#Admin - A bit of admin...

Math Fact-orials has been up and running for roughly 3 weeks and already been hitting milestones I didn't think would be possible so soon, including having nearly 1,000 page views!

I owe much of this success and exposure to two audiences: former users of Socratic.org (which is now a read-only site) and the art community of Sketchbook Skool.

Socratic.org is where I cut my teeth on answering questions online, where I found my love of all things factorial, and saw in action how topics such as budgets, household math, finance, accounting, and so many other topics that are important to people are ignored by academic math sites. One of my main goals is to bring household math into a place where people can use math as a tool and not regard it as a nightmarish exercise in frustration (I feel like I can hear people, whether consciously thinking or unconsciously feeling something like: "Please... whatever we do... whether we choose to buy the new car or lease it... don't make me figure out which one is actually better! Make the numbers stop dancing in my head!").

With that ideal in mind, I've been posting here and there about budgeting and will be adding a few more posts to that conversation. There are already a few posts about household finances and more will be forthcoming (both from me and from you - my readers!)

Sketchbook Skool's response to the post about the numbers of trade items and also the number of unique trades has been nothing short of phenomenal. A thousand and one thank you's to Aleesha, my artistic wife, the source of many of the questions on the blog, and the inspiration for the blog post about Sketchkon and who put the post onto Sketchbook Skool's Facebook page.

Looking ahead, I've found a way to satisfactorily put equations that look like equations onto the blog (thanks to latex.codecogs.com) and so that is what I'll be doing over the course of the next few days. I'm really looking forward to seeing math rendered the way it should look! 

I'll also keep on with Socratic.org Sunday throwbacks, where I'll grab questions and answers from a host of different topics that seemed to grip people's attention. This week's question will be Why Are Arteries So Much Thicker Than Veins?

I'm extremely grateful to my current, past, and future readership and I hope that as the readership grows and develops, the blog can do so alongside so that it is always meaningful and helpful. And the best way to help make that happen is to send me emails, leave comments, and ask questions! 

#Budgeting, #Household Math - Budgeting - Income

Question

I've done the budget process for expenses. Now what?

Answer

Let's now add income to the budget...

Analysis

It's time to add in the Income numbers into the budget and oddly enough this can be the harder part of the budgeting process.

With expenses, we want to identify all the expenses we incur over the course of a year, then display that on a monthly basis (we've done that part in prior posts). We use the Accrual Method to identify expenses as they are incurred so as to prevent surprises. Surprise expenses are no fun.

With income, we want to identify it as it's received - the Cash Method. One of the tendencies in budgeting is to project a rosy future where the promised raise at work is a sure thing, where that tax refund will be large, where a long lost relative died in the Congo ages ago and selfless lawyers have searched for years to find the heir - and it's you. We don't want to budget that in - if it happens, great and if it's periodic, we can budget it in (if the raise does indeed happen, adjust your budget!). Surprise income is a good thing.

For most people, income starts and ends with a salary. When we budget, we're going to want to budget the "take home pay" - not the gross pay. It's great that you have a job that pays $50,000 per year, but if you only take home $40,000 of that, that's what goes in the budget.

This also goes for people who receive pensions and other sources of periodic payments. Include what you know you are receiving. If and when an announcement comes that it's being changed, adjust your budget accordingly - if it's good news and the pension is going up, adjust the budget when you actually have that first payment in the bank. If it's bad news and it's going down, adjust the budget immediately and see if you'll need to change anything in your lifestyle.

Another common way to "overstate income" is to look to bank interest and other sources of investment income like that. Unless you have your finances set up to be living off of investment income (and we'll talk about that below), don't include it.

Ok - people who live on investment income, people who own a small business, or otherwise whose income varies. It's important to pick an income number that focuses more on the lean months than the rich ones - and it may be the case that budgeting into the expense side of things a "float" that income overages can go into and that reverse during the lean months. Doing something like that will require constant vigilance on that account - it's been set up to be there when income is lower, so you need to make sure it's nice and full when income is plentiful.

I've updated the budget example here:

https://docs.google.com/spreadsheets/d/1kCtMSNnKUXhvJT9yif5wtl5jbEsmyFz9mQ-IV62_U4g/edit?usp=sharing

and you'll note that we have a situation where the income is less than the expenses. We'll talk about that situation in the next post.

This post is part of a series on budgeting - Budgeting 101

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As always, questions and comments are welcome!

#Budgeting, #Household Expenses - Budgeting for Expenses - Putting in numbers...

Question

I've made my list of expenses. Now what?

Answer

Let's add some numbers! 

Analysis

In my last budgeting blogpost, I talked about identifying all the expenses and ways that money leaves your pocket. We want to look at the budget over the course of a sensible and useable timeframe, and that's usually one month.

The overall idea here is to budget for expenses using the Accrual Method - as soon as you are obliged to pay an amount, that should be recorded in your budget. This is why credit card payments will not make an appearance on this budget - we don't care how we pay for something, we only care that we need to pay.

Some items in our list of expenses are very easy to figure out monthly. Rent, mortgage payments, car payments, and the like are usually a single monthly payment and are easy to put into our budget sheet.

Some expenses are monthly but fluctuate. Electricity costs, for example, fluctuate based on the season (when it's colder, the costs go up). For costs that fluctuate, cycle, or otherwise change significantly over the course of the year, I'd recommend adding up the amount spent over the course of a year, then dividing by 12.

Other expenses are yearly. For instance, when paying insurance costs, I tend to pay a yearly lump sum, which results in a bit of a discount. Again, drop those costs into the yearly column and divide by 12.

And for costs that are every few months? Find the costs per year and divide by 12.

Here's an example:

https://docs.google.com/spreadsheets/d/1bDvJ0qpCvjIGNMs9AhliwCIlYY8XLLP8dnXbH1TxueE/edit?usp=sharing

This post is part of a series on budgeting - Budgeting 101

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Questions and comments always welcome!

#Budgeting, #Household Math - Budgeting Basics - Expenses

Question

How do I budget for expenses? 

Answer

This will take a few posts to do, but in this one we simply identify all the possible outlays you experience and put them in a spreadsheet.

Analysis

As we start preparing a budget, it's important to first identify where money goes. Do you pay rent or a mortgage? Pay for a car? Insurance? Gas? Or perhaps transit - maybe a daily fare or a monthly transit pass? Utilities? Cable? Phone (landline and/or mobile)? Food?

Let's first list out those items that you know about into a list (we'll be modifying the list, and so using a program like Excel (PC), Numbers (Mac), or Sheets (Google - it's free and can be used online). Here's a sample:

Mortgage
Condo Fees
Condo Insurance

Water
Electricity
Gas (Note: the heater and stove are natural gas)
Cable

Phone, landline
Phone, mobile

Groceries

Dining out

Auto payment
Auto insurance
Auto fuel
Auto maintenance, repairs


And perhaps you have other expenses that need to be added into this list. If you think of it, write it down!

Once you've done that, take a look at your credit card statement for the past few months. Do you see things there that aren't on the list? Clothing? Add it. Video games? Add it. Go ahead and put in all the categories you think of.

I've built a google spreadsheet to follow along with these posts (it's view only):

https://docs.google.com/spreadsheets/d/1ZxwZz7Nn5ZYVV-x6HgPavTP6wkfIswP8-NTvV9gTTR4/edit?usp=sharing

In our next step, we'll add numbers.

This post is part of a series on budgeting - Budgeting 101

~~~~~

As always, questions and comments welcome!

#Budgeting, #Household Math - Budgeting... What's it good for?

Question

It's great that I read everywhere about the need for a budget, but what is it?

Answer

A budget is a tool that people use to figure out their financial health.

Analysis

I like this definition enough that I'll repeat it:

A budget is a tool that people use to figure out their financial health.

The most basic question that can be answered is "Am I living within my means?". More complicated questions can also be answered, such as "Can I afford that expensive thing?". Questions involving more involved financial questions, such as "At what age can I retire?", will probably require a Personal Wealth Plan of some sort - simply analyzing monthly spending probably will be insufficient to answer that kind of question.

The main idea behind the budget is to see where your financial strengths and weaknesses are. Where there are financial weaknesses, you can then develop strategies to deal with them. For instance, if it turns out expenses are higher than income, the budget can identify that that is the case and then steps can be taken to address it.

To budget, we look at the two sides of financial life - Money coming In and Money going Out. In future posts, I'll reference topics in the post about the Statement of Cash Flows for a business because there will be some overlap in concepts.

The first place to start is to think about your expenses and how often they occur. For most people, the big expenses occur once per month (rent/mortgage payment usually being the biggest of them all). And so, in general, it's best to work with a budget that looks at a monthly timeframe (we'll deal with non-monthly expenses and incomes in their respective sections).

I think the last thing to say about what a budget is is that it's something that can be quite individualized. Depending on how exacting you'd like to be can greatly affect the budget. What are the items you want to track? What are the items you don't want to track? Generally if there is a lot of guilt and shame involved, like perhaps the "amount of money spent at coffee shops" or "the amount of money spent online shopping", those are items that need the most attention!

In future posts, we'll talk about the How of budgeting...

This post is part of a series on budgeting - Budgeting 101

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As always, comments and questions are welcome!

#Accounting, #Household Math - Moving the accounting into the home...

Question

Do accounting principals apply to my personal financial life?

Answer

Absolutely! See below for a few ideas...

Analysis

Bookkeeping and accounting really only refer to the tracking of financially-related transactions over the course of the life of a financial entity. That entity can be a company, a government, or a person/family - to anything that conducts any sort of business, accounting applies. Of course, as the complexity of the entity increases, so do the challenges of recording those transactions and making sense of the resulting information.

One of the ways we see how this applies is in the preparation of tax forms. When filling them out, you are essentially asked to account for income that's been made (from various sources and it matters where money comes from because the tax treatment can change based on the source). Alongside that, you are also asked to account for specific types of expenses - say for instance mortgage interest - because those monies spent are treated as deductions (and again, the reasons for those payments will determine how the tax calculations are done). For most people, taxes are a nightmare requiring frequent sleepless nights, gathering information. However, if an accounting system is implemented and used throughout the year, the burden (physically and mentally) of filling out the forms would be greatly decreased.

Another place accounting shows up in a household is through budgeting (company's call it financial forecasting or some such other term). What is anticipated that will be made in income? What is anticipated that will be spent? Is the income number bigger than the expenses number???

And one more place I'll mention is in the area of Needs vs Wants - or the making of financial decisions. For instance, while there is a need for a car, does that mean you need the newest Mercedes? On the other hand, is it financially better to buy an old clunker, given that it'll need more repairs and work?

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Comments and questions always welcome!

#Accounting - The Statement of Cash Flows

Question

If "cash is King" like you said in your earlier post, then is there an accounting statement that shows cash use by a company?

Answer

Yes there is - the Statement of Cash Flows

Analsys

I did previously state that there is an adage in business that "cash is King". And you are absolutely right that there needs to be a report that shows the cash condition of a business. To that end, a report was created that is called the Statement of Cash Flows and it specifically tracks the cash activity of a business. Since it is a report that shows change over a period of time, it is akin to an Income Statement in that it shows a range of time rather than a snapshot of a status (like the Balance Sheet).

The way the report works is that it starts with a company's Net Income number, which is generated under the accrual method of accounting. It then dissects that number, looking at all the changes to cash (and, in fact, the entire balance sheet) due to Operations, Investment activity, and Financial activity.

In the Operation section of the report, all the changes that happen on the balance sheet (say for instance that Receivables increase by $10,000, that number is backed out. If Payables increase by $10,000, that activity is also backed out) that relate to Short Term assets and liabilities (short term meaning those assets and liabilities that are anticipated to be held for one year or less).

In the Investment section of the report, all the changes that happened related to the Long term assets are shown. This will relate to the purchase and sale of fixed assets and other long term assets.

The Finance section of the report shows all the changes related to Long term liabilities and equity, such as changes in bank loans (acquisition of new funding and the paying off of balances), and also changes related to the issuance/cancellation of shares.

All these changes are applied to the cash balance at the end of the prior term and results in the new cash balance (at then end of the current term).

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Comments and questions always welcome!

#Accounting - Cash accounting vs accrual accounting - what's the difference?

Question

What's the difference between cash accounting and accrual accounting?

Answer

Cash accounting focuses on transactions being recorded as monies are received/paid out. Accrual accounting focuses on transactions being recorded as monies are earned/obliged to be paid out.

Analysis

There is an adage in business that "Cash is King" - it means that no matter what else you have - the number of machines that produce products, the number of buildings, the amount of land, etc - that if you don't have cash, your business is in big trouble.

Because of this, and also because it's by far the simpler method to keep track of a business' books, people will use the Cash Method of Accounting. In essence, you only track transactions that involve cash when you actually receive/pay out that cash.

For instance, if a company sells $100,000,000 worth of product on account, under cash accounting, that sale is only recorded when the cash is received. Before then, for the purposes of bookkeeping, it hasn't happened. On the flip side, if a company borrowed $100,000,000 and the payment is due next week, that payment is recorded until the cash is paid. Even if it's paid late.

As you might suspect, while being by far simpler to use (which is why many small businesses use it), cash accounting can severely distort the apparent financial condition of the company. And so another method arose to help better reflect the actual condition of the business - the Accrual Method of Accounting. Using the accrual method, transactions are recorded when amounts are earned (regardless of actually receiving the cash) or obliged to be paid out (again, regardless of actually paying out the cash).

For instance, if the company makes a large sale, the account Sales is increased (Credited). To reflect the fact that money is now owed to the company, a Receivable is also increased (Debited). On the flip side, as interest on that huge loan builds up, it is recorded as a Payable (Credit) and an Expense (Debited).

When financial statements are prepared, an accountant needs to make sure that all amounts that are accruing (such as that interest expense, or as another example a salary expense for salaries earned by workers but as yet unpaid) is updated as of the date of those financial statements.

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Comments and questions always welcome and appreciated!

#Accounting - What's a Balance Sheet? What's an Income Statement?

Question

What's a Balance Sheet? What's an Income Statement?

Answer

They are the two most basic accounting statements/reports. The Balance Sheet answers "Where are we right now?" and the Income Statement answers "How much did we earn over a given period of time?"

Analysis

 I've talked about T accounts and Debits and Credits in prior posts. The Balance Sheet and Income Statement arise directly from the activity recorded in the T accounts.

When preparing an Income Statement, we look at a period of time. For instance, a statement that is being done to show the activity for the year ending December 31, 2018 will be titled "Income Statement for the year, ending December 31, 2018). The report itself lists Sales and other Income related to the ordinary course of business (natural Credits) and subtracts from that Expenses and other costs related to the earning of that income (natural Debits).

When preparing a Balance Sheet, we pick a date that the statement will be of. For instance, a statement that is being done as of December 31, 2018 is titled "Balance Sheet as of December 31, 2018" (exciting stuff, right?). The report itself lists Assets on one side (the natural Debits) and the Liabilities and Equity on the other side (the natural Credits). The activity from the Income Statement is listed as a change in Equity.

Together, the two reports show a company's activity from ordinary activity and can be of tremendous help in guiding management and other decision makers on the health and activity of the business.

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Feel free to ask a question!

#Accounting - What are Assets? Liabilities? Equity? Income? Expenses?

Question

In accounting, what are Assets? Liabilities? Equity? Income? Expenses?

Answer

• The simple way to think of Assets is to think of them as things the company owns. If the company owns equipment, furniture, the building it's in, it's cash - these are all assets. Sometimes things that are assets are not held by the company - money owed it by customers is an asset (called a Receivable) - the company may not have the money in-house but the fact that it is owed money means that it owns the right to that money. Assets tend to be natural Debit accounts.

• Again, working within simple explanations, Liabilities are those things that the company owes. When the company buys things on credit or takes out a loan, these are amounts that are owed by the company to other entities. Liabilities tend to be natural Credit accounts.

• The difference between what the company owns and what it owes is what the company is worth. This is its Equity (oftentimes called Net Equity, Net Worth, Owner's Equity, and other similar names). When a company is incorporated, the shares of the company are part of the equity (there will be some mention as to the equity per share or a way given to calculate it). Equity tends to be natural Credit accounts. 

• The way a company brings in money or other assets through the ordinary course of affairs is called Income (note that this is different than when a company does things such as selling an investment or raises money by obtaining a loan. These activities, while it will bring in money, is classified under Investing and Financing activities). Sales tend to be natural Credit accounts.

• In like manner, when money or other assets are expended through the ordinary course of affairs, these are called Expenses. Expenses tend to be natural Debit accounts.

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Feel free to ask a question!

#Accounting - What's a Debit? What's a Credit?

Question

What's a Debit? What's a Credit?

Answer

 Debit is the Left Side of a T account. Credit is the Right Side.

Analysis

Remember the post about T accounts? Debits refer to the numbers on the left hand side of the vertical bar of the T and Credits refer to the numbers on the right hand side. It's as simple as that - different names for Left and Right.

When I was first learning the concept, at every opportunity I could find, I'd refer to things on my Debit side and on my Credit side. I'd turn Debit and Credit in a car. It was the only way to get the concept firmly planted in my head.

Accounts will hold what is sometimes termed "natural" balances. Assets and Income are typically natural debit balances (that is, to increase the account, we debit it) and Liabilities, Equity, and Expense accounts are typically natural credit balances (that is, to increase the account, we credit it).

At this point, you might be wondering why it is that when you are getting money back from a vendor (say like from the phone company), they say they're going to "credit your account". Or even when you deposit money into your bank account, it's called "crediting your account". Why is that?

The answer is that the customer service people are working from the viewpoint of the company. When they are giving you money, they are decreasing the company's money, or in other words, they are decreasing the company's assets, and that is a credit.

For a bank, it's a bit different. When someone makes a deposit into a bank, we are increasing the bank's assets, which is a debit. But what the bank is really interested in is the fact that they now owe you, the depositor, that same amount of money you just deposited in. In fact, when you, the depositor, get your bank statement saying that you have $1,000 in the bank, the bank has a liability for that amount (we'll talk more about liabilities in a future post) - they owe you that money at a time of your choosing. And so the teller, in working with your assets, is in actuality working with the bank's liabilities. When you had the teller money, you are increasing the bank's liabilities, which is a credit.

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As always, please feel free to ask a question!

#Accounting - What's a T account? Why use them?

Question

What's a T account? And why use them?

Answer

A T account is a simple but effective way to organize the activity in any given account.

Analysis

Let's first talk about accounts. An account is a way to gather similar activity in one place. For instance, over the course of a year, let's have Sample Co. have a number of sales throughout the year. We can sum up those sales to see the sales activity for the year. For an example, let's have Sample Co have sales of $100,000 for the year.

This $100,000 sales figure is made up of smaller sales throughout the year. We list them individually as they happen. A part of that list might look like this:

$500
$1000
$250
$300

and so on.

Some transactions will increase the balance of the account and some will decrease that balance. Take the account Cash for instance - as sales are made, cash comes into the company. As inventory is purchased, salaries are paid, and other outflows are accounted for, the balance of the account decreases.

One way to show this would be to list out all the transactions in a single list:

 $1,000
-$350
-$15
-$25
$300

and so on. Which can get messy.

Another way to look at the accounts is to put all the amounts that increase the account in one list and all the amounts that decrease the account in another list. To save space and to keep things organized, we can draw a T, put the account name above the crossbar of the T, and have amounts on one side of the T's vertical line increase the account and on the other side put those amounts that decrease it. It'll look something like this:


        Cash
------------------
$1000 |
           | $350
           | $15
           | $25
$300   |

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As always, if you have a question, please ask!

#Accounting - Accounting requires organization, not advanced math...

Question

I want to study accounting but I'm afraid to do it because I'm not good at math. What are your thoughts?

Answer

The good news is that accountancy rarely goes beyond basic arithmetic (adding, subtracting, multiplying, dividing). In fact, accountancy is far more about organizing and classifying information rather than manipulating it. 

Analysis

As a for instance, let's take a sample transaction and look at how an accountant would treat it.

Stan's Superheroes (a store specializing in superhero collectables) sold a Baitman figurine (it's a knockoff of Batman - this one is of a cowled fisherman who fights crime on the docks) for $10. The customer paid cash. Stan originally bought the figurine for $3. How do we book this transaction?

And now let's watch how an accountant works through this question.

• Cash has increased by $10, so the account Cash is increased (Debit)
• Sales have also increased by the same amount, and so the account Sales is also increased (Credit)
• The inventory has decreased by the amount originally paid for the figurine, and so it decreases by $3 (Credit).
• The last account, which is the Cost of Goods Sold, increases by $3 (Debit).

Accountancy also gets into reasonableness. For instance, would it be reasonable to conclude that Stan's Superheroes makes $1,000,000 per year from sales of Baitman? Probably not - and it's the role of the Auditor (a type of accountant) to examine those types of situations.

Bottom line, most accounting does not involve anything more than basic math. If however you are interested in stretching your math muscles within the accounting world, Cost Accounting might be for you (it's a type of managerial accounting that does it's best to examine a business from top to bottom, in all its processes, and put them into financial terms so that the management of a company can make better business decisions).

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Questions and comments welcome!

#Admin - A new blog, a new beginning, a new conversation on math-y topics!

Hello one and all and welcome to Math Fact-orials!

In this post, the first of this blog, I'll talk quickly about me, this blog, what I hope to achieve, and all that.

About me

I love thinking and learning and sharing what I'm thinking and learning. Most recently, I was a Hero and Featured Answer Reviewer (Algebra, PreAlgebra, English Grammar) with www.Socratic.org, with (at the time of this writing, with roughly 2 weeks of life left in Socratic):

- over 890,000 views,
- 2400 answers, and
- 700 edits of existing answers.

But since that website is currently scheduled to be shuttered mid-August 2018, I've decided to start my own Question and Answer site (i.e. this blog) that will focus on things I find important/interesting/fun/etc.

Some more things about me:

- Formerly a Certified Public Accountant (in the USA) and a Chartered Accountant (in Canada)
- Holder of a Life Coaching certificate
- Spent a few years in the US Navy as a Supply Corps officer

About the blog

While I don't want to set anything in stone (this is a living blog after all, so it will morph and change as I do), there are a couple of areas I'll tend to focus on at the start: Combinametrics (or the number of ways of doing/arranging/organizing things) and something I'll call Life Math - this will encompass things like Business Math, Budgeting, Investing, Accounting, Financing, and all those non-sexy math topics that academics tend to shun. Life Math, by its very nature, is a bit more "squishy" than academic math - there typically are more "squishy" answers than in academic math. For instance, is a 10% discount on a shirt a good discount? It might be, but then again it might not be - it's up to the reader to decide. But in these kinds of questions and answers, I'll do my best to lay out some things to think about.

I intend to right about how to approach a problem as the first part of any blog post, and then to have an "Answer Key" below, which will show the various answers with changes in the starting facts. For instance, if a shirt that costs $30 has a 10% discount (with a final cost to the customer of $27 before sales tax), the same process will work if the shirt is $40 and there's a 20% discount (with a final cost of $32 before sales tax).

Questions are very welcome!!!

If you have math questions, please do ask! Post a comment (I approve all comments) and I'll be sure to respond and write on the blog in response. No names/specific locations will be used and so don't worry about anonymity!

And I think that just about does it - so Welcome! and I hope to hear from you.

Parz

Update, 22 Aug 2018

Through editing and updating the organization of the blog, I'm hoping it'll be more useful (and easier to find the information you are interested in!). Links, labels, and subjects are all being edited, reworked, and otherwise made better. Get ready for Math Fact-orials 2.0! (or maybe just 2!... - factorials and decimal points don't get along very well...)