RATIO Puzzle

Fill in the missing values on the balance sheet and income statement below for the Adams Company. Use the ratios that are given to calculate the missing values. These ratios are sufficient for you to derive the missing information: 

Current ratio = 3.85416666667; Debt ratio = 0.43910806175; Total asset turnover = 2.04459691252 times/yr; Gross profit margin = 0.77; Net profit margin = 0.16; Inventory turnover = 3.51487179487 times/yr; Receivables turnover = 56.7619047619 times/yr

Sales: (h)
Cost of Goods Sold: (i)
Net Income: (j)

INSTRUCTIONS: Enter your values in the boxes above. When you FINISH, scroll down to check the answers. Each time you load the page, the answers will change.

SOLUTION:

Objective: Use the ratios and the information given to fill in the missing values (items (a) though (j) above) on the Balance Sheet and Income statement.

Step 1:
The first item of business is to make sure that you know the formula for each of the ratios given.

Current Ratio = Current Assets / Current Liabilities.
Debt Ratio = Total Debt / Total Assets OR (Total Equity - Total Assets) / Total Assets
these two formulas are EXACTLY the same since:
Total Assets = Total Liabilities + Total Equity

Total Asset Turnover = Sales / Total Assets
Gross Profit Margin = Gross Profit / Sales (NOTE: Gross profit is also known as EBIT and can be calculated by Sales - Cost of Goods Sold)
Net Profit Margin = Net Income / Sales (NOTE: Net Income is also known as Earnings after Tax)
Inventory Turnover = Cost of Goods Sold / Inventory
Receivables Turnover = Sales / Accounts Receivable

Note that only TWO of these formulas can be used at this time: Debt Ratio and Total Asset Turnover since none of the other ratios use the values given, which are Total Assets ($583,000.00), Common Stock ($86,000.00) or Long-term debt ($208,000.00). You can use the Debt Ratio to solve for Total Debt since you know Total Assets.
You can use the Total Asset Turnover Ratio to solve for Sales since Total Assets is known.
You can't use any of the other ratios yet because you don't know EITHER of the values for the rest. To solve for an unknown, there can only be ONE unknown in the equation.

Step 2: Find Current Liabilities (then Accounts Payable) (e)
Using one of the ratios identified as a starting point, solve for the unknown values.

Debt Ratio = Total Debt / Total Assets = 0.43910806175
since Total Assets = $583,000.00 (given in the problem), Debt Ratio = Total Debt / $583,000.00 = 0.43910806175
We want to solve this for Total Debt so we must get rid of the denominator on the left side.
So, multiply both sides by $583,000.00 and you get,

Debt Ratio ==> (Total Debt / $583,000.00) * $583,000.00 = 0.43910806175 * $583,000.00, which equals
Debt Ratio ==> Total Debt = 0.43910806175 * $583,000.00 = $256,000.00

Note: This is NOT one of the answers. This simply tells us the total amount of debt of the company. HOWEVER, if you remember your basic accounting, this DOES tell you something very important.

Total Debt in this case = Current Liabilities + Long-term Debt
since the only Current Liablity in this example is Account Payable,

Total Debt = Accounts Payable + Long-term debt

Long-term Debt is given as $208,000.00 in the problem. Therefore, Current Liabilities + Long-term Debt = $256,000.00 and you know that Long-term Debt = $208,000.00 so, since the only current liablity is Accounts Payable,

Accounts Payable = $256,000.00 - $208,000.00 = $48,000.00. This is the answer to (e) above.

Step 3: Find Total Liabilities and Owners Equity (g)

Next, if you look at the right side of the balance sheet you should IMMEDIATELY be able to tell the value for (g) . What is this value? Well, since both sides of the Balance Sheet must always EQUAL,
Total Liabilities & Owners Equity (g) = $583,000.00

Step 4: Find Retained Earnings (f)

Now, if you look at your values on the right side of the Balance Sheet, you only have one value remaining, Retained Earnings. So, how do you find retained earnings? Is there a formula that uses Retained Earnings? (No.) Well, the answer to this one is very easy. First, you know that everything on that side of the Balance Sheet must total to $583,000.00. Since we know all of the values except for Retained Earnings, it is simply a subtraction problem.

(f) Retained Earnings = Total Liabilities & Owners Equity - Accounts Payable - Long Term Debt - Common Stock, so
(f) Retained Earnings = $583,000.00 - $48,000.00 - $208,000.00 - $86,000.00
(f) Retained Earnings = $241,000.00

Step 5: Find Sales (h)

Now, the best thing to Solve for is Sales. If you look back at the Total Asset Turnover Ratio you will notice that this ratio is:

Total Asset Turnover = Sales / Total Assets = 2.04459691252

Since we know Total Assets, we can use this ratio to solve for Sales. To do this, follow this:

Total Asset Turnover ==> Sales / Total Assets = 2.04459691252
Total Asset Turnover ==> Sales / $583,000.00 = 2.04459691252
Total Asset Turnover ==> Sales / $583,000.00 * $583,000.00 = 2.04459691252 * $583,000.00 (to get rid of the $583,000.00 in the denominator on the left)
Total Asset Turnover ==> Sales = 2.04459691252 * $583,000.00 = $1,192,000.00

Step 6: Find Cost of Goods Sold (i)

Although there are a couple of things that we could do now, let's solve for Cost of Goods Sold. We know the following:

Gross Profit Margin = Gross Profit / Sales = (Sales - Cost of Goods Sold ) / Sales = 0.77
Gross Profit Margin ==> (Sales - Cost of Goods Sold ) / Sales = 0.77

Now, we need to isolate the Cost of Goods Sold term so first lets get rid of Sales in the denominator on the left

Gross Profit Margin ==> ($1,192,000.00 - Cost of Goods Sold ) / $1,192,000.00 = 0.77
Gross Profit Margin ==> ($1,192,000.00 - Cost of Goods Sold ) / $1,192,000.00 * $1,192,000.00 = 0.77 * $1,192,000.00
Gross Profit Margin ==> $1,192,000.00 - Cost of Goods Sold = 0.77 * $1,192,000.00

Now, we need to get Cost of Goods Sold over by itself. So, let's subtract $1,192,000.00 from both sides

Gross Profit Margin ==> - Cost of Goods Sold = 0.77 * $1,192,000.00 - $1,192,000.00
Gross Profit Margin ==> - Cost of Goods Sold = - $274,160.00
Gross Profit Margin ==> Cost of Goods Sold = $274,160.00 (h)

Step 7: Find Net Income (j)

If you notice the Net Profit margin, you will see that it uses Net Income in its calculation. So, we will use that to find Net income.

Net Profit Margin = Net Income / Sales = 0.16 and we earlier found Sales to be $1,192,000.00 so

Net Profit Margin ==> Net Income / $1,192,000.00 = 0.16
Net Profit Margin ==> Net Income / $1,192,000.00 * $1,192,000.00 = 0.16 * $1,192,000.00
Net Profit Margin ==> Net Income = 0.16 * $1,192,000.00
Net Profit Margin ==> Net Income = $190,720.00 (j)

Step 8: Find Accounts Receivable (b)

If you notice the Receivables Turnover ratio is the only ratio given that uses Accounts Receivable so we will use that to find Accounts Receivable.

Receivables Turnover = Sales / Accounts Receivable = 56.7619047619
Receivables Turnover ==> $1,192,000.00 / Accounts Receivable = 56.7619047619
Receivables Turnover ==> $1,192,000.00 / Accounts Receivable * Accounts Receivable = 56.7619047619 * Accounts Receivable [Multiplying both sides by AR to remove AR from the denominator on the left.]
Receivables Turnover ==> $1,192,000.00 = 56.7619047619 * Accounts Receivable
Receivables Turnover ==> $1,192,000.00 / 56.7619047619 = 56.7619047619 / 56.7619047619 * Accounts Receivable
Receivables Turnover ==> $1,192,000.00 / 56.7619047619 = Accounts Receivable
Receivables Turnover ==> $21,000.00 = Accounts Receivable (b)

Step 9: Find Inventory (b)

If you notice the Inventory Turnover Ratio is the only ratio using Inventory explicitly. So, we will use that ratio to find Inventory.

Inventory Turnover = Cost of Goods Sold / Inventory

Inventory Turnover = Cost of Goods Sold / Inventory = 3.51487179487
Inventory Turnover ==> $274,160.00 / Inventory = 3.51487179487
Inventory Turnover ==> $274,160.00 / Inventory * Inventory = 3.51487179487 * Inventory [Multiplying both sides by Inventory to remove Inventory from the denominator on the left.]
Inventory Turnover ==> $274,160.00 = 3.51487179487 * Inventory
Inventory Turnover ==> $274,160.00 / 3.51487179487 = 3.51487179487 / 3.51487179487 * Inventory
Inventory Turnover ==> $274,160.00 / 3.51487179487 = Inventory
Inventory Turnover ==> $78,000.00 = Inventory (b)

Step 10: Find Cash (b)

If you notice there are no ratios that explicitly use cash given. But, what are the components in Current Assets?

Current Assets = Cash + Accounts Receivable + Inventory

After the last two solutions, we now know all of these Current Assets except for Cash. Also, the Current Ratio was given and the Current ratio is:

Current Ratio = Current Assets / Current Liabilities.

As mentioned previously, the only Current Liability is Accounts Payable so:

Current Ratio = Current Assets / Accounts Payable and this is given as being equal to 3.85416666667. Since we also know Accounts Receivable and Inventory we have:

Current Ratio = (Cash + Accounts Receivable + Inventory) / Accounts Payable = 3.85416666667. If we enter the values that we already know we get:

Current Ratio ==> (Cash + $21,000.00 + $78,000.00) / $48,000.00 = 3.85416666667
Current Ratio ==> (Cash + $21,000.00 + $78,000.00) / $48,000.00 * $78,000.00 = 3.85416666667 * $78,000.00 [to remove Accounts Payable from the denominatory on the left]
Current Ratio ==> (Cash + $21,000.00 + $78,000.00) = 3.85416666667 * $78,000.00
Current Ratio ==> Cash = 3.85416666667 * $48,000.00 - $21,000.00 - $78,000.00
Current Ratio ==> Cash = $185,000.00 - $21,000.00 - $78,000.00
Current Ratio ==> Cash = $86,000.00 (b)

Step 11: Find Fixed Assets (c)

If you notice, Fixed Assets is the only item remaining on the left side of the Balance Sheet. In addition, you know that everythign on the left must add up to Total Assets, which is $583,000.00 so:

Fixed Assets = Total Assets - Cash - Accounts Receivable - Inventory
Fixed Assets = $583,000.00 - $86,000.00 - $21,000.00 - $78,000.00
Fixed Assets = $398,000.00 (c)

Step 12: Celebrate!!

That is it!!!!! You have now successfully completed the assignment. This may seem like a long process, but it is really a very straightforward exercise. This is intended to test and see if you understand how the construction and components of the Balance Sheet and Income Statement. In addition, this tests to see if you understand the relationships between the various ratios.