Study: Expanded Accounting Equation: Computing Changes in Retained Earnings Accounts
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Slides 1-2 (4m:32s):
Links to an external site.Introduction to Accounting Preparing for a User’s Perspective.
Expanded Accounting Equation Computing Changes in Retained Earnings.
You should already be familiar with the expanded accounting equation as introduced in prior videos. The only thing I’m going to change is, instead of calling this Capital Contributions I’m going to change it to be Capital Stock
Links to an external site. as you would see in a corporation. This represents the dollar amount of stock issued to owners for which the company received assets.
What I’m trying to do now is help you understand what causes these two equity accounts to change from one year to the next.
Capital Stock will increase when new stock is issued to owners. Assets will go up and Capital Stock will go up.
The Capital Stock account will decrease when stock is repurchased. This overall Capital Stock [account] will go down as stock is repurchased. Later on you will learn about Treasury Stock but we won’t worry about that right now. The point is that this overall Capital Stock, issued and outstanding, will decrease.
Retained Earnings Links to an external site. increases when the company earns earnings. It will decrease when it incurs losses. Obviously we want to increase retained earnings.
Now if the owners want some of those earnings out [of the company], they can vote and have a Dividend Links to an external site. declared and paid to them. When Dividends are declared, the company’s Retained Earnings will decrease.
You should recognize that these items [Stock Issuances – Stock Repurchases + Net Income – Net Loss – Dividends] are descriptions of how these balance sheet accounts [Capital Stock and Retained Earnings] changed from one year to the next.
Let’s go ahead and work out this problem.
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. No changes in Capital Stock occurred during the year. Dividends paid during the year were $10.
a. Compute Ending Retained Earnings ____
b. Net Income earned during the year (X1) ____
I will first set up the problem as we have been doing with the beginning balance, the ending balance and the change. We will do that for Assets, Liabilities, Capital Stock and Retained Earnings, but then we will say that these changes will be described by Stock Issuances, Net Income, Stock Repurchases and Dividends.
Question 1a: Compute Ending Retained Earnings ____
Beginning Assets are $50, Liabilities are $20 and Capital Stock, beginning, is $5. The unknown in this case would be beginning Retained Earnings. During the year, Assets increased $70. Liabilities decreased $5. No changes in Capital Stock occurred during the year. So, no net changes [occurred]. They could have had some increases [caused by Stock Issuances] or decreases [caused by Stock Repurchases] but they exactly offset [each other] so there are no [net] changes.
Dividends paid during the year are $10.
Compute ending Retained Earnings and the Net Income earned during the year X1.
We can now start solving for the unknown [beginning Retained Earnings].
Right now there are a lot of empty places. All we can do is work with what we know. We can compute beginning Retained Earnings, because $20 [beginning Liabilities] + $5 [beginning Capital Stock] is $25 plus something [beginning Retained Earnings] equals $50 [beginning Assets].
You might recognize that number from a prior problem, $25.
We still can’t compute this [the change in Retained Earnings] so I guess we are going to have to work through and figure that out one-by-one.
Assets went from $50 [beginning Assets], increased by $70 [change in Assets] so that [ending Assets] would be $120.
Assets
Liabilities [beginning Liabilities of $20] decreased by $5, so the ending [Liabilities] would be $15.
Liabilities
That’s back to this old formula.
Beginning + Change = Ending
Bring the $20 [beginning Assets] minus the $5 [change in Assets] equals $15 [ending Assets].
$20 Beginning Assets – $5 Change in Assets = Ending Assets
$5 [beginning Capital Stock] + $0 [change in Capital Stock] = ending Capital Stock
Capital Stock
We have enough information that we can solve for ending Retained Earnings. -$5 [change in Liabilities] + nothing [$0 change in Capital Stock] + something which we don’t know yet equals $70 [change in Retained Earnings]. This [ending Retained Earnings] would have to be $75.
Question 1b: Net Income earned during the year (X1) ____
$75 [change in Retained Earnings] - $5 [change in Liabilities] + $0 [change in Capital Stock] = $70 [change in Assets].
So this [$75] change in Retained Earnings was caused by Net Income, which we don’t know, -$10 [Dividends]. So what would Net Income have to be?
It works like this. The change in Retained Earnings is going to be equal to Net Income minus Dividends. We know that the change [in Retained Earnings] is going to be $75. We don’t know what Net Income is, but we do know Dividends. If we add $10 to both sides, we will realize that Net Income must be $85, minus $10 [Dividends] equals the [$75] change in Retained Earnings.
Beg. Ret. Earnings $25 + Net Income $85 – Dividends $10 = End. Ret. Earnings
If we know that the change in Retained Earnings [Net Income – Dividends] was $75, we started with $25 [beginning Retained Earnings], it increased $75, this [ending Retained Earnings] would have to be $100.
So to prove this out, we are going to say, these Assets are claimed $15 by Liabilities plus $105 by the owners. $105 [total Equity] + $15 [Liabilities] = $120 and we’ve got this question solved.
Ending Retained Earnings are $100. Net Income earned during the year is $85.
We’ve done it.
Slides 3-4 (5m:46s):
Links to an external site.As you have already learned, I like to set up these problems using the expanded accounting equation, and I put down the beginning numbers given, the ending numbers given and then the changes. I put in the all the known information, and then I solve for the unknown.
I think if you will follow this approach, these things are a slam dunk. Let’s go ahead and put in the information that is known.
Question 2: At the beginning of the year (X1), Assets were $90, Capital Stock was $10 and Retained Earnings was $40. During the year, the company earned $80 in Net Income, Assets decreased $20, Liabilities increased $30 and new Capital Stock of $70 was issued during the year, no stock repurchases occurred during the year.
a. Compute beginning liabilities___ and ending assets ___.
b. Compute ending Capital Stock ____ and Retained Earnings____.
c. How much in Dividends were recorded during the year?_____.
d. What was the change in Retained Earnings?___
At the beginning of the year, assets were $90, Capital Stock was $10, and Retained Earnings was $40. The missing piece of information for the beginning of the year expanded accounting equation is the liabilities.
During the year, the company earned $80 in Net Income. What that means is that this change in Retained Earnings, is partially explained by Net Income. All these here explain why the accounts changed from the beginning of the year to the next [end of the year].
I’m going to go ahead and put in some lines so you can see that. Net Income would come in here to explain increases. For Capital Stock, Stock Issuances would explain increases.
Things that would cause Retained Earnings to go down, are your Dividends and any Net Losses incurred. If the company were to buy back its own stock, that would cause [net] Capital Stock to go down.
Let’s put in the information that’s known about Net Income. Net Income is $80. Assets decreased by $20. Liabilities increased by $30 and new Capital Stock of $70 was issued. That’s over here. New Capital Stock Issuances of $70 and no Stock Repurchases occur. That would be zero.
Question 2a: Compute beginning liabilities___ and ending assets___.
Well that’s actually one of our easier ones because we already have enough information to solve for the unknown.
If the company has $90 in assets and $50 of that are claimed by the owners, then that must mean that $40 are claimed by the lenders and creditors. The beginning Liabilities are $40.
Assets $90 = Liabilities + Equity $50 [which is $10 Capital Stock + $40 Retained Earnings]
[Compute] ending Assets. If we know that our beginning [Assets] is $90 and then it decreased by $20, then the ending must be $70.
Beginning Assets $90 + Change in Assets (a decrease of $20) = Ending Assets $70
Question 2b. Compute ending Capital Stock ____ and Retained Earnings____.
Well we know that things that would cause Capital Stock to change would be Stock Issuances, which are $70, and then there were no Stock Repurchases. Therefore, this [Capital Stock] must have gone up $70. The change in Capital Stock is an increase in $70. So if you started with $10, and you increased by $70, you are now up to $80 for your ending Capital Stock.
Beg. Cap. Stock $10 + Stock Issuances $70 – Stock Repurchases $0 = End. Cap. Stock $80
Let’s look at what we can do for Retained Earnings. We don’t have enough information here yet to solve going horizontally [using the expanded accounting equation], but we can solve for ending Liabilities. We started at $40, we added $30, so that is $70.
Beginning Liabilities $40 + Change in Liabilities $30 = Ending Liabilities $70
Now we have enough information that we can solve for the missing [ending balance of] Retained Earnings [using the expanded accounting equation].
$70 in Liabilities plus $80 in Capital Stock, that’s $150. $150 plus something gets us all the way down to $70. This must mean that this [ending Retained Earnings] went down by $80. $150 minus $80 = $70.
If you look at this, the owners have no equity in the business. It is zero, it zeroes out. Why, because all of these [$70] Assets were totally funded by [$70 in] Liabilities. There is nothing left over, the owners don’t own anything [have no net remaining claims against the Assets].
Assets $70 = Liabilities $70 + Capital Stock $80 – Accumulated Deficit $80
If we started with $40 [beginning Assets] and then it went down to $80 [ending Assets]
Assets
If you look at a number line, you are at $40, and then you are going all the way down to negative $80. That swing is $120 negative swing. Retained Earnings decreased by $120
Let’s verify that that is true. If this is $100 [change in Liabilities $30 + change in Capital Stock] minus $120 [change in Retained Earnings], that means this [change in Assets] went down by $20. That’s correct. If your Net Income is $80, the change in Retained Earnings is going to be equal to your Net Income for the year minus your Dividends.
Question 2c. How much in Dividends were recorded during the year?_____.
If your Net Income is $80, you have to deduct something to get to negative $120. In order to get to negative $120, you would actually have to deduct $200. In other words, they paid $200 in Dividends. Let’s verify that out.
Net Income $80 – Dividends $200 = - $120 [change in Retained Earnings]
We’ve already proven that this [the expanded accounting equation for the change in ending balances] works.
+Assets $20 = + Liabilities $30 + Cap. Stock $70 - Ret. Earnings $120
That’s how you solve this problem. Let’s go ahead and put in the information that we now know.
Compute ending Capital Stock $80 and Retained Earnings. Ending Retained Earnings negative $80.
Sometimes I see students compute it correctly but then they write down the wrong answer, so make sure you get the right answer.
How much in Dividends were recorded during the year?
Retained Earnings went down by $120, if we add the Net Income [$80] minus whatever the Dividends are, we will get to [negative] $120, this would have to be $200 in Dividends were paid during the year. We report it as a positive number, but we deduct that positive number to get down to the change in Retained Earnings.
Question 2d. What was the change in Retained Earnings?
Begin. Ret. Earnings $40 less Reduction in Ret. Earnings = End. Ret. Earnings -80
It [Retained Earnings] went down $120.
I will admit, this is a little unusual to have your Retained Earnings be negative, but, you know, it does happen. In start-up companies, you often will see their Retained Earnings be negative. Why, because they are not earning any money yet. They are just incurring losses, as they try to get their business going.
Often if you see a negative Retained Earnings, which we call Accumulated Deficit, it’s often because the company is in the start-up phase of the business. Now if this is a more mature company, and this [Retained Earnings] is still negative, they may be on the way out.
Hopefully this helped you. Wish you all the best.