Monday, December 31, 2018

Accounting Reports

Background

We've talked about how to record transactions, so now let's talk about reporting the summation of those transactions.

Question
Describe the following reports: Balance Sheet, Income Statement, Statement of Equity, Statement of Cash Flows
Answer
Balance Sheet reports on the current financial position.
Income Statement reports on the income and expenses that happened over a given period of time.
Statement of Equity reports on the changes in the reported worth of the financial entity.
Statement of Cash Flows reports on the changes in the cash balance over a period of time (this is usually only used for entities that use accrual accounting). 
Analysis

When the owners of a business receive reports on how that business is doing, there are a few things they'd like to know and the following reports cover those areas.

One thing a business owner would like to know is the financial position of the business. What does it own? What does it owe? That is the role of the Balance Sheet, also known as the Statement of Financial Position.

Another thing a business owner would like to know is the operational result of the business. How much did it earn? What did it cost to make that income? Did the business make a profit - if so how much? Or did it lose money? If so, how much? And why? That is the role of the Income Statement.

These two statements are the basic two. However, there are two others that are oftentimes used to give more supplementary information:

The first of these two is the Statement of Owner's Equity. This report is used to show the change in the value of the business. This report is more helpful with businesses that have more complicated ownership structures, such as with a corporation.

The other of these is the Statement of Cash Flows. This report is used to show the changes in the amount of cash a business has at the end of a period. The reason this report is often used is that cash is by far the most asset any business can have. While there are many different things a business can own, only one, cash, can be used to pay for things. If a business runs out of money, it's in trouble, and so keeping track of cash is vital.

Vocabulary used:

For more information check out these links (comment to add your favourite link):

Where might you have come from?

Fact-orials Index

Accounting Principles:
Where might we go?

Financial Reports:

Admin - 31 Dec 2018

Hey there everyone,

With this being the last day of the year, I thought I'd do my weekly update today.

This week I've worked in a few areas, including Math (Real Numbers, Variables), Geometry (Points, Line Segment, Line), and Accounting (Financial Entity, Comparability of Transactions). I also posted up an entry inviting help to come in - if there is an area where you'd like to contribute (whether writing material, editing, making a financial contribution, or simply liking and sharing, Would You Like to Help?) but felt like you needed an invitation - here it is!

Going forward, I'll continue to develop the section on transaction types with different numbers, accounting topics, geometry topics, and more.

I've opened a new Facebook group associated with Fact-orials at https://www.facebook.com/groups/Factorials- I'll be using it to put different learning paths to make accessing the material easier within Facebook.

I hope 2018 was wonderful and am hoping that 2019 is better.

Until next week,
Parz

Sunday, December 30, 2018

Would You Like To Help?

Hello everyone!

As Fact-orials develops and grows, I'm looking for some help. Interested?

  • Content Contributor - have a desire to write an entry or three? Have a topic or subject you're interested in? Working together, you can write and I can format and edit entries that will be read by folks all around the world.
  • Proofreader - have a desire to check links, test assumptions, and correct my spelling and grammar? If so, working together, we can make Fact-orials better. As any writer will tell you, good writing is the result of good editing and great writing is the result of great editing.
  • Financial Supporter - have a desire to help out financially? From buying and maintaining a domain name to buying software to make better graphics and all sorts of things in between, becoming a Patreon supporter will help me make the site better (the link is in the top line of links at the top of the page)
  • Moral Support - have a desire to let me know you are reading? Hit Like on the Facebook page (there's a link at the top of the page), follow the blog (you can subscribe and receive new posts via email), or post a comment. 
I hope to hear from you!
Parz



Saturday, December 29, 2018

Points, Line segment, Line

Background

We can follow paths off of The Number 1 to talk about more and more complex operations involving numbers. This path is going to follow paths involving shape and form.

Question
  1. Graph a point. 
  2. Graph another point. 
  3. Graph a line segment between the two points. 
  4. Extend the line segment in one direction. What's that called?
  5. Extend the line segment in both direction. What's that called?
Answer
See below for the steps. A ray is a line segment extended in one direction. A line is a line segment extended in both directions.
Analysis

Without worrying about identifying where the point is put, let's just put a point on a page:



And now let's just graph another point:



Perfect. So now let's connect the two dots (we'll use the shortest distance possible, so no twisty lines or anything like that):



The green connector between the two dots is called a line segment.

Perfect! Now let's extend the line segment up and right so that it extends forever (so that if we had a large enough sheet of paper, the line segment would extend for as far as the paper reaches, and then continue even more - the only thing holding back the extension here is the limits of the image):



When we have a line segment that extends off into forever in one direction, this is called a ray.

And now let's extend the line segment in both directions:



A line segment extended in both directions into infinity is called a line.

At this point we might say "so what?". Why go through all this? Well, we've just worked through some of the work done by ancient peoples (the Greeks worked through this and other cultures might have as well. Euclid, in 300 BCE, as you can see in the link below, formalized what we just worked through - we just did the first two of his five geometrical postulates):

  1. It is possible to draw a straight line from any point to any point, and
  2. It is possible to extend a line segment continuously in a straight line


Vocabulary used:

For more information check out these links (comment to add your favourite link):

https://www.storyofmathematics.com/hellenistic_euclid.html
A pdf work (requires a download) at intellectualmathematics.com that takes Euclid's book, Elements, adds illustrations, and leads you through geometry: http://intellectualmathematics.com/geometry/

Where might you have come from?

Fact-orials Index

Numbers:
Where might we go?

Geometry:

Wednesday, December 26, 2018

Variables

Background

It's one thing to figure things out when we know what all the numbers are that are involved, say like 1 + 2 = 3. But what if we don't know what all the numbers are? Like 1 + "something" = 3?

Question
What is a variable? What is a constant?
Answer
A variable is a place holder - it tells us that a number (or a whole bunch of numbers) can go into that spot.
A constant is a number that doesn't change. Any stated number is a constant. 
Analysis

Up to this point, when entries have gone over different kinds of numbers, we've known what those numbers are. There are entries that show how to work with these different kinds of numbers: how to deal with addition between counting numbers, for instance, or exponential expressions using integers. But what if we don't know what some of the numbers are? What do we do?

What we can do is to set up a place holder for the numbers we don't know. We can do that using a letter symbolizing that number. For instance, if I don't know what 1 + 2 equals, I can write this:

1 + 2 = x

We can figure out that 1 + 2 = 3, and so we can say that x = 3.

But what if we know the 1 and the 3 but don't know the 2?

1 + x = 3

We can look at this and figure out that x = 2.

What if all we know is that we want two unknown numbers to add up to 3?

x + y = 3

Then x and y could be all sorts of pairs of numbers. x can be 2 and y = 1. x can be 1 and y = 2. In fact, there is an infinite number of pairs we can work out for this - we'll do that in a later entry.

And so a variable is a symbol that tells us that a number (or numbers) goes in there and we don't know what it is (yet). 

A constant is a stated number, such as 3, 0, and -34. 

While any letter or symbol can be used to indicate a place holder, there are some variables that are more common:

x is probably the most used variable of all. It's commonly the "default" variable - or in other words, if you want to indicate a variable and you don't have a variable that makes more sense, x is the one often used.

y is another commonly used variable and often used along with x.

n is a common variable when looking to talk about the nth term

t is a commonly used when solving problems involving time

d is a commonly used when solving for distance or displacement

v is commonly used when solving for velocity

a is commonly used when solving for acceleration

Vocabulary used:

For more information check out these links (comment to add your favourite link):

Where might you have come from?

Fact-orials Index

Numbers:
Where might we go?

Operations with different kinds of numbers:
Relations:


Graphing:

Financial Entity

Background

We've talked at length about how to do transactions and the importance of having the reporting from those transactions being comparable both to former time periods with the same financial entity and also comparable to other financial entity. But what is a financial entity?

Question
Define what a financial entity is. 
A dentist has a home on one side of town. His dental clinic is on the other side of town. For the following transactions, does it affect the dental business or the dentist?
  1. Paying the rent on the dental clinic space 
  2. Paying the bill for TV cable service at the house
  3. Paying the salary of the receptionist at the clinic
  4. Paying the car loan on the car the dentist uses 
Answer
A financial entity is a person, group, or organization about which we report on the financial activity. A company or other organization has its activity reported on separate and apart from its owner(s) and also separate from any other financial entity.
  1. clinic
  2. dentist
  3. clinic
  4. it depends on which financial entity owns the car - the dentist or the clinic 
Analysis

Let's first talk about what it means to be a financial entity. A financial entity is a person, group, or organization about which we report on the financial activity. A company or other organization has its activity reported on separate and apart from its owner(s) and also separate from any other financial entity.

It isn't always easy to tell what is and what isn't part of a financial entity. The question is designed to highlight this fact.

For many people, they work for a company and are paid a salary for their work (much like the dentist's receptionist - that person works for the dental clinic and is paid a salary for that work). That person is a financial entity - they earn money in the form of a salary, pay for household expenses, perhaps invest for retirement. That person is a financial entity.

On the other end of the spectrum, large corporations such as Apple, Nike, and Amazon are financial entities - they earn money from customers, pay salaries to all the employees, and so on. These companies are financial entities.

So now let's look at the dentist. The dentist owns the clinic, paid money to set it up, earns money based on his education and expertise, approves all the payments, and more. And so in one sense, the dentist and the dental clinic are one and the same - they constitute one financial entity.

However, since we are looking to have the best information available concerning the clinic, we'd want to treat the clinic as a separate financial entity and track all of its activity on its own.

I should note that as the clinic's business speeds up or slows down, the fortunes of the dentist will also change, and so within the dentist's records, we'd show the value of the clinic going up and down accordingly. 

To summarize - the clinic is a separate financial entity - all the activity and transactions related to the clinic will be reflected in any reports done for the clinic. The dentist is also a financial entity and as part of his records, the value of the clinic will increase and decrease.

Let's talk a bit further about this - what would happen if the dentist operated his clinic at his house. Would the whole house be part of the clinic? Part of the house? Any of the house? The answer to this question is up to the dentist - but the best answer would be one that accurately reflects the operations of the clinic separately. So perhaps the clinic pays rent to the dentist for occupying a room of his house?

Let's now answer the second part of the question:

1. For the clinic being in a different part of the city and it needing to operate in a rental space (such as a medical park), the rent paid would be part of the clinic's expenses and so would be reported on the clinic's books:

DR Rent Expense
CR Cash

2. The cable bill for at the dentist's house is not part of the clinic, and so the dentist would report this on his individual books.

DR Cable Expense
CR Cash

3. Paying the receptionist at the clinic is clearly a clinic expense as the receptionist works for the clinic:

DR Salary Expense
CR Cash

4. This one is a bit of a trick question - the question we have to ask is "Who/What owns the car?" If the car was bought by the clinic, then all the expenses related to the car are reported by the clinic. However, if the car was bought by the dentist as an individual, then it'd be reported on the dentist's individual books. In either case, the entry each month, using cash accounting, would be:

DR Interest Expense
CR Cash

(If we used accrual accounting, we'd be reducing the Loan Liability and paying interest this way):

DR Loan Liability
DR Interest Expense
CR Cash

Vocabulary used:

For more information check out these links (comment to add your favourite link):

Where might you have come from?

Fact-orials Index

Accounting Principles:
Where might we go?

Accounting Principles:

Tuesday, December 25, 2018

Real Numbers

Background

We've talked about rational numbers, which are numbers that we can make using fractions of integers (the denominator being non-zero), which also means they can be made by terminating or repeating decimals. We've also talked about irrational numbers, which are numbers that can't be made using fractions of integers, which also means they are made by decimals that neither terminate or repeat. The two types of numbers together constitute the Real Numbers.

Question
What are some examples of Real Numbers?
Answer
All the numbers on the number line are real numbers, such as 
Analysis

Let's first look at the number line between the integers 0 and 1:



Note that between 0 and 1, there are an infinite number of numbers and of those, there are two kinds of numbers: rational and irrational.

For instance, there is 0.3, which is a terminating decimal (the red dot):



There is also the repeating decimal  (the blue dot):



Between those two points, there are irrational numbers such as 0.32332233322233332222.... (purple dot):



No matter what the decimal is, we can find it along the number line. If we graph a point for each rational and irrational, we end up with a solid line:



and, in fact, we can then look at all the rational and irrational numbers between all of the integers - and so we end up with a solid line that runs forever to the left (bigger and bigger negative numbers) and also to the right (bigger and bigger positive numbers)(I'm showing the numbers from -100 to 100 in the graph below, but the graph continues on forever in both directions):



Vocabulary used:

For more information check out these links (comment to add your favourite link):

Where might you have come from?

Fact-orials Index

Numbers:
Graphing:
Where might we go?

Numbers:
Associated Operations:

Monday, December 24, 2018

Comparability of Transactions

Background

We've talked about how to record transactions, but in order to make the information even more useful, it'd be good if we could use it to compare current operations to past operations, and even to compare the performance of one financial entity to another...

Question
What are some ways that financial performance is made comparable to a. other time periods, b. other entities?
Answer
a. The reporting of transactions should cover equal time periods compared to other reported time periods,
b. Rules on how to record different kinds of transactions have been put into place, both in individual countries and internationally, to enhance comparability of financial performance of different entities. 
Analysis

We've talked about the recording of transactions but haven't covered the ways the recording of information can help a financial entity to enhance its performance and enable owners to make better decisions. So let's talk about that!

Let's talk about an example company and work our way through how comparability is important. Let's have that company be a new restaurant. It opens its doors for business at the start of Year 1.

The owners of the business would like to keep track of how the restaurant is doing and so they ask for updates from time to time from the store manager. The store manager, of course, would like to show the owners that he's doing a good job, and so without any further guidance from the owners, the manager will do what he can to make the restaurant look like it's doing well.

One thing the manager might do is to report more frequently when things are going well and less frequently when things are slow. The manager might not even report at all when things are going poorly! The restaurant could be running out of money and the owners wouldn't know!

And so the owners would want periodic reports on a regular basis to know how the restaurant is doing. Most businesses look at their operations on a yearly basis - and oftentimes they look at more periodic time periods as well (such as quarterly, monthly, and even weekly).

This reporting with equal time periods allows owners to compare how one time period (say Year 2) is doing compared to another equal time period (say Year 1). This makes the reporting more helpful - is Year 2 better than Year 1? Is it worse? What might be causing the difference?

This comparability of time periods makes the reports more useful.

Now let's expand this example a little bit.

A big restaurant chain is looking to buy a restaurant in the local area of our example restaurant. Let's say there are five contenders to be bought and our example restaurant is one of them. How will the big chain decide which to buy?

One big factor will be looking at the operating results of each restaurant and seeing which is doing the best. But here's the thing - if each restaurant has its own way of reporting operations, it becomes very hard for the big chain to figure out which restaurant is doing the best.

This type of consideration is why there are rules in place as to how to record transactions - so that different companies can be compared on an equal footing. (I should note that the rules get stricter and stricter as the business gets more and more complicated).

There are different organizations that issue rules about how to account for transactions. Governments will sometimes issue rules on accounting, taxation bodies can do it as well. Organizations such as the Financial Accounting Standards Board (FASB) in the USA issue rules that big companies in the USA are required to follow. And internationally, there is a movement towards having a standardized set of rules so that the accounting rules in the USA and in, say Germany, are the same.

Vocabulary used:

For more information check out these links (comment to add your favourite link):

FASB

Where might you have come from?

Fact-orials Index

Accounting Principles
Where might we go?

Accounting Principles

The Start of Everything - the Fact-orials Table of Contents

Background

Not to sound trite or corny, but there was a time where our ancestors were mostly concerned with surviving - the time and effort (much less the brain power) needed to begin wondering about Life, Death, the Universe, and Everything In It, was just not important. Life was a struggle - wondering and thinking about things other than survival were a waste.

But as man evolved, as society developed, and as survival was no longer a 24/7 challenge, there was time to sit and wonder, to think, to speculate. Stories emerged to help explain some of the mysteries of life, such as the origin of the earth, the existence of different species and how they came about, the seasons, and more.

From those questions and the resulting answers came more questions and yet more answers. And so on. This is still the status quo of humanity - continually developing new social structures, new ways to understand self, the environment, the Universe, and everything within it.

It's from these first thoughts that Fact-orials tries to start - to follow the paths where human thought and endeavour have sprung and where they've gone.

Let's follow some paths.

One set of paths we can follow is the use of numbers to record, transmit, discover, and predict information:

Math Fact-orials - the story here starts with The Number 1, mathematical tools are developed to analyze many different aspects of the Universe.
Vocabulary used:

For more information check out these links (comment to add your favourite link):

The Story of Mathematics

Where might you have come from?

Fact-orials Index

Where might we go?

Sunday, December 23, 2018

Admin - weekly update 23 Dec 2018

Hello everyone,

This has been a great week, both in terms of posting up new material and in terms of exposure for the resource.

Let me talk about exposure first. After witnessing disaster after disaster with Facebook, I did a search for an alternative social media site... which I didn't find. But what I did find was a social media site dedicated to education - one that allows teachers, students, and parents to all be a part of. Schools use it to disseminate lesson plans and learning resources, home schoolers can use it to access the various learning apps and tools that are uploaded to it. And I have shared Fact-orials onto this site - Edmodo.com. Already I'm seeing an uptick in visitors to Fact-orials and I'm hoping I get some feedback from these potential users. I'm quite excited to be a part of edmodo and I hope Fact-orials helps students understand better various topics (primarily math right now but others in the future).

Speaking of math (and other topic) development, I finished working on the Order of Operations in terms of Integer operations. I realized that before I can finish the Rational Numbers, also for the Order of Operations, I had to introduce Irrational Numbers first, and so that has been done. I've also advanced Accounting Fact-orials with a couple of new entries. And lastly I got an entry in on Factorials when working with identical items within the population.

Looking forward to the next couple of weeks, I'll be introducing within Math Fact-orials real numbers, operations with variables, and finishing up operations with rational numbers. I'll also be  advancing Accounting Fact-orials to talk about different types of accounts.

I look forward to continuing to add entries to the resource and hope that users find it useful!

Until next week,
Parz

Irrational Numbers

Background

You might have noticed, when talking about Rational Numbers, that when we dealt with decimals, we only dealt with those that either ended (the technical term is terminated), like , or repeated, like  . So what about decimals that neither terminate or repeat?

Question
What is an irrational number? How many of them sit between 0 and 1? 
Answer
The definition of an irrational number is one of exclusion (in other words, an irrational number is defined by what it isn't rather than what it is). An irrational number is neither rational (that is, can be made be made by a fraction of integers with the denominator being non-zero) nor is it imaginary (we'll talk about what this is in a later entry).
There are an infinite number of irrational numbers between 0 and 1. 
Analysis

We alluded to what an irrational number is in the Background, but let's go over what it is and isn't in more detail here.

Let's take a look at , and specifically the decimal, 0.25. We can express this terminating decimal as a fraction:



And we can go through a process with a repeating decimal to turn it into a fraction:


   

we subtract them to get:





But with an irrational number, we can't simply put a terminated decimal over an appropriate power of 10 (like 100 which is what we used for 0.25) nor can we go through a process to subtract out the repeating decimal like we did with . An irrational number has a decimal that doesn't repeat or terminate, like:

0.123456789101112131415...

The decimals can be random, or there can be a pattern that doesn't repeat (like writing out the natural numbers in order like above).

Notice that we can replace the first 1 in the series with any of the infinite number of natural numbers, and that is simply the first digit (we could do that with any digit!). Therefore, we can say that there are an infinite number of irrational numbers between 0 and 1.

Vocabulary used:

For more information check out these links (comment to add your favourite link):

Where might you have come from?

Fact-orials Index

Numbers:
Where might we go?

Numbers:

Saturday, December 22, 2018

Factorials with Identical Items

Background

We talked about Factorials when we have all the items being distinguishable (we can tell each item apart from each other item). But what happens when we have duplicate items/indistinguishable items?

Question
Stephanie has six special teacups that she wants to display in a row on a shelf. In how many ways can she display them if they:
  1. are all distinguishable (are all different),
  2. are all indistinguishable (are all the same),
  3. five are red and one is blue
  4. four are red and two are blue
  5. four are red, one is blue, and one is yellow
  6. two are red, two are blue, two are yellow 
Answer
  1.  
  2.  
  3.  
Analysis

Before we move into areas dealing with identical items, let's first work through a problem we worked through already in the Factorials entry:

Question 1

Where there are six things that are all different and we're putting them in a row, we can put all of the 6 items into the first place.

We can then take one of the remaining 5 items and place it in the second position.

We can then take one of the remaining 4 items and place it in the third position.

And so on. And so we end up with:

6 x 5 x 4 x 3 x 2 x 1 = 6! = 720

Question 2

Now let's work through a question where all the items are the same. Let's say that each item is labeled R for Red. Let's lay them out:

RRRRRR

It doesn't matter how I shuffle the teacups - it's all the same. Therefore, there is only 1 way to arrange them.

Let's now get to this answer mathematically.

Let's start looking at this by looking at 3 items. If they are all different, we have 3! = 6 ways to arrange the items:

ABC
ACB
BAC
BCA
CAB
CBA

but if B and C are exactly the same so that we have 2 B's, we have:

ABB
BAB
BBA

Let's look at ABB. There are two arrangements in here - ABC and ACB - but because B and C are identical, we don't know which is which.

The same is true of BAB. And also true of BBA.

The way we can express this mathematically is that we start with the total number of items to arrange: 3 in our current example, and take the factorial. Here we have 3!

We then divide by the number of ways we can arrange the different items. For items that are distinguishable, like in Question 1, we can divide by 1! For items that are the indistinguishable, we divide by the number in the indistinguishable items. So for two B's, we divide by 2!. And so we end up with:



We can now work out the question in the original question. There are 6 items we are arranging and there are 6 items that are identical. And so we get:



Question 3

Now we have 5 Red cups and 1 Blue cup. We can work through the arrangements by listing them out:

RRRRRB
RRRRBR
RRRBRR
RRBRRR
RBRRRR
BRRRRR

And we can also work out the problem mathematically:



Question 4

We can list out the different arrangements, but let's do this mathematically first:



RRRRBB
RRRBRB
RRBRRB
RBRRRB
BRRRRB

RRRBBR
RRBRBR
RBRRBR
BRRRBR

RRBBRR
RBRBRR
BRRBRR

RBBRRR
BRBRRR

BBRRRR

Question 5

The number of arrangements is becoming enough that space becomes short. Let's just work this out mathematically. There are 4 Red teacups, 1 Blue, and 1 Yellow. Therefore, we take as the numerator 6! and we divide by 4! (the number of ways to arrange the 4 Red teacups) and 1! each for the 1 Blue and 1 Yellow teacups:



Question 6

We now have three groups of two colours each. We therefore have 6! in the numerator and then we divide by 2! for each of the three groups (which we can express in exponential form):



Vocabulary used:

For more information check out these links (comment to add your favourite link):

Where might you have come from?

Fact-orials Index

Combinatorics:
Where might we go?

Thursday, December 20, 2018

Cash vs Accrual Accounting

Background

We now know how to record transactions. The next question is when to record them...

Question
On Feb 1, a plumber goes to a customer's business to clear a clogged drain. The customer asks for a bill to be mailed. On Feb 2, the bill is mailed to the customer. On Feb 3, the bill arrives at the customer's business. On Feb 4, the customer mails a check. On Feb 5, the plumber receives the check. 
For the plumber and the customer, walk through when transactions are recorded. Do two timelines for each - one for cash accounting and one for accrual accounting.
Answer
Plumber, cash method:
Feb 5, DR Cash, CR Income 
Plumber, accrual method: 
Feb 1, DR Accounts Receivable, CR Income
Feb 5, DR Cash, CR Accounts Receivable
Business, cash method:
Feb 4, DR Expense, CR Cash
Business, accrual method: 
Feb 1, DR Expense, CR Accounts Payable
Feb 4, DR Accounts Payable, CR Cash 
Analysis

Before we get into how to record transactions under different types of accounting schemes, let's talk about the two basic types and why we might use each.

Cash accounting is the easier to understand of the two systems. Essentially, you record income transactions when you receive money and you record expense transactions when you pay money. Because the system is based on the receipt and payment of cash, knowing when to record transactions is simple and straightforward.

So let's track the accounting of our question for the plumber on the cash method:

On Feb 1, the plumber does work but isn't paid. No transaction is recorded. In fact, all of that stuff with the bill being sent out has no effect on the plumber. We're waiting for the receipt of cash.

On Feb 5, when the plumber receives the check from the customer, he has now received money and so records a transaction:

DR Cash
CR Income

(DR is short for Debit and CR is short for Credit)

Now let's do the same for the business on the cash method:

On Feb 1, the business has work done but doesn't pay for it that day. Since money hasn't left the business yet, no transaction is recorded. In fact, it's only when a check is sent to the plumber that an entry is made:

Feb 4
DR Expense
CR Cash

Now let's talk about Accrual accounting. Essentially, you record income transactions when income is earned and you record expenses when they are incurred.

How does this play out for the plumber and the business? Let's watch the plumber first:

On Feb 1, the plumber does work. He has earned income. It doesn't matter that he hasn't received cash yet - he records income. We'll also record that he is owed money:

DR Accounts Receivable (i.e. he is owed money)
CR Income

On Feb 5 when he receives the check in the mail, he has now been paid. We reduce the account that says he is owed money and increase the account that says he has money:

DR Cash
CR Accounts Receivable

And now let's do the business:

On Feb 1, the business called in the plumber. An expense has been incurred which will eventually need to be paid. We record the expense and we also record that money is owed to the plumber:

DR Expense
CR Accounts Payable (i.e. the business owes money to someone)

On Feb 4, the business sends payment to the plumber. The debt is paid and cash is decreased:

DR Accounts Payable
CR Cash

*****

So let's now talk about why we might use the accrual method vs the cash method of accounting.

Clearly, using the accrual method requires more work - it took twice as many entries to record the transactions under the accrual method than under the cash method. So whatever reasons there are to use accrual accounting, it has to be worth the extra work.

One reason the accrual method is preferred is that it follows something called the Revenue Recognition principle - which is what we described above when the plumber recorded income when it was earned and not when the bill was paid.

For accountants, it's important that income transactions properly follow when income is earned. The payment of cash isn't always a good indicator of when income is earned. For instance, what if the plumber had had to wait 3 months for payment? It wouldn't be fair or right for the plumber to not record the income until he got paid.

Another reason is that the accrual method also follows something called the Matching Principle - which means that expenses are recorded only when they can be properly matched to the income they were incurred to produce.

A prime example of this, which we'll discuss in a later entry, is depreciation. Depreciation is the recognition of wear and tear on machinery and other expensive assets in order to make income. For instance, let's say a business that will make widgets is getting started. The company has a large factory built. Should the company be able to record the building of the factory as an expense all at once? Or should it be reduced in value over time as the wear and tear of making widgets decreases its value? The Matching Principle says it should happen over time.

*****

One more note before closing this entry - the use of accounting method is independent of other businesses. The plumber could easily be using the cash method while the business is using accrual, and vice versa (the plumber could be using accrual accounting and the business using cash accounting).

Vocabulary used:

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Wednesday, December 19, 2018

Exponentials and Integers - Practice Problems

Background

Let's work some more problems involving exponentials and integers. Keep in mind that even though we are inputting integers, we'll usually end up with fractions, i.e. rational numbers.

Question
Evaluate:
  1.  
  2.  
Answer
  1.  
Analysis

Since we're working specifically with exponentials, I'll do the work in terms of exponentials. Keep in mind that we could also get to the same answers by using fractional operations.

Question 1

Let's first put the terms into exponential forms:









And now we can do some exponential operations:





And now let's do the fractional operations:











Therefore:



Question 2



Let's once again put this into terms of exponentials:













And so therefore:



Vocabulary used:

For more information check out these links (comment to add your favourite link):

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Operations with different kinds of numbers:
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Operations with different kinds of numbers:
  • Exponentials and Rational Numbers - Practice Problems