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Expanded Accounting Equation: Computing Changes
In Ending Balances - Video Slides 1-4

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Slides 1-2 (4m:56s)Welcome to Introduction to Accounting Preparing for a User’s Perspective.
Expanded Accounting Equation: Computing Changes in Ending Balances

Question 1: At the beginning of the year (X1), Assets were $50, Liabilities were $20, and Contributed Capital was $5. During the year, Assets increased $70, Liabilities decreased $5 and Retained Earnings increased $40.

Compute assets at the end of year X1_____
Compute liabilities at the end of year X1_____
Compute Contributed Capital at the end of year X1_____
What was the change in Contributed Capital during the year X1_____
What was Retained Earnings at the beginning of year X1_____
Compute Retained Earnings at the end of year X1_____

In the prior two videos, I introduced the balance sheet equation which is Assets = Liabilities plus Equity and then in the second of those two videos I showed how that Equity gets expanded into its two component pieces: the contributed equity, which is Contributed Capital, and the earned equity, which is Retained earnings.

What we will do now, instead of just focusing on computing a missing piece of ending balances, we may give beginning and ending and ask you to do [compute] the change, or something like that. We are just stepping it up a little level to make sure that you fully understand how this all builds up so you can fully handle a large expanded accounting equation.

What I like to do is, I like to first put down my expanded accounting equation, and then I write down the beginning, ending and then the change. I just set up a format into which I can put the given information and then I will solve for the unknown.

Beginning Balance + Change in the Balance = Ending Balance

At the beginning of the year X1, Assets were $50, Liabilities were $20 and the Contributed Capital was $5. So we don’t know beginning Retained Earnings.

During the year, Assets increased by $70. So they went from beginning plus the change equals the ending and the ending is something we don’t know yet.

Liabilities decreased by $5, so they went down by $5. So we had a beginning, we had the change (and this is actually going to be a minus $5) equals ending and we don’t know the ending.

Retained earnings increased by $40. Now in this case, we don’t know the beginning or the ending, so we’ll have to use the expanded accounting equation working horizontally to solve for that.

That’s really all we’ve been given, so these others we also don’t know: ending Contributed Capital and the change in Contributed Capital.

Now let’s read the question and see what it is actually asking for.

Question 1a: Compute assets at the end of year X1_____

Since we know the beginning [Assets] to be $50, we know the change [in Assets] to be $70, therefore we know that the ending [Assets] is $120. $50 [beg. Assets] went up by $70 [change in Assets] to get to $120 [end. Assets]. Let’s go and put that number in here $120.

Question 1b: Compute liabilities at the end of the year X1_____

We know the beginning [Liabilities] was $20. It reduced by $5 to get down to the ending [Liabilities] of $15.

Question 1c: Compute contributed capital at the end of X1_____

Well, we cannot work vertically in this case because there are three variables and we are missing two. We cannot solve that problem with the information given. However, we can solve horizontally for the change and then we can solve for the ending. Let’s do that.

As you know these [ending] assets [of $120] must be claimed either by the lenders and creditors or by the owners. $40 [change] of Retained Earnings minus $5 [change in Liabilities] we are down to $35; therefore, the missing piece must be $35 [change in Contributed Capital].

Prove out your work. We have $75 in Equity [change in Contributed Capital $35 + change in Retained Earnings $40] minus $5 [change] in Liabilities equals $70 [change in Assets], so we are good there. But we are still trying to get this answer [Contributed Capital at the end of year X1]. We can’t solve that yet without knowing the change [in Contributed Capital]. Now that we have the change we can work our way through it.

Take our beginning [Contributed Capital $5] plus our Change [in Contributed Capital $35] equals our ending [Contributed Capital $40]. Beginning is $5 the change is $35 equals $40 ending Contributed Capital.

Now we have the information to fill in. Compute Contributed Capital at the end of the year X1. That is $40. The change was up $35.

Question 1d: What was Retained Earnings at the beginning of year X1_____

Now let’s go over to retained earnings. Once again we cannot solve this vertically because we don’t know the beginning or the ending. We are missing too many pieces, but we can work horizontally. These [Beg. Liabilities $20 + Beg. Contributed Capital $5 + Beg. Retained Earnings ?] should add up to $50 because they have to claim all $50 of the assets.

What we now need to do is solve for the missing piece here [Beg. Retained Earnings]. $20 [Beg. Liabilities] + $5[Beg. Contributed Capital] is $25 plus something [Beg. Retained Earnings] equals $50. This [Beg. Retained Earnings] has to be $25. So that’s at the beginning.

Question 1f: Compute Retained Earnings at the end of year X1_____

We can also work horizontally to determine what this missing piece [End. Retained Earnings] is. $15 [End. Liabilities] + $40 [End. Contributed Capital], that is $55. $55 plus something [End. Retained Earnings] equals $120. This [End. Retained Earnings] has to be $65. $65.

Once you’ve done that, prove out your work. It [Retained Earnings] went from $25 [Beg. Retained Earnings] up to $65 [End. Retained Earnings] at the end so it must have increased by $40.

You should prove your work horizontally and prove your work vertically. Once you have gone through and verified all of those numbers, you know you’ve got this computed correctly.

ExpandedAccountingEquationQ2-6c-Question1FullSolution.png

Slides 3-4 (5m:02s): Question 2: At the beginning of the year (X1), Assets were $90, Contributed Capital was $10 and Retained Earnings was $40. During the year, Assets decreased $20, Liabilities increased $30 and Capital Contributions increased $70.

Compute assets at the end of year X1_____
Compute year X1 beginning liabilities_____
Compute Contributed Capital at the end of year X1_____
Compute Retained Earnings ending balance _____
How much did Retained Earnings change during year X1? _____
What was TOTAL equity at the end of the year X1?

Question 2, once again you have been given information from the expanded accounting equation, beginning and ending and you will be asked to solve for the unknowns.

At the beginning of the year X1, as you know, I like to put up a beginning row, an ending row, and a change row. So, at the beginning of the year, assets were $90. Contributed Capital was $10 and Retained Earnings was $40. The unknown for that row [beginning balances] is Liabilities.

During the year, assets decreased by $20. Put a minus $20 there. So the missing piece here is ending Assets.

Liabilities increased by $30. The missing piece here is ending Liabilities. And Capital Contributions increased by $70.

Question 2a. Compute assets at the end of year X1_____

Now it is going to ask us to compute Assets at the end of the year. You know the basic formula. If you take your beginning Assets and you add the change during the year you are going to get your ending Assets [Beginning Assets + Change in Assets = Ending Assets].

$90 [Beginning Assets]. Now this [Change in Assets] is actually a reduction. So $90, down by $20 gets us down to $70. Our ending assets are $70,

[Beginning Assets $90 + Change in Assets - $20 = Ending Assets $70]

Question 2b. Compute year X1 beginning liabilities_____

Compute beginning liabilities. Well, we don’t know beginning Liabilities. And we can’t solve this vertically using beginning + change = ending, because we only have one of the three variables. We would need at least two of these variables to solve for the unknown.

However, looking horizontally, we know that all $90 of these [beginning] assets must be claimed by the lenders and creditors or the investors. The equity in these assets is $50; therefore, the difference, which must have been funded by debt, is $40. Compute beginning liabilities.

Question 2c. Compute Contributed Capital at the end of year X1_____

We know the beginning to be $10. We know the change of $70. Therefore the ending Contributed Capital must be $80.

[Beg. Cont. Capital $10 + Change in Cont. Capital $70 = End Cont. Capital $80]

Question 2d. Compute Retained Earnings ending balance _____
Question 2e. How much did Retained Earnings change during year X1? _____

Well this one is a little tricky because we know we don’t know the ending [Retained Earnings] but we also don’t know the change [in Retained Earnings]. If we wanted to solve this horizontally, we can’t because we are missing an additional variable. We would need at least to know that ending [Liabilities] which we could solve right now, but let’s say we don’t know it and we don’t know the change.

So, what do we do? We could take the approach of solving for ending Retained Earnings because all of this, lenders’ and creditors’ claims [End. Liabilities $70] and the owners claims [End. Contributed Capital $80 + End. Retained Earnings?] must add up to a negative $20. So, if you take all of this [End. Liabilities $30 + End. Contributed Capital $70], that $100 plus something [+ End. Retained Earnings] equals negative $20. The only way for that to work out would be for this [End. Retained Earnings] to be a negative $120. So $100 and then you take away $120.

It’s like you are out here on a number line. Here’s $100 and you are trying to get to negative $20. That swing here is a minus $120.

Now that we know the change in Retained Earnings, we say, if we take our beginning [Retained Earnings] of $40 and we have our change which was down $120, we would get our ending [Retained Earnings]. So $40 minus $120, take away $120, is negative $80. Start with $40 [Beg. Retained Earnings] and you take away $120, you will get negative $80 [End. Retained Earnings].

That means they don’t have positive Retained Earnings, they have negative Retained Earnings. What that means is not only that they did not have income that they retained, but rather they have losses that they retained. They had net losses and those net losses are reducing owners’ equity.

So that is, ending Retained Earnings is negative $80. So that is actually not even Retained Earnings. We actually call that, Accumulated Deficit, is the actual name for that in a corporation.

Now how much did Retained Earnings change? It went down $120, probably due to net losses or they could have paid out a lot of Dividends, more than they should have.

Question 2f. What was TOTAL equity at the end of the year X1?

In order for this to work out [take] the beginning [Liabilities] of $40 plus the change of $30 it will equal the ending [Liabilities] of $70.

If you work this out horizontally, you will see this is $150 [End. Liabilities $70+End. Cont. Capital $80] minus $80 [End. Retained Earnings] equals $70 [End. Assets].

Work it out horizontally, work it out vertically and you’ve got this type of problem nailed down.

TOTAL Equity. Now be careful that you read the question carefully. What was TOTAL equity at the end of the year. TOTAL equity is these two pieces [End. Cont. Capital $80 + End. Retained Earnings -$80] combined. That’s TOTAL equity and TOTAL Equity is actually $0. The owners have no equity in this business. All of the assets are fully claimed by the creditors and investors because this nets to zero.

Please practice these problems, then go ace the quizzes.