousand

pesos so the amount paid by kyj store

is seventeen thousand pesos and the

trade discount is three thousand pesos

let's move on to the next example so

what is

the discount rate if the net price of an

item is 7500 vessels

after giving a discount of 2500

so before we solve this problem let's

identify

the cuban so take note that the net

price is equal to 7500

while the trade discount is 2500

but we do not know the least price as

well as the discount rate

so we want to find out first that is

price

now take note in order to find the list

price

that is actually net price plus the

trade discount

then we will plug in the numbers of

7500 plus 2500

so the list price is equal to 10 000

pesos next we want to find out the

discount rate

now in order to find the discount rate

we'll start with the formula of

discount or trade discount is equal to

list price

times discount rate but take note that

trade discount is equal to 2500

while the list price is equal to ten

thousand and

unknown discount rate so if we will

divide both sides of the equation by

ten thousand so we will have discount

rate is equal to two thousand five

hundred

divided by 10 000 so the discount rate

is equal to 0.25

or this country is equal to 25

so there are four so the discount rate

is

25 percent

to summarize our list of uh formula so

we have trade discount is equal to this

price times discount rate

while the net price is equal to this

price minus straight discount

trade discounts are often listed in a

series this means that a manufacturer

open these two or more trade discount

percentages

which may apply to the same this price

so this

is what we call trade discount series

here are the reasons for using discount

series

so number one is to okay encourage

volume purchases

the other one is also to promote special

or

seasonal items and finally to entice new

clients

three discount series or chain discount

it means that

it is additional discounts that are

deducted one

after another from the list price

take note that the single equivalent

rate

of discount is not simply the sum of the

individual discounts

let's have our example number one our

departure

offers a refrigerator of 25 000 pesos

plus trade discounts of 30 20

and 10 so what is the net price

also how much is the trade discount and

finally

what single trade discount is equivalent

to the series of discount

so let's have our stat number one so we

want to find out or we would like to

compute the net price

applying the trade discount of 30 take

note that

in our given so the list price is equal

to 25 000 pesos

and the discount rate is 30 percent

and we would like to find the net price

so we will apply the formula of this

price times 1 minus discount rate

and we will plug in the list price of 25

000

and the discount rate of 30 so we come

up with 25 000 pesos times 70

so we come up with the net price of 17

500 pesos so this is applying

the trade discount of 30 but take note

you still have 20 and 10

so next compute the net price applying

the trade discount of 20

so this time our list price is

17 500 while the discount rate is 25

20 so we would like to find out the net

price

now so again we will apply the net price

is equal to this price times one minus

discount rate

such that our list price now is equal to

seventeen thousand five hundred

times one minus twenty percent

so we have seventeen thousand five

hundred times eighty percent

this time our net price is 14

500 applying the trade discount

of 20 so this is your net price

next we still have the 10 discount

so step number three compute the net

price

applying the trade discount of 10

so this time our list price is actually

14 000 pesos

and the discount rate is ten percent

so we want to find out the net price

again we will plug in the formula of

this price times one minus

the discount three

so our list price now is fourteen

thousand times one

minus ten percent so we have now

talking fourteen thousand times ninety

percent

or the net price is twelve thousand

six hundred pesos so applying the thirty

percent

twenty percent and ten percent so the

net price of twenty five thousand pesos

is now twelve thousand six hundred

pesos okay next we want to find out

now the trade discount

such that the given or the list price is

actually 25 000 pesos

and the net price is actually 12 600

pesos

so using the formula of trade discount

is equal to this price

minus the net price so we have here

25 000 pesos minus twelve thousand six

hundred

so we have the trade discount of twelve

thousand four hundred pesos meaning to

say

this is the amount to save applying

thirty percent twenty 20 and 10

series of trade discount

next

we want to find out also the single rate

of the trade discount

so the list price is 25 000 pesos

while the trade discount is 12 400 pesos

so in order to find the discount rate

so let's recall that trade discount

all over the list price is equal to

discount rate

and plug in the numbers of 12 400

divided by 25 000 pesos

so we have now the discount rate of 49.6

percent

so single rate equivalent to 30

20 and 10 is 49.6 percent

so let's have the formula that we will

use for the net price in a series of

discounts so we have net price is equal

to least price

times 1 minus discount rate 1 times 1

minus the

discount rate 2 times 1 minus discount

rate 3

until 1 minus discount rate

n for the single rate equivalent so we

have

sre is equal to 1 minus the quantity 1

minus discount rate 1

times the quantity 1 minus discount rate

2

times the quantity 1 minus this country

until

the quantity 1 minus discount rate sub n

let's apply the formula based on the

previous

example so we will focus on the two

questions namely

what single three discount equivalent to

this serious

uh discount and what is the net price

so let's focus first on what is the net

price so again so the given are 25 000

for the list price

discount rate one is 30 discount rate 2

is 20

and discount rate 3 is equal to 10

now since our formula now is

net price is equal to this price times 1

minus discount rate one

times one minus discount rate two times

one minus discount rate three

and until one minus discount rate

and so on but we will focus on the three

discounts

namely 30 20 and 10

so we'll come up with net price is equal

to 25

times 70 times 80 times

90 so using our calculators and the net

price

is equal to 12 600

pesos next

we would like to find out what is the

single tree discount equivalent

again so the given r

this discount rate 1 is 30 this country

2 is 20 discount rate 3 is 10

so applying the formula so we have 1

minus discount rate

1 times 1 minus discount rate 2

times 1 minus discount 3 3. so we will

focus

only on the 3 discount rates so namely

30

20 and 10 so we have here one

minus the product of seventy percent

eighty percent

and ninety percent so using our

calculator

so the single trade discount rate

equivalent is forty nine point six

percent

so the single trade discount equivalent

is 49.6

let's have another example a new model

of cell phone is 40 000

five hundred pesos subject to fifteen

percent discount

twenty percent discount and five percent

discount

so what is the single rate equivalent so

again we will identify the given

so the least price is equal to forty

thousand five hundred pesos

discount rate one is fifteen percent

this country two is twenty percent

and discount rate three is five percent

so we will plug into this

away these numbers to our formula such

that the single rate equivalent

is equal to one minus one minus discount

rate one

times one minus discount rate two times

one minus discount rate three and so on

but we have only three discount rates so

we have here

1 minus 1 minus 15

times 1 minus 20 percent times 1 minus 5

so we will come up with 1 minus the

product of 85 percent

80 percent and 95 so we will come

up with a single rate discount

equivalent of 35.4

so we can say that the single rate

equivalent of

15 percent 20 and 5

respectively is equal to 35.4

using the same problem from the previous

example

so a new model of cell phone is forty

thousand five hundred

subject to fifteen percent twenty

percent and five percent discount

so this time we would like to find out

the net price

so what is the net price so given that

our

list price is equal to forty thousand

five hundred

and the single rate equivalent or the

discount rate

is equal to thirty five point four

percent now

so we can apply the formula of net price

is equal to this price times one minus

discount rate

okay take note that the single rate

equivalent is now equal to discount

three

so plug in the numbers so we have here

this price is equal to forty thousand

five hundred times one minus thirty five

point four

percent based on the previous

computation

so we have here now that price is equal

to twenty six thousand

one hundred 163

so the net price is 26

163 pesos

again using the same example in number

two

so a new model of cell phone is forty

thousand five hundred

subject to fifteen percent twenty

percent and five percent discounts

so this time we want to find out the

trade discount

so if we are talking about the trade

discount this is the summation now

of 15 20 and 5

respectively again so the list price is

equal to 40

500 well this time the net price is 26

163 based on the previous computations

so take note that the trade discount is

equal to list price

minus the net price so 40 thousand

hundred minus twenty six thousand one

hundred sixty three

so the trade discount is equal to

fourteen thousand three hundred

thirty seven it means that this is the

total discounts

that you can save from 40 500

applying the 15 20 and 5

discounts so therefore so trade discount

is 14

337 pesos

to summarize our discussion in the

series of discounts so the net price

is equal to this price times 1 minus

discount rate 1

times 1 minus discount rate 2 times 1

minus discount rate 3

until and so on and so forth for the

single 3 discount rate equivalent

or we can rename this one a single

discount equivalent

so it has a formula of 1 minus

as a quantity 1 minus discount rate 1

times 1 minus discount rate 2

times 1 minus discount rate 3 and so on

and so forth