Stocks, flows, financial statements

These slides define stocks and flows as these concepts are used in accounting, economics, and finance. The main financial statements are used to illustrate them.

1. Basic math tools:
Stocks, ows, and nancial statements
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August 30, 2011

2. Topics
Stocks and ows
Accounting fundamentals

3. Stocks and ows
In economics (as in the physical sciences), empirical observations
and measurements are made either at a point in time or over a
period of time. As a result, the basic variables can be either
stocksorows. Astockmeasure refers to the value of a variable
at a given point in time. Aowmeasure refers to the value of a
variableover a given period of time. On top of these basic
measures, a host of derivative measures (e.g.ratiosof ows to
ows, ows to stocks, stocks to ows, and stocks to stocks) can
be determined. This distinction is extremely useful in accounting,
economics, and nance.

4. Stocks and ows
Consider this gure:
It shows a container with a certain liquid (e.g. water), one pipe
delivering it into the container, and a pipe leaking it out.
Physicists and engineers call it a simple \hydrodynamic system."

5. Stocks and ows
Basically, we can measure the performance of this system by
measuring
Ithe amount of liquid in the container at given points in time
(e.g. on Sundays at noon, on the last day of each month) and
Ithe amount of water that ows through the container over
given periods of time (e.g. a week, a month).
Then, by combining both forms of measurement, we get a richer
view of the functioning of the system. The stock measures may
help us correct errors in the measurement of ows or, vice versa.
(The termstockhas several meanings in economics. It also refers
to the \equity" or legal ownership of a company traded in the
market. The context should make it clear when we use the term in
one or the other sense.)

6. The algebra of stocks and ows
Let the upper-case letters denote stocks and the lower-case ones
ows. LetXtbe the amount of water in the vessel at point in time
t,xitthe amount of water owing into the vessel during the
month, andxotthe amount of water owing out of the vessel
during the month. Then:
Xt+1=Xt+xitxot
The amount of water in the container att+ 1 isequal tothe
amount of water in the container attplusthe water that got in it
during period (t;t+ 1)minusthe water that leaked out during the
same period.
1
1
Assume no evaporation or, alternatively, that the water leaked out in the
period includes evaporated water.

7. The algebra of stocks and ows
Example: On November 1 (t= 0), the amount of water in the
container is 10 gallons (X0= 10). The water owing into the
vessel during November is 40 gallons (xit= 40) and the water
owing out of the vessel is 39 gallons (xot= 39). Calculate the
amount of water in the container on December 1:
X1=X0+xi1xo1= 10 + 4039 = 11:
If the stock of water on December 1 is any dierent from (greater
than or less than) the result above, we have made errors in our
measurements. The new measure of the water level can help us
correct them.

8. Some accounting
The two basic nancial statements that accountants produce are
thebalance sheetand theincome statement. These nancial
statements provide a detailed picture of the ongoing nancial
performance of a business.

9. Balance sheet
The balance sheet of any organization (e.g. a business) has two
sides. The left-hand side reports the value of all the organization's
assets at a given point in time, typically at the end of a year. The
assets are the resources the organization manages measured at a
point in time. The right-hand side reports the source of the assets
listed on the left-hand side. They are either owed to others
(liabilities) or \owned" by the legal \owners" (equity or net worth).
The fundamental balance-sheet equation is:
At=Lt+Et
wheretindicates a point in time (e.g. the last day of the year),A
is total assets,Lis total liabilities, andEis total equity.
2
2
To separate an organization from its individual owners, it may be
convenient to state the equation asA=L, i.e. assets equal liabilities. They are
liabilities to either others or to the individual \owners" of the organization. In
this interpretation, the equity of the legal owners of, e.g., a business is
considered a special type of liability.

10. A typical balance sheet
ABC Inc.
Balance Sheet
12/31/06
Assets Liabilities and Equity
Cash and liquid securities $ 10 Payables $ 20
Inventories 50 Other short-term debt 40
Receivables 60 Mortgages 80
Trucks (net) 25 Other long-term debt 250
Oce equipment (net) 10 Liabilities 390
Machinery (net) 45 Equity 120
Buildings (net) 220
Other xed assets (net) 90
Assets $ 510 Liabilities plus Equity $ 510

11. Income statement
The income statement reports on its top line the total ow of gross
income (e.g. sales revenues) received by the organization during a
period of time (e.g. a year). The next lines report the various
expenses that the activity of the organization incurred during the
period to sustain its gross income. These expenses { sorted out as
production costs, operating expenses, nancial expenses, and taxes
{ are deducted or subtracted from the top line. The bottom line of
the income statement indicates the ow of net income or net prot
during the period. The fundamental equation is:
NIt=GItPCtOEtFEtTt
wheretis the period of time from point in timet1 to point in
timet,NIis the residual or net income (prot if positive, loss if
negative),GIis the gross income (typically, sale revenues),PCis
the total cost of goods sold (e.g. the cost of raw materials, storage
costs, wages and benets of factory-oor workers),OEare the
operating expenses (sales and administrative expenses, including
salaries and commissions of administrative and sales personnel,
depreciation of buildings and equipment),FEare the nancial
expenses (interest payments), andTare the taxes.

12. Income statement
A typical income statement:
ABC Inc.
Income Statement for
1/1/07 through 12/31/07
Sales revenues $ 200
(-) Cost of goods sold 90
Gross prot 110
(-) Operating expenses (includes depreciation) 40
Operating prot 70
(-) Interest paid 10
Taxable prot 60
(-) Taxes 10
Net prot $ 50

13. Summary
Note that:
Iall items in the balance sheet arestockmeasures (\water in a
container" at a point in time),
Iall items in the income statement areowmeasures (\water
that ows in/our" over a period of time),
Ithe balance sheet and the income statement are related in
multiple ways,
Iassets are \positive water stocks" while liabilities and equity
items are egative water stocks" (if that makes sense), and
Isale revenues are \positive water ows" and costs and
expenses are egative water ows'.'

14. Summary
Every time an organization conducts an operation or transaction,
every time a business takes raw materials from its inventories and
have its workers process them on the factory oor, every time its
sales people sell a batch of goods or its administrative personnel
orders a shipment from its suppliers, every time a payment is made
or received, there is \water" owing from one balance-sheet
container into another one. At the end of the given period (and
beginning of the next period), the balance sheet reports the
adjusted levels of \water" in each container at that point in time.
Also at the end of the given period (beginning of the next), each
spurt of \water" that owed from container to container during
the period is added up (aggregated) into its respective category
and recorded in the income statement. The legal owners of the
organization (if a corporation, the legal owners are called
stockholders) pay most attention to the level of \water" in their
equity \container."