# 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

*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]*

__from__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]

**Conclusion**

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. (6^{th} 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.