Quantitative Tools in Accounting - Module 6 of 6

Quantitative Tools in Accounting - Module 6 of 6

Quantitative Tools in Accounting

Ratio Analysis and Operating Ratios

To gauge the financial health of a business, accountants use “ratio analysis.”[1]  Ratio analysis consists of examining the proportional relationship of multiple accounts.  Ratios can be compared over time in what is called “time trend analysis” to see if a company is improving or declining in its financial health.[2]  Businesses can also compare their ratios to peer competitors to see how they are faring in their respective industries.[3]  Investors can use ratios to establish their investment expectations and lenders may even include ratios as promises in loan agreements.  Breach of these ratio-based covenants can result in the lender acting against the borrower.[4] 

For example, Acme Corporation carries $1,000,000 in debt and another $3,000,000 in shareholder equity.  Its “debt to equity” ratio is therefore 1 to 3.  For every three dollars of equity Acme carries one dollar of debt.  Acme acquires a $500,000 new lease on production equipment, but instead of recording the lease as an expense, Acme records the lease as a $500,000 loan and Acme's debt to equity capital structure now changes to a new ratio of $1,500,000 to $3,000,000 or 1 to 2.   

Another measure of financial health is working capital, which is the amount by which current assets exceed current liabilities.[5]  It is a measure that indicates how well a business can pay its debts as they become due. Too much working capital may indicate a business is not properly investing its available capital while too little working capital can indicate an inability to meet its expenses and credit obligations.  An ideal working capital amount can be derived by comparing the amount to another metric, such as sales, and is normally industry-specific.  For example, a supermarket's optimal working capital may be 15 to 20 percent of sales while for an airplane manufacturer it may be 25 to 30 percent of sales.[6]

Another way of assessing working capital is to divide current assets by current liabilities, which gives what is called the "current ratio."[7] 

For example, assume Acme Corporation has $120,000 in current assets and $80,000 in current liabilities.  Dividing Acme's current assets by its current liabilities results in a current ratio of 1.5 to 1, which means for every dollar of current liabilities coming due in the next year, there is about $1.50 of liquid assets available to meet that obligation.   

Note that some assets, such as inventory or prepaid expenses, may not be converted into cash for several months, so a more immediate measure that only includes liquid accounts such as cash and marketable securities can more conservatively estimate a business's ability to meet its current obligations.  That test is called the "quick ratio" or "acid test ratio."[8] 

For example, assume Acme Corporation has $120,000 in current assets, but we will now subtract prepaid insurance and tax expenses, along with inventory to give us current assets of $100,000 consisting solely of cash and marketable securities.  Dividing by $80,000 in current liabilities we get 1.25 to 1.  Therefore, for every dollar of current liabilities, Acme has $1.25 in liquid current assets.

Another operating measure focuses on inventory.  We can measure how quickly inventory turns over, which means it sells completely over the course of a year.[9]  We divide the cost of goods sold found on the income statement by the average inventory during the year.  

For example, assume Acme Corporation's cost of goods sold was $254,000.  Its beginning inventory was $72,000 and its ending inventory was $78,000.  Its average inventory total was therefore $75,000. Dividing the costs number of $254,000 by the average inventory number of $75,000 gives 3.39, which means Acme's inventory turned over 3.39 times for the year.  Dividing 365 days by 3.39 gives about 108 days as an average turnover time.   

Note that this measure may be affected by accounting methods used and/or seasonal considerations.  Inventory that turns over too slowly may be absorbing costly storage fees and may be subject to spoilage.  These factors are industry-dependent, as   food needs to turn over faster than consumer goods.[10]

Another current asset that provides an operating metric is the “accounts receivable turnover.”[11]  This measures the degree to which a business is collecting the monies owed by its credit customers. Accounts receivable turnover divides total credit sales by the average amount of accounts receivable. This demonstrates how quickly a business's customers pay their bills.

For example, assume Acme Corporation has credit sales of $425,000, a beginning accounts receivable amount of $64,000 and an ending accounts receivable amount of $42,000.  The average accounts receivable amount is thus $53,000.  The credit sales amount of $425,000 divided by the average accounts receivable amount of $53,000 is 8.02.

This means Acme's receivables turn over about 8 times a year or, dividing 365 by 8.02, about once every 46 days.  If a company’s customers have 60 days to pay their respective bills, then this is a satisfactory result. But if they only have 30 days to pay their respective bills, this could indicate a collection issue.   

A final operating measure is the debt-to-equity ratio, introduced earlier.  A high ratio may indicate excessive debt. 

Profitability and Performance Ratios

In addition to operating ratios, accountants use profitability and performance ratios to gauge the financial health of a business.[12] To determine a business's profitability, we can divide its operating income by its net sales to get its "profit margin."[13]  Operating income is income after operating expenses are deducted, but before interest and taxes and is also refereed to as earnings before interest and taxes or “EBIT.” The net sales amount is the company’s revenue after sales discounts and returns have been deducted.[14]

For example, assume Acme Corporation has $85,000 in EBIT and $452,000 in net sales.  Its profit margin would be 18.8%.   

Another measure of profitability would compare changes over time. One approach is to express a series of metrics as a percentage of sales.[15]  Costs, EBIT and net income are amounts that can each be divided by sales to yield percentages. Any such percentage can then be compared to previous years.

For example, assume Acme Corporation earned $470,000 in net sales this past year.  Acme also had costs of goods sold of $236,000 which is 50.2% of net sales.  The company’s EBIT was $83,000 which is 17.7% of net sales and net income of $47,000 which is 10% of net sales. While none of these numbers may be significant in a vacuum, we can compare these numbers to those of previous years or of other companies in the industry to gauge the company’s trajectory and competitiveness.

Another class of ratios pertains to the coverage of specific expenses.  The “times interest earned ratio” shows how many times a company can pay its interest.[16]  

For example, assume Acme Corporation shows an EBIT amount of $45,000 and interest expense of $5,000.  The company can pay its interest nine times over.  

There are other coverage ratios.  A similar measure, the “fixed charge coverage ratio,” shows how many times a company can pays its fixed expenses.  A company can similarly determine its ability to cover its dividends.[17]

Profitability measures can also indicate how well the firm is generating a profit for its investors.  One significant indicator is called “earnings per share” which is retained earnings divided by the number of shares of outstanding common stock.[18]

For example, Acme Corporation pays a preferred dividend of $112,000 from its earnings of $367,000 leaving $255,000 to be apportioned among its common stockholders.  Acme has 100,000 shares of common stock currently owned by shareholders, so its EPS is $2.55.  Note that the shareholders might not receive $2.55 in dividends; rather, EPS is simply an accountant’s measurement of a company’s value and its wealth generation for its shareholders.   

The price-earnings ratio, or “PE ratio,” builds on EPS by tying in the price of common stock.  The PE ratio is the market price for a share of common stock divided by the EPS.[19]

For example, assume Acme Corporation has an EPS of $2.55 and Acme’s common stock is selling at $32 per share.  Acme’s PE ratio would therefore be 32 divided by 2.55, or 12.5.  Analysts typically compare PE ratios over time and with that of other peer companies.      

Another measure compares earnings to investments to generate a rate of return.  A company’s “return on assets” is its net income divided by its average assets while a company’s “return on equity” is its retained net income divided by its average common stockholders’ equity.[20]  

For example, assume Acme Corporation has $414,000 in net income and average assets worth $4,600,000.  Acme’s return on assets would be 9 percent.

A company’s leadership may also issue a Management Discussion and Analysis where it adds a qualitative dimension to its portrayal of the company’s financial health.  In this section, company management may explain apparent inconsistencies or anomalies to shareholders.[21]

For example, assume Acme Corporation’s sales show a dramatic drop from a reduction in productivity because it re-tooled a manufacturing plant. The MDA section might explain that this investment actually increased Acme’s profitability, even though it temporarily reduced revenue. 

Time Value of Money

While money may seem static, the value of money changes over time.  A dollar today is worth more than one dollar a year from today.  Money can earn interest so a person would have more of it in the future. $1,000 invested today will yield a thousand dollars plus interest in a year, while a thousand dollars received in a year has no interest.  Think of money as a revenue-generating asset.  It’s revenue generation aspect only works if it has time to accumulate value.[22]

Still, three considerations affect this generalization. The first consideration is utility.  People prefer instant gratification to self-restraint of waiting a year to be paid.  Another consideration is risk.  There is an inherent risk in future funds.  The monies might not be there because, for example, the person making payment becomes insolvent.  A final consideration is opportunity cost, which is the cost of not pursuing alternative options.  For example, a person takes the available money now to invest and obtain interest.  If the person did not invest the money then she loses the interest, which is the lost opportunity cost.[23] 

For example, assume First Bank pays 8% interest on a bank account.  Sharon invests one hundred dollars today and expects to receive $8 interest in a year.  She leaves her money in the account for a second year, thus receiving 8% interest on the principal and interest from the first year (the $108), for a total of $116.64.  That might not seem like a particularly big gain but if it is a $1,000,000 trust fund, the fund would reflect a $166,400 gain in interest in the two years.   

We can see that the interest from each succeeding year earns interest in future years.[24]  Interest earns interest upon interest, a phenomenon called “compounding interest,” and is a significant factor in wealth generation.  Of course, it works the other way against borrowers who accumulate interest upon interest.  Given a particular interest rate, principal amount, compounding period and a certain amount of time, one can calculate the future value of an investment.  Financial value formulas and software programs such as Microsoft Excel can be used to perform these functions.[25]

For example, Andrew invests $30,000 at age 25 in a bank fund that pays 9% annually.  At age 65 he will have accumulated $942,282.  This amount is given by the formula 1.09 raised to the power of 40, which is the number of compounding periods, and then multiplied by the principal amount of $30,000.[26]   

It works the other way too.  A person can calculate the present value of a future amount by a process that is called “discounting.” We discount the future value to the present.   

For example, Andrew wants to retire with at least $1,000,000 at age 65.  He wants to know how much he needs to invest today at 9% to achieve his goal.  The answer is $31,837.58.  This amount is given by the formula of the principal amount of $1,000,000 divided by 1.09 raised to the power of 40, which is the number of compounding periods.[27]

In some cases, there may be more than one payment.  A series of periodic cash flows yielded by an investment is called an annuity.[28]  An annuity may consist of a series of payments into an investment fund, such as a college savings fund, or a series of payments from an investment fund, such as a retirement fund.  Each cash flow in the stream of payments would be discounted from its future value to its present value and then added together in order to ascertain the fund’s overall worth.[29]

For example, Acme Corporation pays $10,000 annually into a fund that pays a 9% rate of interest on the principal amount and interest accumulated thus far.  At the end of ten years Acme would have about $175,603.  The amount is determined by calculating the first payment of $10,000 plus interest on the initial $10,000 compounded for nine periods. 

The formula is 1.09 raised to the power of 9, then multiplied by $10,000.  Then the value of the second payment would be calculated at 1.09 raised to the power of 8, then multiplied by $10,000.  Then the third would be 1.09 raised to the power of 7, then multiplied by $10,000 and so on.  Note that the exponential power decreases which reflects the decreasing number of compounding periods.  Acme would then add the value of all of the cash flows to get the future value of the annuity.

The converse is also possible. Assuming level payments, a certain amount of time, and a fixed discount rate, the present value of an annuity may be determined from successive cash flows.[30]

The time value of money analysis applies primarily to determining the value of financial instruments such as bonds with coupon payments and stock with dividend payments.       

Company Valuation

There are many ways to value a company.[31]  There are analysts who believe that a company’s balance sheet is the best way to determine its value.  The residual amount after subtracting a company’s liabilities from its assets yields one measure of value, called “book value.”  However, since assets are recorded under the rules of accounting at historical cost, an “adjusted book value” may be needed to more properly reflect the current market value of the assets, though that determination might be subjective.  “Liquidation value” would be the worth of a company if it sold all of its assets and paid all of its liabilities.  These amounts would need to be reduced because the asset prices at selloff are probably less than their full value.  Another method to value a business would be to calculate its reproduction cost if a new entrant to the industry were to be constructed from scratch.[32]      

The balance sheet methods focus on asset values, but another way to measure the value of a business would be its income statement.[33]  Estimating future earnings requires forecasting future numbers by using past amounts.  It also requires making reporting judgments as to how such accounts as inventory, depreciation, and bad debts will be reported.   

The rate in valuing a business is called its “capitalization rate.”  This is the rate of return required by an investor to invest in the company. The rate reflects the level of risk in the investment.  Lower risks mean lower capitalization rates.  The value of the company is determined by dividing the earnings estimate, as reflected by a company’s earnings per share, by the capitalization rate.[34]

For example, assume Acme Corporation earns $2.00 per share and its capitalization rate is estimated at 8%.  Therefore, Acme’s value is $25.00 per share.  Alone, this number may not mean much but viewed in the context of different cap rates and estimated earnings, a range of values can approximate Acme’s worth. 

Another way of using earnings to measure a company’s worth is to examine the price-earnings ratio.  This metric compares a price of publicly-traded stock with its earnings per share.  The “implied cap rate” is the reciprocal of the PE ratio.[35]

For example, assume Acme Corporation stock sells for $30 per share and earnings per share is $2.00.  We would divide Acme’s share price of $30 by its earning per share of $2.00 to get a PE ratio of 15.  Acme’s implied cap rate would be the reciprocal amount, which is 1 divided by 15 or about 7%.   

A third method of business valuation involves an analysis of dividend cash flows.[36]  Future cash flows are first estimated and then discounted to their present value using discounted cash flow formulas described earlier.[37]  The result is the value of a share of the company’s stock.    

Note that cash flows can be measured in different ways and may not present a complete depiction of a company’s operations.  Determining growth variables can become speculative.  To overcome the inherent limitations of the individual valuation techniques, some analysts will use several approaches to get a fuller image of a company’s financial health.[38]


            Thank you for participating in LawShelf’s video-course in the basics of financial accounting. We hope that this course has made you familiar with accounting concepts that are important in providing legal and accounting services for businesses. We hope that you will take advantage of our other business law courses and we encourage you to contact us with any questions or feedback.

[1] See Lawrence A.Cunningham. Introductory Accounting,Finance and Auditing for Lawyers. (6th ed.) 179-195. 2006; David R. Herwitz and Matthew J. Barrett. Accounting for Lawyers: Concise Fourth Edition. (4th ed.) 270-280. 2006; Charles H. Meyer. Accounting and Finance forLawyers in a Nutshell. 16. (6th ed.) 397-417. 2017.

[2] Cunningham, 186-187.

[3] Cunningham, 175-176.

[4] See Meyer’s example, 275.

[5] Cunningham, 179.

[6] Cunningham, 179.

[7] Meyer, 408; Cunningham, 180.

[8] Meyer, 409; Cunningham, 181-182.

[9] Meyer, 413; Cunningham, 182-183.

[10] Cunningham, 183.

[11] Meyer, 412,413; Cunningham 183-184.

[12] See generally, Cunningham, 185-189.

[13] Meyer, 414; Cunningham, 185-186.

[14] Cunningham, 189, 463, 470.

[15] Cunningham, 187-189.

[16] Meyer, 410-411.

[17] Cunningham, 189.

[18] Meyer, 397-399; Cunningham 189-191.

[19] Meyer, 416; Cunningham, 191.

[20] Meyer, 414-415; Cunningham, 191-192.

[21] For a detailed treatment of the MD&A see Cunningham, 195-206.

[22] Meyer, 491-492; Cunningham, 245-246.

[23] Cunningham, 245-247.

[24] Meyer, 493-495.

[25] Meyer, 495.

[26] $30,000 x (1 + .09)40.

[27] $1,000,000/(1 + .09) 40.

[28] Meyer, 498-503.

[29] Cunningham, 247-251.

[30] Cunningham, 251-257.

[31] See Cunningham, 269-278 (Introductory Parable: The Old Man and the Tree).

[32] Cunningham, 278-281.

[33] Cunningham, 283-289.

[34] Cunningham, 286.

[35] Cunningham, 288.

[36] Cunningham, 289-291.

[37] The discount rate here is the cost of equity (the cost a company incurs in having stock) minus the assumed dividend growth rate.  A discussion of this computation would require much more analysis and risks undermining the simplicity of this introduction to valuation.

[38] Cunningham, 294-295.