Study: Expanded Accounting Equation: Compute Revenues and Expenses
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Slides 1-2 (4m:25s)
Links to an external site. Welcome to Introduction to Accounting Preparing for a User’s Perspective.
Expanded Accounting Equation: Computing Revenues and Expenses.
Slide 2
This is the last in a series on the expanded accounting equation. You’ve already learned all of these pieces of the expanded accounting equation in prior videos.
What we’ve done [in the Complete Expanded Accounting Equation above] is shown is that Equity can be expanded into its two component pieces:
Contributed Stock (i.e. Capital Stock
Links to an external site., Contributed Capital, there’s a number of different names) and Retained Earnings
Links to an external site..
Capital Stock is what’s been contributed by owners and Retained Earnings is what the company has earned and the owners have elected to keep in the business.
Then what we said is “Capital Stock increases when new stock is issued and it decreases when that stock is repurchased.”
Retained Earnings increases, when the company has Net Income, and decreases, when Dividends Links to an external site. are paid.
If there are Net Losses, that will also reduce Retained Earnings. But then we need to go one step further to say, “Well, how is Net Income computed?” Net Income is computed by Revenues, which increase Net Income, which increase [Retained Earnings] and increase Equity, and [are] decreased by expenses, which decrease income, decrease [Retained] earnings and decrease Equity.
That [above] is the complete expanded accounting equation.
I remember watching one video by a fellow professor, Matt Fisher, and what he uses is an acronym. His acronym is WIRE. I’ll just write that down over here. WIRE, that is his acronym for remembering the expanded accounting equation.
In other words, all of equity can be explained by this acronym [Equity = WIRE].
W = Withdrawals. Withdrawals would be these Dividends. Stock repurchases would also be classified as withdrawals, but they are withdrawing the original capital they invested.
I = Investments. That would be here, stock issuances.
R = Revenues.
E = Expenses.
His WIRE acronym actually is represented by what I show here [in the Complete Expanded Accounting Equation diagram above], so if it works for you, I hope you will use it.
Question 1: At the beginning of the year (X1), Assets were $50, Liabilities $20, and Capital Stock was $5. During the year, Assets increased $70, Liabilities decreased $5 and Retained Earnings increased $40. Dividends paid during the year were $10.
If Expenses during the year were $80, compute the year’s Revenues ____.
In this problem [Question 1] as you can see, this information about the changes in the accounts, I’ve moved down a little bit so I can use the format above [the Complete Expanded Accounting Equation] a little more efficiently.
We’ll have beginning and ending in these accounts, and then the changes will branch off from there. Here’s our Assets, Liabilities, Capital Stock, Retained Earnings.
Assets were $50 at the beginning of the year, Liabilities were $20, and Capital Stock was $5.
During the year Assets increased by $70.
Liabilities decreased by $5
and Retained Earnings increased by $40.
Dividends paid during the year were $10.
If Expenses during the year were $80, compute the year’s Revenues.
If we knew the Net Loss, we could solve for Revenues
Links to an external site., but we don’t. But we do know that Retained Earnings increased by $40, and we know that the change in Retained Earnings, is going to be equal to Net Income minus Dividends [which is the same as the change in Retained Earnings].
Beginning Retained Earnings
+ Net Income
– Dividends
= Ending Retained Earnings
We know the change in Retained Earnings [caused by Net Income – Dividends] is $40. Net Income, we don’t know yet, but we do know that Dividends are $10, something [Net Income] minus $10 equals $40 [change in Retained Earnings], and that would have to be $50 [Net Income].
$50 [Net Income] minus $10 [Dividends] = $40 [Change in Retained Earnings]
Net Income must be $50.
Now that we know Net Income and we know that Net Income is equal to all of the Revenues minus its Expenses, we can put in the known information.
Net Income $50 = Revenues (which we don’t know) - $80 in Expenses
So something [Revenues] minus $80 [Expenses] = $50 [Net Income].
If you add $80 to both sides, to get Revenues by itself, you will realize that Revenues must be $130. Revenues are $130.
If we wanted to, we could go and solve for beginning Retained Earnings Links to an external site.. We could solve for all of the ending balances here, we could solve for the change in Capital Stock, but for this particular problem, all it asked for is the year’s Revenues which we’ve concluded are $130. So, if you are kind of in a rush, you may not have to go through and compute all of those other numbers.
If you really want to make sure you’ve got it right [which I recommend] it’s helpful to fill in all of the other numbers and prove the math horizontally using the expanded balance sheet equation, or vertically, just using the idea that the beginning number, plus the change equals the ending.
That’s a great way to prove your work. Accountants are known for reconciling. They reconcile their work and make sure that everything works together and balances [see the solution to Question 1 below].
Slides 3-4 (5m:46s)
Links to an external site.
Let’s go to Question 2.
Question 2: Beginning balances: Assets $100, Capital Stock $10 and Retained Earnings $50. During the year, Assets increased $60, Liabilities increased $20, and Capital Stock increased $40. If the company recorded $10 of Dividends and $90 of Revenues during the year compute the following:
a. Ending Retained Earnings ____.
b. Net Income for the year _____.
c. Expenses for the year ____.
Beginning balances were Assets of $100, so I’m going to put my beginning [balances], and my ending [balances], and my change here, for each of these accounts and I will put in the information given. $100 beginning Assets, Capital Stock had a beginning balance of $10, Retained Earnings had a beginning balance of $50. During the year, assets increased by $60. Liabilities increased by $20, and Capital Stock increased by $40.
If the company recorded $10 of Dividends, reducing Retained Earnings and $90 of Revenues during the year, compute the following: Ending Retained Earnings. So we are looking for that piece of information right there.
Net Income, we are looking for this piece of information right there and Expenses, that piece of information right there.
So I’m only going to put a box for the missing information.
Question 2a. Ending Retained Earnings ____.
Can we solve for any of these right off the bat? The answer is, we really can’t without some additional work. You need to look at each of these as a formula. There are horizontal formulas and vertical formulas.
[A] Horizontal [formula] uses the balance sheet equation and [a] vertical [formula] uses the idea Beginning + Change = Ending.
I’m going to solve for this, horizontal expanded accounting equation.
Change in Assets = Change in Liabilities + Change in Capital Stock + Change in Retained Earnings
$20 of [change in] Liabilities plus $40 of [change in] Capital Stock gives us $60 plus something equals $60 [change in Assets].
Change in Assets $60 = Change in Liabilities $20 + Change in Cap. Stock $40 + Change in Ret. Earnings
Well, that something [change in Retained Earnings] would be zero. Mathematically that works out.
Retained Earnings didn’t change. If Retained Earnings didn’t change and we started with $50 in Retained Earnings and they didn’t change at all, then that must mean that we ended the year with $50 of Retained Earnings.
Next, so we’ll put that in.
Question 2b. Net Income for the year.
Retained Earnings didn’t change, and the basic formula for Retained Earnings is your beginning Retained Earnings plus your Net Income, minus your Dividends, equals your ending Retained Earnings. Beginning Retained Earnings are $50. Net Income, we don’t know yet, but we do know our Dividends are $10 and we do know that we ended with $50 [see the Retained Earnings formula noted below]
Beginning Retained Earnings $50
+ Net Income ????
– Dividends $10
= Ending Retained Earnings $50
If you just solve for the unknown as we’ve shown all along, $50 [beginning Retained Earnings] plus something [Net Income] minus $10 [Dividends] equals $50 [ending Retained Earnings]. Net Income has to be $10.
It goes up by $10, and then they [the earnings from Net Income] get all paid out. They go up by $10 because you earned some Net Income, then you pay them all out in the form of a Dividend, thus leaving [ending] Retained Earnings at the same $50 that you began with. This [Net Income] would be $10.
Beginning Retained Earnings $50
+ Net Income $10
– Dividends $10
= Ending Retained Earnings $50
Question 2c. Expenses for the year.
The formula for Net Income is:
Net Income = Revenues - Expenses.
As you can see here, Revenues minus Expenses equals Net Income.
We know the Revenues to be $90. We don’t know the Expenses, that’s what we are trying to find out, and our Net Income is $10.
$90 [Revenues] minus something [Expenses] = $10 [Net Income].
That has to be Expenses of $80.
Let’s go back and look at our question. [Question 2b] Net Income for the year is $10 and [Question 2c] Expenses for the year are $80.
If you wanted to, you could go ahead and solve for all of these other unknown pieces of information.
Although it wasn’t required, I went ahead and computed the missing pieces in the remaining portion of the expanded accounting equation. If you take your beginning Assets [$100] plus $60 [change in Assets] you get $160 [ending Assets].
In order to determine the [beginning] Liabilities, we had $100 in [beginning] Assets, $60 of which is claimed by the owners [$10 Capital Stock + $50 Retained Earnings] therefore $40 [in Liabilities] must have been funded through lenders and creditors.
Once we have that, then we can continue to work our way down.
[Beginning] Capital Stock started with $10 plus $40 [change in Capital Stock] gives us $50 [ending Capital Stock].
[Ending] Liabilities, we just computed $40 [beginning Liabilities], so $40 plus $20 [change in Liabilities] equals $60 [ending Liabilities].
And those are all of the numbers.
Hopefully that’s helpful to you, but you need to be able to see the big picture of the expanded accounting equation and solve problems such as this. We’re going to have lots of quiz questions on it.
Aloha.