Solutions for Reconstruction Case

I would like to thank you all for the Algebra lessons last night.   The effort was appreciated however I am concerned that after using this case for four previous classes I just keep making "mistakes", or do I? 

Before you all think I have gone off the deep end, I would like to clarify what happened last night from my perspective.  When I provided the answer to the amount of long-term liabilities and you disagreed the audience was immediately split into groups who were trying to support my supposedly poor algebra skills,  a group who attacked those same skills and a group who wasn't quite sure which group to join.  While this clearly indicated the amount of uncertainty in the class with regard to the material (as happens in every class I make the "mistake") it also points out the need to consider what the ratios really mean. 

I may have irritated some of you because I seemed to persist with what appeared to be a really stupid answer and your proof was that my algebra was incorrect.  However, the proof really lies in how the ratios themselves are constructed.  They have their existence based on a fixed environment called a balance sheet and income statement.  Once I provided the ratios we used to reconstruct the balance sheet and income statement (as well as current liabilities and revenues) I limited the possible answers that could have existed regardless of "bad algebra". 

Therefore the real response to "bad algebra" is to point out where in this limited environment those numbers simply could not work. In this case the very ratio I was using simply would not produce the .6215 long-term debt ratio given in the problem.  I hinted at that during the discussion and finally at the end after almost everyone had gone someone came up and said "that answer can't be right because your ratio doesn't work";  that is the correct response.  If I were sitting in an exam I wouldn't want to be worrying about my algebra skills since there is no benchmark for determining whether I made a mistake or not.  By understanding how the puzzle relating to the balance sheet and income statement and the ratios fit together I am handed many benchmarks for determining the validity of my numbers. 

I apologize if many of you were irritated but I hope you see my point, believe the accounting system environment because it works and operates in the same way every time. See you after thanksgiving for the presentations.  The "true solution" as well as the spreadsheet we discussed in class will be on the page today.

Tom Omer

Here is a followup question to my note above and my response.

My question is: when there is a conflict between acounting rules and math rules, which one should you(we) follow?

I would be more than happy to answer this question because the answer is
there is never a conflict between a math rule and an accounting rule.  What
I did last night is a common mistake students make on an exam.  In the rush
to complete the exam the object they are solving for is lost in the simple
algebraic manipulation and they are surprised when the number they report
for the result is wrong.  All I am suggesting is than instead of depending
on the rusty algebra, depend on the current knowledge of how the ratios are
created and what is used to create them.  Much like math problems, closed end
problems dealing with balance sheet and income statement numbers have
limited solutions.  Therefore if you understand the environment and its
limits you always have a benchmark to check your numbers.

Reconstruction of Financial Statements
from Financial Ratios

Given 	Revenues $10,281
	        Current Liabilities $2,285

Current Assets can be obtained by solving:

X / $2,285=1.172 (Current Ratio) X=$2,678

Accts Receivable can be obtained by solving:

X / ($10,281/365)=39.66  X=$1,117

 
 Accounts Receivable turnover could be obtained by solving 365 / X = 39.66.  Once the turnover number was
determined the revenue number could be divided by turnover to obtain 
accounts receivable.  Thus Accounts Receivable = 10,281/9.2 or 1117.5.  The
approach indicated above makes the calculation
using a single step approach.  If we know the number of days for the accounts 
receivable to turnover we merely need to multiply the sales per 
day (10,281/365) times the number of days to turnover the accounts 
receivable.  Thus,  X / ($10,281/365) = 39.66 or 28.167 X 39.66 = $1117.5 

Cost of Goods Sold can be obtained by solving:

($10,281-X)/$10,281=.1512  X=$8,727  Gross Margin is $1,554

Inventory can be obtained by solving:

$8,727/ X =10.005  X=$872

Total Assets, Long Term Debt plus Stockholders Equity,
and Total Liabilities and Stockholders Equity
can be obtained by solving :
 
Revenues divided by Invested Capital equals Invested Capital Turnover.

$10,281 / X = 2.091  X=$4,917 (Long Term Debt plus Stockholders Equity)

Total Liabilities and Stockholders Equity= Current Liabilities plus
Long Term Debt plus Stockholders Equity

$2,285 + $4,917=$7,202

Total Assets = Total Liabilities and Stockholders Equity.

Total Assets=$7202

Net Income can be obtained by solving:

Net Income divided by Sales = Profit Margin Percentage

X / $10,281 =0.02831  X= $291

Cash plus Accounts Receivable can be obtained by solving:

X / $2,285= .671  X=$1,533

Cash plus cash equivalents can be obtained by solving:

$1,533-$1,117=X  X=$416.

Prepaid Expenses can be obtained by solving:

Current Assets ($2,678) 
minus Accts Rec ($1,117)
minus Inventory ($872)
minus Cash ($416)
= $273

Long Term Debt can be obtained by solving:
Long Term Debt Divided by Long Term Debt +Stockholders Equity

X / ($4917)=.6215   X=$3055

Stockholder's Equity can be obtained by solving:

Long-Term Debt + Stockholders Equity minus Long Term Debt.

4917-3055=X, X=1862

Return on Equity can be obtained by

Net Income/Stockholder's Equity or $291/1862= .156

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