Public Financial Management combined lecture packet

POLS 7830 PUBLIC FINANCIAL MANAGEMENT
LECTURES 1 & 2: COST CONCEPTS
• Types of costs
• Cost concepts
• Break-Even Analysis
• Break-Even Analysis with Multiple
Products
• Marginal Cost Analysis
• Cost Allocation

How Much Does Something
Cost?
• It depends on how the manager looks at and
analyzes cost information
– Why is the analysis being done?
• Cost Objective: The focus of the cost
analysis
– Unit of service
– Program
– Department

How Much Does Something
Cost?
• Relevant Costs: Costs that have an impact
on or are impacted by the decision the
manager is considering. Determining what
costs are relevant depends upon
– Cost objective
– Time frame for the analysis
– Expected range of volume
– Relevant range of production analyzed

Cost Definitions
• Full Cost= Direct Costs + Indirect Costs
• Full (Total) Cost: The sum of all costs associated
with the cost objective
• Direct Costs:
– incurred within an organizational unit
– cost of resources used to produce a good or service
• Indirect Costs (Overhead)
– assigned to a unit from outside
– resources not used directly to provide a service

What is Direct? Indirect?
Cost Objective Indirect Costs Direct Costs
Patient Unit, department &
hospital
administration
Direct care and
supplies
Surgical Unit Department and
Hospital
Total patient costs and
unit management
Surgical
Department
Hospital Total unit costs plus
department
administration
Hospital None Total departmental
costs plus hospital
administration

More Cost Definitions
• Relevant Range: The normal range of
expected activity, the anticipated range of
service volume
• Variable Costs: Costs that vary directly with
changes in the volume of service units over
a relevant range of activity

More Cost Definitions
• Average Cost: The full cost of a cost object
divided by the number of units of service
provided (Total Cost/Volume)
• Fixed Costs: The costs that remain
(relatively) unchanged in total for some
time period as the volume of services
changes over a relevant range of activity

Fixed Costs
0
20000
40000
60000
0 100 200 300 400
Units of Service
Cost($)
Fixed Cost

Variable Costs
0
1000
2000
3000
0 100 200 300 400
Units of Service
Costs($)
Variable
Costs

Total Cost
39500
40000
40500
41000
41500
42000
42500
0 100 200 300 400
Units of Service
Cost($)
Fixed
Costs
Variable
Costs

Average Costs
0
10000
20000
30000
40000
500001
200
400
600
Units of Service
Cost($)
Variable
Costs

Even More Cost Definitions
• Step costs (Semi-variable): Costs that are
fixed over ranges that are less than the
relevant range
• Mixed Costs: Contain both fixed and
variable components
• Marginal Costs: The additional costs
incurred as the result of providing one more
unit of service (Incremental Costs)
– Note: Marginal costs are equal to variable costs
unless there are changes in step costs

Relevant Cost Analysis
• Example: Ineedaspleen Hospital has fixed
costs of $300,000 and variable costs of
$250 per patient. What would the cost
structure look like?
Volume Fixed
Cost
Variable
Cost
Total Cost Average
Cost
100 $300,000 $25,000 $325,000 $3,250
500 $300,000 $125,000 $425,000 $850
1,500 $300,000 $375,000 $675,000 $450
2,500 $300,000 $625,000 $925,000 $370
3,000 $300,000 $750,000 $1,050,000 $350

Making a Cost Based Decision
• The Hospital treats 2,500 patients per year.
An HMO offers them 500 additional
patients and offers to pay $300 for each one.
Should the hospital accept the HMO’s
patients?
– The average cost per patient at 2,500 is $370
– The average cost per patient at 3,000 is $350
– The variable cost per patient is $250
• What should you do recommend for
Ineedaspleen Hospital?

Making a Cost Based Decision
• Key Question: How much additional cost will
be incurred by accepting this deal?
• Answer: $250, the amount of the variable costs
per unit (the fixed costs remain constant over
the additional units)
• So, ACCEPT the deal!
– (This was a simple marginal cost analysis)
• What problems are raised by accepting this
proposition?

Problems
• Possible fixed cost increases
• Possible variable cost increases
• Other insurers may want the same rate

Break-Even Analysis
• Method to identify the break-even price or
quantity for a particular service
• VC= Variable Costs
• FC=Fixed Costs
• TC=Total Costs (Variable + Fixed Costs)
• P=Price
• BEQ=Q=Break-Even Quantity

Break-Even Analysis
TR= P * Q
TC= FC+(VC * Q)
Break-Even: TR = TC
(or) P*Q=FC + (VC*Q)
(P*Q)-(VC*Q)=FC
Q*(P-VC) = FC, So...
Q= and P= TR/Q
FC
P-VC

Break-Even Analysis
0
200
400
600
800
1000
0 5 10 15 20 25 30
Units of Service
$
Fixed
Costs
Total
Costs
Total
Revenue
Profit
Loss
Break-
even
point

Contribution Margin
• Key to using B-E analysis is to pay
attention to the Contribution Margin
• The Contribution Margin indicates the
amount available to contribute to paying the
fixed costs of the organization
– How much of the unit price remains after
paying the variable costs for that unit?
• Contribution Margin= P - VC

Contribution Margin
• The Feed-a-Fish foundation raises small
vermin to feed to endangered flesh eating fish.
They sell 3,000 moles each month at $0.68 a
piece and have fixed costs of $1200 per month
and variable costs of $0.18 per mole.
• The contribution margin is (0.68-0.18) = $0.50
• $0.50 from each sale goes toward the fixed costs.
• Note: $1200/$0.50 = 2400 =BEQ (CM can
substitute for P-VC when finding BEQ)

Break-Even Analysis with Multiple
Products

What if there is more than one
product or service?
• The B-E formula assumes just one item for
sale.
• When faced with different prices and
different variable costs per service, we must
use all of them!
• Key: Find the weighted average
contribution margin.
– The weighted average contribution margin may
be divided into fixed costs to find BEQ

The Feed-A-Fish Foundation sells moles,
voles and shrews as fish food for endangered
fish. The variable costs associated with
hunting and capturing these animals are $0.18,
$0.23 and $0.48, respectively.
• The prices for the vermin are $0.68, $0.75
and $1.09.

Multiple Product Break-Even
Analysis
Price VC
Contribution
Margin (P-VC)
Moles $0.68 $0.18 $0.50
Voles $0.75 $0.23 $0.52
Shrews $1.09 $0.48 $0.61
Now we need to know the proportion of sales
in each category...

Analysis
• In order to find the break-even level for a
multiple product business we
– Find the proportion of sales in each category
– Multiply that proportion by the contribution
margin
• The result is the weighted average
contribution margin!

Analysis
Volume
(Units) Share
Contribution
Margin (P-VC)
Weighted
Average
Contribution
Margin
Moles 3000 54% $0.50 $0.27
Voles 1350 24% $0.52 $0.13
Shrews 1175 21% $0.61 $0.13
Total 5525 100% $0.53

Analysis
• Next: Substitute the weighted average
contribution margin for (P-VC) to solve for
the BEQ!
$ 1200
0.53
= 2264 units

Target Profit
• Not-for-profit organizations typically seek
to generate a surplus
• This creates the need to set prices such that
they yield a ‘target profit’
• We can find the Target Profit Quantity
(TPQ) by adding a target profit to the
numerator of the BEQ equation:
FC + TP
TPQ = P - VC

Marginal Cost Analysis
• Key Question: How much additional cost
will be incurred by making one choice
versus another?
• Provide in-house (Make) when marginal
cost of producing the additional units is
below the market price.
• Contract-out (Buy) when marginal cost of
producing the additional units is above the
market price.

Should Millbridge Schools Contract
Out?
• Millbridge township has 2,500 students and
expects the number of students next year to
be 3,000. The average cost per pupil is
presently $8,000 and the adjacent town of
Millboro has excess capacity it is willing to
sell for $7,000 per student.
• Should Millbridge contract out for the
additional 500 students?

Should Millbridge Schools
Contract Out?
Average Cost Estimates
Student
Volume
(A)
Fixed Cost
(B)
Variable Cost
(C=$3,000 x A)
Total Cost
(D=B+C)
Average
Cost Per
Student
(E=D/A)
1,500 $15,000,000 $4,500,000 $19,500,000 $13,000
2,500 $15,000,000 $7,500,000 $22,500,000 $9,000
3,000 $15,000,000 $9,000,000 $24,000,000 $8,000

• Marginal costs (MC) are the additional
costs implied by the policy choice
– For Millbridge, this is the cost of adding 500
students (not just one)
– Absent some fixed costs increases, the MC =
VC per unit of service.

Contract Out?
Marginal Cost estimates without fixed cost increases
Student
Volume
(A)
Fixed Cost
(B)
Variable
Cost
(C=$3,000
x A)
Total Cost
(D=B+C)
Average
Cost Per
Student
(E=D/A)
Marginal
Cost per
Additional
Student
1,500 $15,000,000 $4,500,000 $19,500,000 $13,000 $3,000
2,500 $15,000,000 $7,500,000 $22,500,000 $9,000 $3,000
3,000 $15,000,000 $9,000,000 $24,000,000 $8,000 $3,000

• Two notions of Marginal Cost
1. The added cost of the next unit produced
Used for comparing costs within a relevant range
2. The added cost of the next level of production
Used for comparing various levels of service that
exceed the current relevant range

• Sometimes Marginal Costs (MC) include
increases in both fixed and variable costs!
– E.g. When fixed costs increase across the next
levels of service and you are reporting MC for
the step to the next level of production
– If Millbridge needs to build a new school for
the 500 students, fixed costs would increase in
addition to the total variable costs.
• MC would increase!

• Sometimes Marginal Costs (MC) include
increases in both fixed and variable costs!
– When fixed costs increase across the next levels
of service
– If Millbridge anticipated a constant enrollment,
but wanted to contract out and could close one
school, fixed costs would decrease.
• MC would decrease!

MC w/ increasing FC
• When a decision option requires fixed costs
to increase…
– Include the increase in the VC calculation
– Compute the MC for the whole step in
production
– The new per/unit MC within the new relevant
range may be the same as before
• The decision-maker cares about the MC of the step
as a whole

Marginal Cost estimates with fixed cost increases
Student
Volume
(A)
Fixed Cost
(B)
Variable
Cost
(C=$3,000
x A)
Total Cost
(D=B+C)
Average
Cost Per
Student
(E=D/A)
Marginal
Cost
1,500 $15,000,000$4,500,000$19,500,000 $13,000 Base scenario
2,500 $16,500,000$7,500,000$24,000,000 $9,600 $4,500
3,000 $30,000,000$9,000,000$39,000,000 $13,000 $13,000
Contract Out?
Note: The marginal cost of moving from 1500 to 2500 students is
$4500 (24000-19500).
Marginal
$3,000
$3,000
$3,000
Cost
Per unit(Step)

Cost Allocation
• Indirect costs must be assigned to
appropriate functions of the organization in
order to capture the real costs for each
function
• The process of allocating these costs can be
complicated

Terms
• Cost center: Unit or department for which
manager is assigned responsibility for costs
• Mission center: Cost center that produces the
final product or service
• Cost base: The unit of analysis (basis) for
allocating overhead (e.g. bed days, person
hours)
• Cost pool: A grouping of costs to be allocated
• Cost objective: Item for which a cost is desired
(unit of service, program, department, etc.)

Terms
• Direct costs: Costs resulting from direct
production of a good or service
• Indirect costs: Costs that are assigned to an
organizational unit from elsewhere in the
organization (not from direct production)
• Full cost: All costs associated with a cost
objective (indirect and direct)

Allocation approaches
• Direct distribution: allocating indirect costs
solely to mission centers
• Multiple distribution: allocation of support
center costs to all other support centers,
then to mission centers, remaining support
center costs then allocated
• Step-down distribution: form of multiple
distribution where support center costs are
allocated to every other center that has not
yet allocated its costs

Cost Locations
• Mission Center: A cost center that produces
the final product or service
• Support Center: A cost center that produces
assistance to mission centers, but does not
produce a final product or service

Cost Allocation
• Your department produces lime Jello cubes for the
Jiggling Food Foundation
• Indirect costs from the purchasing department are
allocated based on the number of department
purchase orders placed
• The cost pool is the TC of the dept. of purchasing
• The cost base is the number of purchase orders
• If the departments costs were $68,000 across 46,800
orders, then the cost per order would be: 618/468 =
$1.45

Cost Allocation
• Assume that there are two other cost
centers, one each for custard and pudding
production at the same level of purchase
order generation.
• Across 140,400 (3*46,800) orders, the
cost per order would be: 618/1404 =
$0.44

How to choose a base
• What base should you choose for allocating
overhead?
• Allocation factors create incentives that
managers can use to control costs or promote
organizational goals
• Rule of thumb: If one cost center can affect the
costs of another then the base should relate to
usage (rather than space, FTE, etc.)
– The cost of tracking and allocating the usage
should not outweigh the value of the information

Allocating Costs, Steps
1. Classify each center as either a mission
center or a support center
2. Apply the cost test (can mission centers
impose costs on support centers)?
3. Select the allocation base and method
4. Allocate the support costs to the mission
centers
- Do not allocate support center costs to the
same support center

Allocating Shelter Costs
• The shelter has two mission centers:
Feeding and Counseling
• The shelter has two support centers:
Purchasing and Administration
• The base for purchasing is purchase orders
• The base for administration (supervision) is
the number of employees

Direct Purchasing Administration
Cost Center Cost $ P.O. % Personnel %
Support
Purchasing 25000 2
Administration 280000 95
Mission
Soup Kitchen 500000 1 92
Counseling 50000 4 6
Total Cost $855,000 100% 100%

Direct Distribution
• Support centers are only allocated to
mission centers
– Most applicable when the organization must
show all costs issuing from mission centers
• When allocated on the base of use, the
proportional use of the mission centers is
used
– Even if the mission centers represent the
smallest portion of the use

Direct Purchasing Administration
Cost Center Cost $ P.O. % Personnel %
Support
Purchasing 25000 2
Administration 280000 95
Mission
Soup Kitchen 500000 1 92
Counseling 50000 4 6
Total Cost $855,000 100% 100%
20%
80%
94%
6%

Direct Distribution
Direct
Cost Center Cost $ Purchasing Administration Total
Support
Purchasing $25,000 ($25,000) $0 $0
Administration $280,000 $0 ($280,000) $0
Mission
Soup Kitchen $500,000 $5,000 $262,857 $767,857
Counseling $50,000 $20,000 $17,143 $87,143
Total Cost $855,000 $0 $0 $855,000
20%
80%
94%
6%

Step Down Distribution Method
• Support center costs are allocated to both
support centers and mission centers
• The process begins with one support center
allocating its costs to all other mission and
support centers
• The process continues with the next support
center allocating its costs to all remaining
mission and support centers
• The process continues until no support
center costs remain unallocated

Purchasing
Administration
Jello
Custard
Pudding

Administration
Jello
Custard
Pudding

Jello
Custard
Pudding

1%
4%
94%
6%
95%
Direct
Cost Center Cost $ Purchasing Subtotal Administration Total
Support
Purchasing $25,000 ($25,000) 0 $0 $0
Administration $280,000 $23,750 303750 ($303,750) $0
Mission
Soup Kitchen $500,000 $250 500250 $285,153 $767,857
Counseling $50,000 $1,000 51000 $18,597 $87,143

• Problem: Which support center should go
first when allocating by the step cost
method?
– Results change significantly
• Solution: Choose the allocation order that
produces the most accurate view of costs
where they accrue!

Other Allocation Approaches
• Algebraic approaches (reciprocal)
– Costs distributed to all centers
– Matrix algebra is used to solve a set of
simultaneous equations to distribute the support
costs that remain after the allocation to the
remaining units

Other Allocation Approaches
• Activity Based Costing
– Goal: To minimize the distortion and
inaccuracy in other allocation methods
• Method: Identifying cost drivers and
determining how much of each cost driving
activity is required by each mission center

LECTURE 3:ACCOUNTING CONCEPTS
• Managerial accounting
• Financial Statements
• Fundamental equation of accounting
• Balance Sheets
• Debits and Credits
• Measurement Focus and recording basic
transactions
• Operating and Cash Flow Statements
(Introduction)

Managerial and Financial
Accounting
• Managerial Accounting: Internal Focus
– Planning
– Implementation
– Control
• Financial Accounting
– Record events or transactions
– Report financial position and results of
operations

The Financial Statements
• Balance Sheet: A snapshot of the resources,
obligations and worth of an organization at
a specific point in time. (Stock)
• Income Statement: Measures the cumulative
resource inflows for an organization over
some specified period of time. It is the
reporting equivalent of an operating budget.
(Flows)

• Cash Flow statement: measures the
cumulative cash inflows and outflows for an
organization over some specified period of
time. It is the reporting equivalent of a cash
budget. (Flow)
The Financial Statements

Financial Statement Concepts
• Generally Accepted Accounting Principles from
FASB (non-profits and healthcare) or GASB
(governments)
• Entity: The organizational component that the
accounting seeks to describe
• Objective evidence: Values must be based on an
objective valuation of resources
• Cost convention: Cost is used when value is in
dispute, or not reasonable to obtain

Financial Statement Concepts
• Conservatism: Anticipate entity losses, but not
gains
• Going concern: Assumption that organization will
continue in operation
– Bankruptcy value is typically much lower
• Materiality: Report detail only to the level
necessary for decision-making.
• Accrual concept: Revenues are recorded when the
organization entitled to them and expenses when
resources are used

Assets
• Anything of value owned by the accounting
entity
• (Alternative definition:) Anything that the
entity owns that will better enable it to meet
its mission
• Generally, assets are any valuable resources
owned by the organization

Assets
• Identifying Assets: Easiest when items have clear
market value and physicality
– Automobiles
– Respirators
– Artwork
• Identifying Assets: Harder when assets are less
corporeal
– Taxes owed -Insurance
– Bequests stated -Good will

Assets
• Key: An organization’s assets may be worth
more than the balance sheet suggests
• The typical reason for this is that certain
assets exits that are not readily measurable,
or for which no exchange transaction exits
to help identify its value.

Liabilities
• Obligations to other entities
– Obligations to other funds (government)
• Each time an event happens that causes an
entity to owe money to another, a liability
has been created
– Supplies ordered
– Staff hours worked

Liabilities
• Money owed
• Collateral: some security (asset) pledged
against the money owed
– If the borrower defaults, the collateral becomes
the property of the lender
• Accounts payable: List of money owed
– A/P is an balance sheet account, recorded on
the liability side of the balance sheet

Equity
• Where did the capital come from to acquire
the assets?
– Borrowing (liability)
– Value of owner shares (equity)
• What would be left if all of the assets of the
entity were sold off to pay liabilities?
– The difference between assets and liabilities is
equity (or, net assets or fund balance)

Equity=Net Assets=Fund Balance
• Equity: Value of owners shares in a for-
profit corporation
• Net assets: The difference between assets
and liabilities in a not-for-profit corporation
• Fund balance: The difference between
assets and liabilities in a government (fund)
• Note: These are the same concept with
different labels!

Fundamental Equation
ASSETS = LIABILITIES+EQUITY
ASSETS= LIABILITIES+ NET ASSETS
ASSETS=LIABILITIES+FUND BALANCE

Fundamental Equation
• The fundamental equation of accounting is
always in balance.
• Each transaction that affects a balance sheet
account must be exactly offset by another
that equals it on the opposite side of the
balance sheet
• That’s why it’s called a balance sheet!

Balance Sheet
ASSETS
LIABILITIES+
NET ASSETS
=

Balance Sheet
Sample U.S. Corporation Balance Sheet
Assets Liabilities + Equity
Current Assets $11,000 Current Liabilities$5,000
Fixed Assets $9,000 Long Term Debt $10,000
Equity $5,000
Total$20,000 $20,000

Balance Sheet
Sample Local Government Balance Sheet
Assets Liabilities + Fund Balance
Current Assets $11,000 Current Liabilities$5,000
Fixed Assets $9,000 Long Term Debt $10,000
Fund Balance $5,000
Total$20,000 $20,000

Balance Sheet Elements
• Asset subgroups (listed in order of liquidity)
– Current Assets (Assets in cash or equivalents, or will be
within one year)
• Cash
• Marketable securities
• Money markets
• Current Receivables
– Note: classification may depend on the entity’s
intentions

• Asset subgroups (listed in order of liquidity)
– Long term assets (greater than one year)
• Fixed Assets (property, plant, equipment)
• Investments (Stocks, bonds, other financial
ownership interests)

• Liability subgroups
– Current Liabilities (Obligations presently due,
or due within one year)
• Notes payable
• Letters of credit payable
• Accrued payroll (wages) payable
• Accounts payable

• Liability subgroups
– Long-term Liabilities (Obligations payable
across more than one year)
• Long term debt
– Leases -Secured/unsecured loans
– Bonds payable

Asset Groups
• Cash and cash equivalents
• Accounts receivable
• Inventory
• Prepaid Expenses
• Fixed Assets
– less depreciation
• Sinking funds

Balance Sheet Concepts
• Current refers to the next twelve months
– Also: short-term, near-term
• Long-term refers to time periods longer than
twelve months
• Current assets and current liabilities are
highlighted on the balance sheet to allow readers
to determine if the organization is likely to have
the resources needed to pay its near-term
obligations

Liability Groups
• Accounts/Wages payable
• Long-term debt
• Secured and unsecured loans
• Bonds payable

Marketable Securities
• Marketable securities include equity and debt
instruments than can be bought and sold in public
and private markets
• The values of marketable securities are reported
by governments and not-for-profit organizations at
fair market value. For profit organizations use fair
market value for reporting most of their
marketable securities.

Long-Term Assets
• Long Term Assets are generally divided into three
categories
– Fixed Assets
• property (land) usually recorded at cost
• plant (buildings) recorded at cost and reported at net book
value
• equipment recorded at cost and reported at net book value
– Investments
– Intangibles

Plant and Equipment
• Recorded at cost when acquired
• Reported net of accumulated depreciation
on the balance sheet
• Example: Feed-A-Fish buys a van for
$30,000 and expects to use it for 5 years
and sell it for $5,000. At what value would
it appear on the balance sheet after two
years?
[(30,000-5,000)/5]*2=$10,000 depreciation
$30,000 - $10,000 = $20,000

Fixed Assets on the Balance
Sheet
•Note: show cost, accumulated depreciation and net
book value
Museum A Museum B
Net Fixed Assets $1,000,000 $1,000,000
PP&E at Cost $40,000,000 $2,000,000
Accumulated Depreciation ($39,000,000) ($1,000,000)
Net Book Value $1,000,000 $1,000,000

Recognizing Asset Transactions
• Financial events are recorded at the time of recognition
• Asset transactions are recognized when
– they are owned by the organization
– they have a monetary value
– that monetary value can be objectively determined
• Which of the following should be recognized as assets?
– The amount due on a bill sent to an insurance company
– an overhead projector
– a fundraising mailing list of organization donors

Short term liabilities
• Short-term liabilities typically include
– payables due within thirty days
• wages payable
• accounts payable
• notes payable
– the current portion of long-term debt (that due
within the coming year)

Long term liabilities
• Long term liabilities include:
– Long term debt
• Capital leases
• Long-term unsecured loans
• Mortgages
• Bonds payable
– Pension liabilities
– Contingent liabilities

Recognizing liability transactions
• Liabilities are recognized when
– they are legally owed
– have to be paid
– the amount to be paid can be objectively measured
• Which of the following should be recognized as a
liability
– a bill received from a vendor
– wages that are due to a worker
– a $5 million lawsuit filed against an organization

Amortizing Long term debt
• $25,000 of the $32,000 Feed-A-Fish van is
financed for five years at 8% interest. The
loan calls for annual payments of $6261.
– How much of each year’s payments would be
interest?
Beginning
Balance
Total
Payment
Interest
Portion Principal
Ending
Balance
Year 1 $25,000 $6,261 $2,000 $4,261 $20,739
Year 2 $20,739 $6,261 $1,659 $4,602 $16,136
Year 3 $16,136 $6,261 $1,291 $4,971 $11,166
Year 4 $11,166 $6,261 $893 $5,368 $5,798
Year 5 $5,798 $6,261 $464 $5,798 $0

Net Asset Categories
• The net worth of an organization represents the sum of
the organization’s earnings from inception plus any paid-
in capital (for-profit firms) less any payments that have
been made to owners (e.g. dividends)
• Net Assets
– Unrestricted Net assets (cumulative profits appear here)
– Temporarily restricted net assets (use restricted by donors)
– Permanently restricted net assets (restricted in perpetuity)

Assets Liabilities
Short TermAssets Short TermLiabilities
Cash 514 Accounts Payable 5250
Accounts Receivable 15325 Wages Payable 0
Inventory 950 Long TermLiabilities
Total Short TermAssets 16789 Mortgages 28000
Total Liabilities 33250
Long TermAssets
Buildings 114000 Net Assets
(Less Depreciation) 77600 Unrestricted 9339
Buildings (Net) 36400 Temporarily restricted 600
Permanently restricted 10000
Total Net Assets 19939
Total Assets 53189 Total Liabilities+ 53189
Net Assets
Make-A-Wish Foundation
Balance Sheet
31-Jan

Generating a Balance Sheet
• Generating a balance sheet involves:
– Beginning with the starting balance sheet
– Recording all of the transactions for the period
– Adding the impact of the transactions to the
starting balance sheet
– Formatting the resulting balance sheet accounts
in the balance sheet reporting format

Recognition
• In accordance with GAAP, one must first
record all financial events
– Liabilities are recognized (accrual) when they
are legally owed and will have to be paid
• Once the amount to be paid can be objectively
measured
• E.G. Once an employee has worked a shift, the
amount to be paid should be recorded as a liability.

Recognition
• In accordance with GAAP, one must first
record all financial events
– Assets are recorded (recognized) when:
• Owned by the entity
• Have monetary value
• Monetary value can be objectively measured

The truth about debits and credits
Debits and credits have no implicit
meaning. They were designed as a
convention in recording movements of
financial resources. In that system debits are
recorded on the left hand side of a ledger
and credits on the right.

Debit Credit
Every entry made in an
bookkeeping system has a
debit and a credit.
The basic tool for examining
these entries is the ‘T’
account.

Different kinds of
financial activity is
recorded on different
sides of the T account,
based on the
fundamental
accounting equation.
Account Increases Decreases
Asset Debit Credit
Liability Credit Debit
Equity/NA Credit Debit
Revenue Credit Debit
Expenditure Debit Credit

Date Account Debit Credit
1/12/02 Office Equipment 24000
Accounts Payable 24000
2/1/02 Accounts Payable 24000
Cash 24000

2/1/02 Prepaid Insurance 12000
Cash 12000
2/1/02 Insurance expense 1000
Prepaid Insurance 1000

The bookkeeping process
1. Each financial event (transaction) is recorded in
the (General) journal in chronological order.
2. Adjusting entries are made to record corrections
and non-transaction changes (depreciation,
consumption, corrections).
3. Periodically (monthly), entries from the journal
are posted to the ledger by account category.
4. Reports are generated based on these records of
financial events (Balance sheet, revenue and
expense)

Accounting Terms
• Expense: Consumption of an asset
• Expenditure: Reduction in cash (or increase
in a liability) associated with asset
acquisition
• GASB: Government Accounting Standards
Board
• FASB: Financial Accounting Standards
Board

Accounting Terms
• Chart of Accounts: Standardized list of
categories in which to classify and
document financial events
• Journal: Document for recording the
financial events of an entity as they occur in
time
• Ledger: Document for recording financial
events as they affect a particular account

Measurement Focus
• Flow of current financial resources
– Reports only current assets
– Goal is to report whether the fund is better off
financially
– Reports revenues and expenditures
– Capital outlays recorded as expenditures
– Principal payments: reductions in asset (cash)
– Depreciation is not recorded

Measurement Focus
• Flow of economic resources
– Reports all assets and all liabilities
– Goal is to report whether a fund is better or worse off
economically
– Reports revenues and expenses
– Capital outlays recorded as creation of a fixed asset in
exchange for another asset (cash)
– Principal payments: reductions in an asset and a
liability
– Depreciation is recorded as the asset is consumed

Basis of Accounting
• Accrual
– Used by business firms, proprietary funds,
nonexpendable trust funds and pension trust funds
– Used when funds measure the flow of economic
resources
– Reports revenues and expenses
– Revenues are recognized when services provided
– Expenses recorded when benefit produced is received,
regardless of when payment occurs.

Basis of Accounting
• Modified Accrual
– Used by governmental funds and expendable trust
funds
– Used when funds measure the flow of financial
resources
– Funds report revenues and expenditures
– Revenues are increases in current financial resources
– Revenues recognized when measurable and available
– Expenditures (not expenses) are recognized when a
transaction can be measured

Balance Sheet Transactions
(Journal Entries)
• The Feed-a-Fish foundation purchases two large
tropical fish tanks at $3,500 each.
Assets = Liabilities +Net Assets
Accounts Payable
$7,000 (CR)
Equipment
$7,000 (DB)

(Journal Entries)
• The Feed-a-Fish foundation purchases an $800
supply of rodents as food for the fish.
Inventory
$800 (DB)
Cash
$800 (CR)

(Journal Entries)
• The Feed-a-Fish foundation purchases two large
tropical fish tanks at $3,500 each. They pay
$3,000 in cash.
Accounts Payable
$4,000 (CR)
Equipment
$7,000 (DB)
Cash
$3,000 (CR)

Journal  Ledger
• Journal entries document each financial
transaction
• Over a month many thousands of transactions
accumulate
• How can this information be presented in a form
that managers find useful?
– Post all journal transactions into account ledgers
– Generate a balance sheet

Assets Liabilities
Long TermAssets
Buildings 114000
(Less Depreciation) 78600 Net Assets
Buildings (Net) 35400 Net Assets 28775
Net Assets
Balance Sheet
31-Dec
Feed-A-Fish Foundation

General Journal
Date Description Account Debit Credit
1-Jan Pay Rent Rental Expense 1200
Cash 1200
1-Jan Pay Electric Utilities Expense 136
Cash 136
6-Jan Buy Fishtanks Equipment 7000
Cash 3000
10-Jan Buy Rodents Inventory 800
12-Jan Staff Wages Wages Expense 1500
Wages Payable 1500
15-Jan Payroll Wages Payable 1500
Cash 1500

General Ledger
Cash
Debit Credit
31-Dec Balance 6350
1-Jan Pay Rent 1200
1-Jan Pay Electric 136
6-Jan Buy Fishtanks 3000
15-Jan Payroll 1500
31-Jan Balance 514

General Ledger
Accounts Payable
Debit Credit
31-Dec Balance 450
6-Jan Buy Fishtanks 4000
10-Jan Buy Rodents 800
31-Jan Balance 5250

General Ledger
Wages Payable
Debit Credit
31-Dec Balance 0
12-Jan Wages Earned 1500
15-Jan Payroll 1500
31-Jan Balance 0

Assets Liabilities
Long TermAssets
Buildings 114000
(Less Depreciation) 77600 Net Assets
Buildings (Net) 36400 Net Assets 19939
Net Assets
Balance Sheet
31-Jan

Journal  Ledger
Cash 100
Cash 2000
2/12/02 Inventory 3000
2/16/02 Cash 12000
Accounts Receivable 12000
General Journal
Date Activity/ Event Debit Credit
2/1/02 Opening Balance 52000
2/1/02 Pay insurance 100
2/10/02 Pay for supplies 2000
2/16/02 Collect revenue 12000
2/28/02 Ending Balance 61900
Ledger Account: Cash

Journal  Ledger
Cash 100
Cash 2000
2/16/02 Cash 12000
General Journal
Date Item/event Debit Credit
2/10/02 Pay fire insurance 2000
2/12/02 Buy Inventory 3000
Ledger Account: Accounts Payable

Journal  Ledger
Cash 100
Cash 2000
2/16/02 Cash 12000
General Journal
2/12/02 Buy Inventory 3000
2/1/02 Buy Fire Insurance 100
Ledger Account: Prepaid Insurance
Ledger Account: Inventory

A Non Transaction
• HOS signs a binding contract to buy and X-ray
machine that will cost $50,000
• The event will not give rise to a journal entry
because it does not meet the rules for recognition!
– The value of the transaction is known
– The timing of the transaction is known
– But HOS does not yet own the equipment (there has
been no exchange!)

A Non Transaction?
• The Town of Madison signs a binding contract to
buy a copier that will cost $50,000
• This event will give rise to a journal entry because
it meets the rules of recognition for a government
entity
– The value of the transaction is known
– The funds have been obligated (encumbered)

A Non Transaction
• The Town Manager of Madison decides to
renovate the planning department offices. She has
budgeted $15,000 for the renovation.
• This event will not give rise to a journal entry
because it fails to meet the rules of recognition for
a government entity
– The value of the transactions are not yet known
– The timing of the transaction is not known
– The funds have not been obligated (encumbered)

A Non Transaction?
• The Town Manager of Madison decides to
renovate the planning department offices. She
signs a purchase order for $5,000 of painting
services next month.
• This event will give rise to a journal entry because
it meets the rules of recognition for a government
entity
– The value of the transactions is known
– The funds have been obligated (encumbered)

Cash Flow Production Cycle
Cash
Accounts
Receivables
Inventory
Fixed Assets
Equity &
Liabilities
Collection of
Receivables
Cash
Sales
Credit
Sales
Production
Investment
Interest, Taxes
& Dividends
Source: Higgins (1998)
Depreciation

D Cash + D in All Other Assets = D in Liabilities + D in Net Assets
OR
D Cash = D in Liabilities + D in Net Assets - D in All Other Assets
OR
D Cash = D in Liabilities + (Rev-Expenses) + D in Other Net Assets -
D in All Other Assets
SO
We are seeking to show the route to (end of period) cash as affected
by changes in net income, assets, liabilities and net assets.
Understanding the Cash Flow
Statement

Statement
• Indirect Method
– Uses Net Income and Non-Cash transactions, and
Operating Cash transactions to adjust cash balance
– Less Transparent in reporting cash activity
– May be easily calculated from other financial
statements

Statement of Cash Flows
Indirect Method
• Start with Net Income from Op Statement
• Adjust cash flows for each non-cash balance sheet
transaction
– Add decreases in assets
– Subtract increases in assets
– Add increases in liabilities
– Subtract decreases in liabilities
• Add Non-cash expenses
• Adjust for flows from investing/financing

Statement
• Direct Method
– Uses Cash Transactions alone to adjust cash
– More transparent (better reflects cash activities)
– Requires information from ledgers

LECTURE 4: OPERATING AND CASH FLOW
STATEMENTS
• More balance sheet concepts
• Operating Statements
– Recognizing expenses
– Recording revenues
• Analyzing the operating statement
• Depreciation
• Where the income statement and balance
sheet meet
• Statement of Cash Flows

The operating and cash flow
statements
• Operating Statement
– compares an entity’s cumulative revenue and support to its
expenses for any period of time -like a fiscal year.
– Shows whether the organization was able to cover its costs
• Names for an operating statement: Income statements,
Activity Statement, Statement of revenues and expenses,
P&L
• The Cash Flow statement looks at where an entity obtained
its cash and where it spent cash during some period of time

Operating Statement
• Revenues and Support
– represent inflows that the organization has received or
is entitled to receive
– result in an inflow of assets to the organization and an
increase in net assets
• Revenues are generally the result of an exchange
for goods and services that the organization has
provided
• Support is the result of gifts, grants and other
contributions to the organization

Operating Statement
• Expenses
– represent the recognition of the use of an asset to
generate revenue and support or otherwise carry on the
operations of the entity
– result in an outflow of assets and a decrease in net
assets
• Net Income (difference between revenues and
expenses)
– Profits are an excess of revenues over expenses. Also
called a surplus or excess revenues over expenses
– Losses are an excess of expenses over revenues. Also
called a deficit.

Recognizing Revenue and
Support
• Revenue is recognized if:
– the goods or services have been provided to the
customer
– the amount owed can be objectively measured
– there is a reasonable likelihood of collection
• Support is recognized if
– all of the conditions of the gift have been met
– the value of the pledge can be objectively
measured
– there is a reasonable likelihood of collection

Operations and the Balance Sheet
• At the end of the accounting period, the
total Revenues-Expenditures is used to
adjust net assets
– Only changes, or their effects, show on BS
Net Assets (11/30) 950
Net Assets - Revenue 1500
Net Assets - Expenses 1400
Changes in Net Assets 100
Net Assets (12/31) 1050

Recognizing Expenses
• Expense Recognition depends on the type of
expense
– Product costs are those directly connected to providing
goods and services. They are recognized:
• based on the matching principle which holds that expenses
should be recorded in the same period as the revenue they were
used to generate
– Period costs (like rent) are those related to the passage
of time. They are recognized:
• in the time period when they are incurred

Expired and Unexpired Costs
• Suppose Meals for the Homeless bought 100 canned hams
at a cost of $1,000 in March
– At acquisition, Meals would recognize the hams as an asset
(inventory). They are also an unexpired cost.
– If they paid for the hams in cash, cash would decrease by $1,000
• In May, meals used 50 of the hams to produce meals.
– At use, the hams become an expense (expired cost) of $500 and the
value of the asset (inventory) is reduced by $500.

Classifying Revenues and
Expenses
• Revenues and support may be classified and reported based
on:
– nature (gift, grant etc.)
– source( government, foundation, patients)
– organizational unit (University, College, School)
• Expenses may be classified and reported based on:
– nature or object of expense (salaries, supplies, rent)
– function (provide housing, meals, medical care)
– organizational unit (opera, ballet, theatre)
• Why is it useful to be able to report on these different
bases?

2000 1999
Revenues and Support
Meals
Client Revenue $10,000 $8,000
County Revenue 20000 16000
Shelter Counseling
Client Revenue 1000 1000
County Revenue 10000 10000
Fundraising
Foundation Grants 70000 50000
Annual Ball 12000 11000
Telephone Solicitation 25000 28000
Mail Solicitation
Direct Mail Campaign 48000 45000
Total Revenues and Support $196,000 $169,000
Expenses
Food $17,000 $16,000
Kitchen Staff 35000 33000
Counseling Staff 35000 34000
Rent on Kitchen Locations 15000 14000
Administration and General 75000 65000
Bad Debts 4000 4000
Depreciation 10000 10000
Total Expenses $191,000 $176,000
$5,000 ($7,000)
Excess of Revenues and Support
over Expenses
Meals for the Homeless
Activity Statement

Analyzing the Operating
Statement
• Why are two years of statements shown?
• Administrative and General expenses rose by
$10,000. What is included? Should Meals’ board
be concerned about the increase?
• Meals’ clients only paid the organization $11,000
for meals and counseling this year. Operating and
Administrative expenses were $191,000. Can the
organization survive?
• What other items deserve further analysis?

• Bad debt expense represents the portion of the
revenues earned for that period of time that is
unlikely to be collected
– Reflects bad debts from a period of payables
accumulation
• Allowance for uncollectable accounts is the
portion of receivables not expected to be collected
– Reflects the sum of unlikely receivables at a moment in
time
Uncollectable Accounts
(Bad Debts)

(Bad Debts)
Balance Sheet
(fragment)
Assets
Current Assets
Pledges Receivable $13,000
Allowance for Uncollectable Pledges -$4,000
Pledges Receivable, Net $9,000
Contra
Account

1998
Debit Credit
03/08/98 Pledges Receivable $50,000
Pledge Revenue $50,000
03/08/98 Bad Debt Expense $4,000
Allowance for Uncollectable Pledges $4,000
05/25/98 Cash $32,000
Balance Sheet for 12/31/98
(fragment)
Assets
Current Assets

1999
2/5/1999 Pledges Receivable $50,000
Pledge Revenue $50,000
2/5/1999 Bad Debt Expense $4,000
Allowance for Uncollectable Pledges $4,000
5/15/1999 Cash $5,000
Balance Sheet
(fragment)
Assets
Current Assets

Charlie Smith Dies
6/1/1999 Allowance for Uncollectable Pledges $500
Pledges Receivable $500
Balance Sheet after adjusting entry
(fragment)
Assets
Current Assets

• Assume that Meals begins the year with $125,000 in
pledges receivable, and $15,000 in the allowance for
uncollectable pledges contra account.
• During the year $50,000 of new pledges are made, but
cash is not received. Experience shows 10% of pledges
are never collected.
• During the following year it is decided that specific
pledges totaling $3,000 will never be collected

Balance Sheet
(fragments)
Assets
Pledges Receivable 125000
Allowance for Uncollectable debts (15000)
Debit Credit Pledges Receivable, Net 110000
Cash 50000 Assets
Pledges Receivable 50000 Pledges Receivable 175000
Pledge Revenue 100000 Allowance for Uncollectable debts (15000)
Pledges Receivable, Net 160000
Note: Record pledges

Bad Debt Expense 5000 Assets
Allowance for Uncollectable Debts 5000 Pledges Receivable 175000
Note: Estimated Uncollectable debt Pledges Receivable, Net 155000

Allowance for Uncollectable Debts 3000 Assets
Pledges Receivable 3000 Pledges Receivable 172000
Note: Write off Uncollectable debt Pledges Receivable, Net 155000

Depreciation Expense
• Depreciation expense represents the current
periods’ share of the cost of using a capital
asset over its life
– This illustrates the matching principle (HOW?)
– Depreciation expense may be calculated either
on a straight-line or an accelerated bases. Why
would you want to use accelerated
depreciation?

Straight Line Depreciation
Example
• Cost of a van $32,000
Less Salvage (Residual) value 2,000
Depreciable amount $30,000
(Divide across useful life) five years
Depreciation expense/year $6,000

Sum of Years Digits
Depreciation
• Calculates the sum of the digits in the years of the
life of the asset.
• Subtracts salvage value first
• The sum simply consists of adding from 1 to the
last year of the asset’s life (inclusive)
– An asset with a six year life would have a depreciation
denominator of 21
• 1+2+3+4+5+6 = 21
– First year’s depreciation = residual value * 1/21

Sum of Years Digits
Depreciation Example
Less Salvage (Residual) value 2,000
Depreciable amount $30,000
Sum of Years Digits (1+2+3+4+5) = 15
First year depr. at 5/15 $10,000
Second year depr. at 4/15 $8,000
Third year depr. at 3/15 $6,000
Fourth year depr. at 2/15 $4,000
Fifth year depr. at 1/15 $2,000

Double Declining Balance
Depreciation
• Starts with a depreciable base EQUAL to the total
asset cost
– Ignore salvage value when determining annual amount
of depreciation
• The cost is multiplied by double the straight line
ratio
• Does not shorten the asset life!
– Each year the previous year’s depreciation is
subtracted from the existing depreciable base to get a
new depreciable base
– Last year’s depreciation expense=salvage value minus
the depreciable base at that point

Double Declining Balance
Depreciation Example
Ignores Salvage value 0
Depreciable base $32,000
First year depr. At 2/5 -$12,800
Second year depr. At 2/5 -$7,680
Third year depr. At 2/5 -$4,608
Fourth year depr. At 2/5 -$2,765
Fifth year depr. (balance) -$2,147*

Cost $2,400 $2,400 $2,400
Base $2,100 $2,400 $2,100
Term 6 Years 6 Years 6 Years
Salvage
Value 300 300 300
Depreciation
Depreciation
Ratio
Residual
Value Depreciation
Depreciation
Ratio
Residual
Value Depreciation
Depreciation
Ratio
Residual
Value
Year 1 $350 1/6 $2,050 $800 2/6 $1,600 $600 6/21 $1,800
Year 2 $350 1/6 $1,700 $533 2/6 $1,067 $500 5/21 $1,300
Year 3 $350 1/6 $1,350 $356 2/6 $711 $400 4/21 $900
Year 4 $350 1/6 $1,000 $237 2/6 $474 $300 3/21 $600
Year 5 $350 1/6 $650 $158 2/6 $316 $200 2/21 $400
Year 6 $350 1/6 $300 $16 2/6 $300 $100 1/21 $300
Total
Deprecia
tion $2,100 $2,100 $2,100
DEPRECIATION METHODOLOGIES
Straight Line Double Declining Balance Sum of Years Digits

Inventory Expense
• Inventory expenses represent the cost of
using supplies to operate an organization.
Inventory expense and the ending inventory
value are calculated using the following
relationship
Beginning inventory + purchases
– Consumption = Ending Inventory

Inventory Systems
• Periodic
– Inventory is ‘taken’ (counted) annually or semiannually
and accounting adjustments are made accordingly
– Difficult to make informed ordering decisions
– Not suitable for inventory based enterprises (where
inventory is a significant input in service production,
e.g. hospitals, clinics, print shops)
– Inexpensive method
– Poor as a control system

Inventory Systems
• Perpetual
– Each use of inventory is recorded as it occurs
– Items removed for reasons other than sale are
recorded as they occur
– Perpetual systems can be very costly
(technology, labor)
– Good for control systems

Perpetual Inventory Systems
• Economic Order Quantity
– Tracks system wide variables
• Shelf space
• Storage costs
• Account activity
• Historical levels of inventory
• Carrying costs
• Ordering costs
– Executes orders automatically when system
variables combine to indicate optimal time

Perpetual Inventory Systems
• Just-in-Time Inventory
– Focused on minimizing carrying costs
– Contracts with vendors specify precise hour of
delivery
– Eliminates need for most warehousing
– Mostly applied in manufacturing/ repetitive
industries
– Input prices may bear a premium from JIT
requirement

FIFO and LIFO
Inventory
Method
Beginning
Balance Purchases
Consumption
(Inventory
Expense)
Ending
Balance
LIFO $20,000 $45,000
3000*$15
=$45,000 $20,000
FIFO $20,000 $45,000
2,000*$10+1,000*
$15=$35000 $30,000
NY City’s subway system started the year with 2,000 railroad ties that
cost $10 each and bought 3,000 more during the year for $15 each. If
they had 2,000 left at the end of the year, what was their inventory
expense and how much was the remaining inventory worth?

Deferred Revenue
• Deferred revenue arises when an organization is
paid in advance for goods or services
– Why is this a liability?
• A museum sells a five year membership for $250.
– How much of the $250 should be recorded as deferred
revenue?
– How much of the $250 would the museum recognize as
revenue during the first year of the membership?

Deferred Revenue
• Deferred revenue arises when an organization is
paid in advance for goods or services
– Why is this a liability?
• A museum sells a five year membership for $250.
– How much of the $250 should be recorded as deferred
revenue? $200
– How much of the $250 would the museum recognize as
revenue during the first year of the membership? $50

A mixed Balance Sheet and
Operating Statement Transaction
• HOS paid $48000 in wages. $30,000 for
money owed to employees for work performed
last year and $18,000 for this year’s work.
Debit Credit
Labor Expense 18000
Wages Payable 30000
Cash 48000

A mixed Balance Sheet and
Operating Statement Transaction
• HOS paid $48000 in wages. $30,000 for
money owed to employees for work performed
last year and $18,000 for this year’s work.
Assets= Liabilities + Revenues- Expenses
-Cash = -wages pybl +no change -labor expense
-$48000= -30000 -18000

(2) Operating Statement Transaction(s)
• HOS provided services and billed patients
$81,000. It consumed $4,000 worth of
inventory to deliver the services.
Debit Credit
Revenue 81000
Debit Credit
Supplies Expense 4000
Inventory 4000

A Non-Cash Transaction
• HOS owed its staff $27,000 for wages for
the last two weeks of the year which were
not due until the first week of the new year.
Debit Credit
Wages Payable 27000
Wages Expense 27000

Where Income Statement and
Balance Sheet Meet
Event Statement Impact Note
Revenue
Recognized
You provide
a service and
earn revenue.
AR or Cash 
Revenue 
BS
IS
AR is a 'holding
area' for unpaid bills
you have sent out.
No impact
on revenue
Someone
pays a bill
you sent
AR 
Cash 
BS
BS
No impact
on expenses
You purchase
Something
AR 
Inventory 
BS
BS
AP is where you
keep track of what
you owe to others.
Expense
Recognized
When you
use
something
Asset  (or)
Liability 
Expense 
BS
BS
IS

Reflecting Net Income on the
Balance Sheet
• Net income is reported as a change in net
assets on the balance sheet
Total Revenue/Support $81,000
Total Expenses ($80,050)
Net Income $950
Unrestricted Temp. Rest. Perm. Rest.
Beginning Balances $113,000 $15,000 $10,000
Changes in Net Assets $950
Ending Balance $113,950 $15,000 $10,000

The Cash Flow Statement
• The Statement of Cash Flows focuses on the
sources and uses of cash for the
organization. It divides those cash flows
into:
– Cash flows from operations
– Cash flows from investing
– Cash flows from financing

The Cash Flow Statement
• The first approximation of cash flow is net
income. Why isn’t this adequate?
• The first adjustment is for “Expenses not
requiring cash” (e.g. depreciation,
amortization, depletion)
• The remainder of the adjustments to
operating cash flow are for changes in
balance sheet accounts related to operations

Cash Flows fromOperating Activities 2000 1999
Net Income $5,000 ($7,000)
Add Expenses Not Requiring Cash:
Depreciation $10,000 $10,000
Other Adjustments:
Add Decrease in Inventory $2,000 $2,000
Add Increase in Notes Payable $1,000 $3,000
Subtract Increase in Receivables ($17,000) ($12,000)
Subtract Decrease in Wages Payable ($1,000) $0
Subtract Decrease in Accounts Payable ($1,000) ($2,000)
Subtract Increase in Prepaid Expenses ($1,000) $0
Net Cash used for Operating Activities ($2,000) ($6,000)

Cash Flows fromInvesting Activities
Sale of Stock and Investments $4,000 $5,000
Purchase of Delivery Van ($32,000)
Net Cash fromInvesting Activities $4,000 ($27,000)
Cash Flows fromFinancing Activities
Increase in Mortgages $25,000
Repayments of Mortgages ($5,000) ($4,000)
Net Cash fromFinancing Activities ($5,000) $21,000
Net Increase/(Decrease) in Cash ($3,000) ($12,000)
Cash, beginning of year $5,000 $17,000
Cash, End of year $2,000 $5,000

Analyzing the Cash Flow
Statement
• Meals bought a van for $32,000. What was the
probably source of funding?
• Meals’ net cash flow increased across the past
year. What are the major causes of this increase?
• The change in accounts receivable used $17,000 in
cash. Could this be the sign of a problem?
• Can Meals continue to operate in this fashion?

Cash Flow and the Balance Sheet
• Rules of thumb:
– Asset increases consume cash
– Asset decreases provide cash
– Liability increases provide cash
– Liability decreases consume cash

LECTURE 5: CASH MANAGEMENT
MANAGING SHORT TERM RESOURCES/OBLIGATIONS
• Working Capital
• Short term Obligations (Current Liabilities)
– Accounts Payable
• Short term Resources
• Cash Management
• Accounts Receivable
• Inventory
– Economic Order Quantity

Working Capital Management
• Working capital management focuses on
making sure that the organization has the
resources it needs to operate during the
current year. It is a continuous process!

Working Capital Management
• Net Working Capital is defined as the difference
between the resources that an organization can use to
provide goods and services over the next year (Short-
Term Assets) less what will have to be paid to other
organizations and individuals over the coming year
(Short-term liabilities)
Net Working Capital=Current Assets
-Current Liabilities

Short Term Obligations
• Accounts Payable
• Payroll Payable
• Notes Payable
• Taxes Payable
• Remittances/Transfers pending

Current Liabilities
• Short-term payables
– Amounts owed by the organization that have not
yet been paid. Specific “payables” accounts can be
set up for any general category of creditors

Current Liabilities
• Short-term payables
– Accounts Payable- for goods and services
– Payroll/wages payable- for salaries and benefits
due to employees
– Interest payable- for amounts due on loans
– Taxes payable- for tax obligations that have not
yet been paid

Calculating Short Term Interest
• Interest=loan amount (principal) * Annual
interest rate*fraction of year
• Example: HOS borrows $1m at an annual
interest rate of 5.5$% for 45 days. How much
interest will they have to pay?
$1,000,000*.055*.123288 (45/365=.123288)
=$6,780.82

Payroll Deferral
• The choice of when to make payroll
distributions can seriously affect cash
position and interest earnings
• Example: The Town of Toxic Dales is
considering changing from a weekly to
monthly payroll. Payroll is $24m per year
and the interest cost is 8% per year. How
much would they save through change?

Payroll Deferral
Each Month
Length of
Deferral Portion
of Year in
Weeks
Amount
Deferred
Interest @
8% per
year
Week 1 3/52 $500,000 $2,308
Week 2 2/52 $500,000 $1,538
Week 3 1/52 $500,000 $769
Week 4 - $0 $0
Monthly Total $4,615
Annual Savings= $4,615 * 12 = $55,384.62

Accounts Payable
• Strategies for A/P cost savings
– Take advantage of pre-payment discounts that
pass a cost/benefit test
– Manage payroll to maximize expense to
payment period, and float
– Establish electronic transfers to submit payroll
taxes and withholdings
– Capture economies of scale with sole source
vendors (selected by bid)

Accepting a pre-payment discount
The city of Billious Hills receives a bill from
Billious Power and Light for $94,000 on the first
of March for services in February. The payment is
due on March 31st, and a late fee of $1410 will be
assessed if it does not arrive by April 7th. BP&L
indicates that Billious hills need only pay $93,365
if their payment is received by March 7th. Today
is March 7th. Should Billious Hills accept the
discount? If not, what should they do?

• Option A:
– Invest $94,000 for one month at k%
– Pay $94,000 and keep the investment earnings
• Investment earnings = m
• Option B:
– Pay $93,364 and invest $636 for perpetuity
– Decision depends on the value of k: What is a
reasonable return to expect on a one month investment?
• To accept the offer k must be large enough that m is greater
than $636 (plus one month of interest)

Option A Earnings FV Interest Option A Option B
FVof $94,000 at 2.00% for 1/12 of one year = $94,156.67 $156.67 $156.67 $637.06

Finding the discount rate
The decision about whether to take the discount or not depends upon what
the implicit interest rate is in the discount, and how that compares with prevailing rates.
To find the discount rate simply take the amount of the discount and divide it into the
undiscounted total:
Period Discount
Base
X # of Annual
Periods
100X
In our example:
636
94000
= .006766 X 12 = .08119 X 100 = 8.12
%
So, we only choose option A if the return on our investment will be at an annual
rate of at least 8.12%.

Short Term Resources
• Cash
• Accounts receivable
• Notes and agreements receivable
• Inventory
• Remittances/transfers pending

• Cash Resources
– Cash for transactions, investment and as a safety
margin
• Cash for daily operating transactions
• Short-term investments to provide income from idle cash
• Cash on hand for unanticipated events
– Managed by cash budgeting, cash management and
credit management (who to sell to on credit, whether to
give a discount)

Too much cash?
• Under what circumstances does an organization
have too much cash?
– When cash on hand is much greater than routine cash
flow needs
– When the opportunity cost of cash on hand exceeds
short term cash benefits
• E.g. long term investment rates typically exceed short term
rates
– When the organization is undercapitalized
• Response: Move cash to investments, or spend in
mission areas of the organization

• Accounts receivable: bills that have been
sent out by the organization but have not yet
been collected
– Managed through credit policies, collection
efforts and billing controls
– Aging schedules are a valuable management
tool

Short term cash management
strategies
• Interest bearing operating accounts
• Strategic use of ‘float’ and overnight
deposits
• Certificates of deposit
• Concentration banking
• Objective hierarchy: Legality, maintain
liquidity, minimize risk, maximize earnings
(yield)

• Inventory
– Supplies on hand for use in operations/
production
– Managed with periodic and perpetual control
systems

Short term investments
– Equities
• Shares
– Values fluctuate with market performance and anticipated
per-share earnings
– Non-Equities
• Bonds, notes, other debt instruments
– Values more inversely with market interest rates

Short term investments
• Certificates of Deposit
– Bank-held - FDIC Insured
– Non-negotiable - Fixed rate
• Money Market accounts
– Bank or fund held -Variable rate
– MM bank accounts are FDIC insured
• T-bills (three months to one year)
– Discounted to PV at prevailing interest rate
• Commercial paper
• Repurchase agreements

Repurchase Agreements
(REPOS)
• Short term collateralized securities
• Typical agreements last between 1-30 days
• Organization with idle cash provides it to
the borrower at an agreed-upon interest rate
– Borrower creates (and sells the lender) a money
market instrument and agrees to buy it back on
the specified date

Unsuitable investments
• Any leveraged securities
• Derivatives, in general
– Returns are not know in advance and risk can be higher
than average as a result
– not necessarily poor choices for larger and longer term
funds due to the ability to present a risk hedge
• Stocks
• Low quality bonds
• Personal notes

Accounts Receivable
• Strategies for A/R cost savings
– Offer only those pre-payment discounts that
pass a cost/benefit test
– Recapture the cost of extending credit through
bank cards
– Establish direct bank transfers with regular
customers
– Implement a collections protocol while tracking
aged accounts

Payer 1-30 Days 31-60 Days 61-90 Days 90+ Days Total
Medicare $4,400,000 $3,200,000 $2,000,000 $1,000,000 $10,600,000
Medicaid $3,800,000 $2,400,000 $1,500,000 $125,000 $7,825,000
SuddenDeath HMO $2,500,000 $1,300,000 $800,000 $450,000 $5,050,000
SlowDeath HMO $3,100,000 $800,000 $400,000 $0 $4,300,000
Blue Cross/Blue Shield $842,000 $419,000 $210,000 $49,000 $1,520,000
Self-Pay $2,000,000 $1,000,000 $750,000 $150,000 $3,900,000
Totals $16,642,000 $9,119,000 $5,660,000 $1,774,000 $33,195,000
Amounts by Percent
Medicare 41.51% 30.19% 18.87% 9.43% 100%
Medicaid 48.56% 30.67% 19.17% 1.60% 100%
SuddenDeath HMO 49.50% 25.74% 15.84% 8.91% 100%
SlowDeath HMO 72.09% 18.60% 9.30% 0.00% 100%
Blue Cross/Blue Shield 55.39% 27.57% 13.82% 3.22% 100%
Self-Pay 51.28% 25.64% 19.23% 3.85% 100%
Totals 50.13% 27.47% 17.05% 5.34% 100%
Carvaspleen Hospital
Accounts Receivable
Aging Schedule

Accounts Receivable
• Billing
• Aging
• Lock Boxes
• Electronic payments

Inventory
• Supplies and items used to produces goods
and services
• Objective: Keep inventory at the lowest
level at which operations may continue
unimpeded
• Periodic systems (count and order annually)
• Perpetual systems ( count and order as
supplies are consumed)

Economic Order Quantity
• Inventory costs include
– Cost of the items
– Cost of the space to store the items
– Cost of the insurance for the items on hand
– Costs of ordering and shipping items
• Problem: How much should be ordered,
how often and with how much on hand?
• Answer: Economic Order Quantity

Total Inventory Cost= Purchase Cost +
Carrying Cost
P=Price per unit
CC=Total Carrying costs
OC=Total ordering costs
N=Total number of annual units ordered
TC= (P*N) + CC + OC

• Whenever we order we will have some quantity of
inventory on hand between 0 and the maximum
quantity included in any inventory order
• Consequently, on average, at any given time, we
will have half of the order quantity on hand (all of
it at first, none of it at last)
• So, the average number of units on hand at any
given time = Q/2

CC= Carrying Cost= C* =
C=Annual carrying Cost for one unit per year
CC=Total Carrying costs for all units per year
• Note: CC is different when maintaining a
minimum stock (MS):
– The MS may be ignored when finding the EOQ
2
Q
2
CQ
MS
CQ

2

OC= Ordering Cost= O* =
O=Cost of completing one order
OC=Cost of placing one order (O) multiplied times the
number of orders placed per year
Q
N
Q
ON

• Example: Meals pays $2 per sack for rice
and each order costs $8.075 of labor cost
and $1 of delivery cost. The opportunity
cost of capital is 8% which adds $0.16 per
sack (8%*$2 =$0.16). Other carrying costs
are $3 per sack per year.
• What is the total cost of inventory, given 10
orders per year?

P*N=$2*2,000=$4000
CC=($3*200)/2 = $300
OC=($9.075*2000)/200=$90.75
TC= (P*N) + CC + OC, so
TC= $4000 + $300 + $90.75 = $4,390.75
Great, but what about EOQ???

So, in our example...
=110
C
ON
Q
2
* 
3$
2000*075.9$*2
*Q
What are the costs at this volume?

What are the carrying costs at this
volume?
2
CQ
CC 
165$
2
110*3


What are the ordering costs at this
volume?
Q
ON
OC 
110
2000*075.9$

= $165

The total costs are
= $4,330
TC= (P*N) + CC + OC
TC= $4000 + 165 +165
Which is less than the $4,390.75 when ordering 200

• Key: determining the carrying and ordering
costs
– These may be hard to measure precisely
– Labor costs are generally available
– How should the cost of storage be treated?
• Average or marginal cost?

POLS 7830
PUBLIC FINANCIAL MANAGEMENT
LECTURE 6: FORECASTING REVENUES
AND EXPENDITURES

• Definitions
• Purposes
• Forecast Types
• Financial Forecasts
• Forecasting Problems
• Forecasting Methods
• Evaluating Forecast Accuracy
• Models of trends
LECTURE 6: FORECASTING REVENUES AND
EXPENDITURES

Forecasting
• “Any statement about the future”
• The methods used to predict outcomes
• Public sector applications
– benefit/cost analysis
– revenue forecasting
• forecasting tax and fee proceeds
• forecasting donations and service revenues
– cash flow forecasting
– expenditure forecastings
• forecasting demand/expenditure need
• forecasting factor/input prices

Purposes of Forecasting
• Process
• Prediction
• Control

Purposes of Forecasting
“ …a multi-year forecasting model
necessarily forces managers to lengthen
their time perspective by giving some
thought to what might be in store for a
jurisdiction a few years ahead…the forecast
can show managers and staff how their own
agencies fit into the overall scheme of
government, thus broadening their
perspective.” -Larry Schroeder

Process Forecasting
• Predicting important elements of repetitive
processes inside a public organization
– Cash flow analysis
– Revenue planning
– Expenditure tracking
– Transaction analysis

Process Forecast
• Purpose
– To anticipate the size or magnitude of recurring events
– To try to anticipate potential problems so that corrective
action can be taken
• Time Horizon
– Short to medium term (typically 2 years or less)
– Fixed forecast duration (e.g. monthly, quarterly,
annually)
• Frequency
– Repeated on a regular basis

Prediction Forecast
• Purpose
– Analyze likely impact of a policy or program to help in
its development and selection
• Time Horizon
– Medium to long term (2- 5 Years)
• Frequency
– Typically a one time analysis
• Example
– Projected benefit stream for CBA

Corn Price
0
200
400
600
800
1000
1200
1400
1850 1900 1950 2000
($)Price

Control Forecast
• Purpose
– Set objectives and goals
• Time horizon
– Any length
• Frequency
– Depends on planning function
• Content
– Follows goals statements and attaches them to
quantifiable measures of accomplishment
– Assigns projected values to potential outcomes

The Use of Forecasts
Type Use Characteristics Example
Process/
Projection
Extrapolation of
ongoing process
Recurring at fixed
intervals Cash flow forecasting
Fixed forecast
horizons
Revenue and expenditure
forecasting
Short to medium
term
Service demand
forecasting
Prediction Prediction of Policy oriented Policy analysis
events and/or Non-recurring Tax reform
influence of events Variable forecast Economic development
Medium to long Planning
term Macroeconomic forecasts
Control Evaluation Normative Service planning
Reflect goals and Setting service targets
objectives Performance audits
Political Influence

Financial Forecasts
• Expenditure Forecasts
• Revenue Forecasts
• Cash flow projections

Revenue Forecasting
• Forecast object: Tax, fee or sales revenue due to a
government or enterprise
• Forecast objective: Develop accurate, reliable,
(and methodologically transparent) judgement of
what revenues will be at a later point in time
– Revenue forecasts used in budgeting to identify
allocation base for future fiscal year(s)
– Revenue forecasts used by non-profit managers to make
decisions about demand and service levels

Expenditure Forecasting
• Forecast object: Classified government
expenditures for a future period
• Forecast objective: Improve planning and
budgeting ability by determining in advance the
likely costs of programs and services
– Heavily used in planning entitlement spending
– Used less in discretionary spending categories
• Political factors
• Incrementalism

Cash Flow Projection
• Start with reconciled cash balance at present
time
• List by date each anticipated increase
(debit) to cash
• List by date each anticipated decrease
(credit) to cash
• Strategize to cover deficits

3/1/1999 MDMH Revenue $39,218 $39,433
3/15/1999 Payroll $38,912 $521
3/29/1999 MDMH Revenue $39,218 $39,739
4/12/1999 Payroll $38,912 $827
4/26/1999 MDMH Revenue $39,218 $40,045
5/10/1999 Payroll $38,912 $1,133
5/24/1999 MDMH Revenue $39,218 $40,351
6/7/1999 Payroll $38,912 $1,439
6/21/1999 MDMH Revenue $39,218 $40,657
7/5/1999 Payroll $41,810 -$1,153
7/19/1999 MDMH Revenue $39,218 $38,065
8/2/1999 Payroll $41,810 -$3,745
8/16/1999 MDMH Revenue $42,546 $38,801
8/30/1999 Payroll $40,810 -$2,009
9/13/1999 MDMH Revenue $42,546 $40,537
9/27/1999 Payroll $40,810 -$273
10/11/1999 MDMH Revenue $42,546 $42,273
10/25/1999 Payroll $38,912 $3,361
11/8/1999 MDMH Revenue $42,546 $45,907
11/22/1999 Payroll $38,912 $6,995
12/6/1999 MDMH Revenue $42,546 $49,541
12/20/1999 Payroll $38,912 $10,629
12/29/1999 MDMH Revenue $42,546 $53,175
1/15/2000 Payroll $38,912 $14,263
1/30/2000 MDMH Revenue $42,546 $56,809
2/15/2000 Payroll $38,912 $17,897
2/28/2000 MDMH Revenue $42,546 $60,443
3/15/2000 Payroll $38,912 $21,531
.
List cash adjustments 0
End of period projected balance: $21,531

Forecast Types
• Qualitative Forecasts
• Univariate Forecasts
• Multivariate Forecasts

Qualitative Forecasts
• Forecasting techniques where the method is
implicit or intuitive
• Use either no data, or qualitative data
• Use in control forecasts
– Used in setting goals and objectives
– Representative of decision-makers intentions
• Use in process forecasts
– To make predictions about some variable
– E.g. Georgia revenue forecasts historically based on the
expert judgement of one expert

Qualitative Forecasts
• Strengths
– Inexpensive
– Quick
– Could be reasonably accurate
– Best for control forecasts, value judgements
• Weaknesses
– Quality is only as good as the expert
– Errors may be random or systematic
– Hard to make judgements about accuracy attributable to
the method

Univariate Forecasts
• Time series
• Use historical information as the source of
data about the prediction phenomenon
• Use no other variables to predict outcomes
• May introduce corrections for ‘randomness’

Univariate (time series) Forecast
• Key issues for employing time series
– Past history must be a good predictor of the
future
– Principal objective of the forecast must be to
predict, not to analyze why past is a good
predictor of future (e.g. revenues or
expenditures)

• Cash flow projection: Process forecast for
which a univariate method is appropriate
– Primary objective is accurate prediction
– Intervention requires no underlying causal
understanding
• Exception: When cash flow is consistently short
– e.g. NYC in the mid 1970s
– e.g. HNHS in the early 1990s

• Strengths
– Consistently the most accurate method of
process forecasting of short and medium term
phenomena
– Low data demands (just historical data)
– Easy to complete

• Weaknesses
– Little information provided about underlying
causal structure
– Cannot adjust forecast based on changes in core
assumptions
• E.g. forecasting MARTA ridership from 1999 and
2000 using information from 1990-1999 but without
adjusting for changes in gasoline prices

Multivariate Forecast
• Models the relationship between the variable of
interest and several other factors that may be
affecting it.
• Multivariate forecasts come in two forms
– Stochastic process models
• Allow for random variation in process
– Deterministic models
• Assume direct relationship between explanatory variables and
variable of interest
– Expenditure forecasts for entitlement programs typically employ
deterministic models

• Strengths
– Can provide sophisticated understanding of why certain
phenomena are occurring and how they affect the
outcome of interest
• Better explanations to provide to decision-makers
– Allow for the introduction of random effects or
“shocks” into the system observed
– Allow for the analysis of the impact of unforseen events
– Best for predictive forecasting

• Weaknesses
– Requires much more data
• Historical series, data on all independent variables
– Resource hungry
– Time
• Recommendations
– Start with the simplest models first
– Increase complexity only as it becomes apparent that
prediction error is reduced
– E.g. OLS, 2SLS, 3SLS, REMI...

Forecasting Problems
• Searching for an unknown value
• Less tolerance for errors in prediction than in
estimation
– Prospective focus means decision makers are relying
upon this data for policy choices
– Large amounts of funds involved make small error rates
important
• Small fund areas are more numerous and errors offsetting
• e.g. general fund vs. license funds

General
Fund Licenses Courts Recreation
Predicted $46,500,000 $112,000 $215,000 $43,000
Actual $45,570,000 $109,200 $220,375 $40,850
Error $ -$930,000 -$2,800 $5,375 -$2,150
Error % -2.04% -2.56% 2.44% -5.26%
Prediction Error in Government Fund Groups
Government Revenue
Fund Group

• Forecasts are only as good as the assumptions that
feed them
• Many factors that influence the volume of
revenues and expenditures are not easily
quantifiable or knowable
– Shifts in attitudes, preferences, expectations
– Political factors
• Actions and choices of decision makers
• Influence of interests

• Technical expertise is in methods of
forecasting, not in formulating and revising
assumptions
• All forecasting includes subjective
judgements
– The most sophisticated methods may
incorporate very large numbers of assumptions
• Periodicity

Prediction Error
• The prediction error is the difference
between the predicted value and the actual
value
• Error = XXe  ˆ

Dealing with Prediction Errors
• Organizations strategies:
– Contingency planning
• Savings, “rainy day funds”
• Response plans
– Lobbying, advocacy
• Political strategies
– Use knowledge of bias as basis for contingent
agreements (“If revenue is X we spend on Y”)
– Assure bias is open, consistent and not politically
motivated
– Consensus forecasting (deliberative technique)

Dealing with Prediction Errors
• Methodological considerations
– Sample size
– Data quality
– Incorporating errors from previous predictions
• Introduction of systematic bias
– Consistent use of lower revenue projections and higher
expenditure projections
– Preference for explicit adjustment or decision rules

Evaluating Forecast Accuracy
• Seek measures of prediction error which
ignore direction
• Mean absolute deviation (MAD)
– Mean of the summed absolute values of the
errors
• Mean square error (MSE)
– Mean of the sum of the squares of the errors
n
e
MAD

||
n
MSE
e
2

Forecasting Methods
• Note: Endogeneity of bias for projections of
government revenue and expenditure
– Governments not only predict but determine
what revenues and expenditures will be
– Local governments and districts may determine
revenue needs and levy to meet them
• Forecasting may facilitate projections of collection
and appeals rates

Forecasting Methods
• Time Series Techniques
– Trendline: Predict value of Xt+1 based on Xt, Xt1, Xt-2...
• Assumes no error or change
• Constant unitary growth
Xt+1= Xt+k, where k = units of growth/period
• Constant rate of (exponential) growth approach
Xz= Xt*rz, where r = (Xt/Xt-1)1/N and z = t+1,
t+2, etc.

Forecasting Methods
– Moving Average
• Predicted value is the average of the N most recent
period values
• Emphasis placed equally on all observation periods
• Most reasonable where the inter-period variation is
not significant
– Even if some growth

Moving Average





 


N
Nttt yyyf ...
t
21

Example: Forecasting pork tax
revenues (with 2000 outbreak
of Mad Pig Disease)
• Fixed number (five) years used
for each prediction
• Set of years advances (moves)
each year to reflect the same
distance from t (t-1,t-2…)
• Best for stable phenomena
• Poor method when shocks are
present
Pork Tax
Revenues
(Millions)
Five Year
Moving
Average
Prediciton
Error
2000 $2,221.60
1999 $1,788.00 $2,366.00 32.33%
1998 $2,265.00 $2,395.00 5.74%
1997 $2,245.00 $2,453.00 9.27%
1996 $2,385.00 $2,504.80 5.02%
1995 $2,425.00 $2,577.40 6.28%
1994 $2,510.00 $2,604.00 3.75%
1993 $2,410.00 $2,672.00 10.87%
1992 $2,535.00 $2,704.80 6.70%
1991 $2,644.00 $2,749.20 3.98%
1990 $2,788.00 $2,889.20 3.63%
1989 $2,643.00 $2,950.20 11.62%
1988 $2,750.00 $3,051.80 10.97%
1987 $2,699.00
1986 $2,866.00
1985 $3,488.00
1984 $2,948.00
1983 $3,258.00
Moving average

t yt ft=.5yt-1+.3yt-2+.2yt-3
0 9
1 11
2 12
3 16 .5(12)+.3(11)+.2(9)= 11.1
4 11 .5(16)+.3(12)+.2(11)= 13.8
5 17 .5(11)+.3(16)+.2(12)= 12.7
6 11 .5(17)+.3(11)+.2(16)= 15
7 15 .5(11)+.3(17)+.2(11)= 12.8
8 13 .5(15)+.3(11)+.2(17)= 14.2
Three Year Weighted Moving Average

Forecasting Methods
• Distributed lag models include not only the
current but the lagged (past) values for the
independent variables:
yt=a + b0Xt + b1Xt-1 + b2Xt-2 + et
• Autoregressive models include one or more
lagged values of the dependent variable as
independent variables.
yt=a + bXt + dyt-1 + et

Forecasting Methods
– Exponential smoothing methods
• Weight forecast values based on the size and
direction of the previous prediction errors
– Key is value attributed to a
)*(ˆ
11   ttt eXX a

Exponential Smoothing
• The predicted value for each period is
adjusted to correct for the error from the
previous period
• The weight placed on the previous error can
be set to reflect how rapidly changing the
phenomenon is that is being forecast
• Alpha weight is set to minimize the error

• Moving Average where weight on past
observations decline exponentially
• Weights based on a single parameter called
the smoothing coefficient (alpha)
• 0 <= a <= 1
• Small alpha generates an average using
more historical data, a larger alpha uses less
historical data

Simple Exponential Smoothing
• alpha = 1 is the same as the Naive model
• Simple Exponential Smoothing
• Or, for estimation purposes…
ttt yyy ˆ)1(ˆ )1( aa 
ttt yyyy )ˆ(ˆˆ )1(  a

Calculation of SES
• Y(t) = a Y(t-1)+a(1-a) Y(t-2)+a(1-a)2 Y(t-3)+ ... +E(t)
• Data(t) = MODEL(t-1) + ERROR(t)
• FORECAST(t) = MODEL(t-1)
• F(t)=aY(t-1)+[a(1-a) Y(t-2)+a(1-a)2 Y(t-3)+ ...]
• F(t) = a Y(t-1)+(1-a) F(t-1)
• F(t) = F(t-1) + a [Y(t-1) - F(t-1)]
• F(t) = F(t-1) + a e(t-1)

Exponential Smoothing: Alpha tables
a= 0.01 0.1 0.25 0.5 0.8
t-1 0.0100 0.1000 0.2500 0.5000 0.8000
t-2 0.0099 0.0900 0.1875 0.2500 0.1600
t-3 0.0098 0.0810 0.1406 0.1250 0.0320
t-4 0.0097 0.0729 0.1055 0.0625 0.0064
t-5 0.0096 0.0656 0.0791 0.0313 0.0013
t-6 0.0095 0.0590 0.0593 0.0156 0.0003
t-7 0.0094 0.0531 0.0445 0.0078 0.0001
t-8 0.0093 0.0478 0.0334 0.0039 0.0000

Forecasting Methods
• Simple regression
yt=a + bxt +et
• Multiple regression
yt=a+bx1+bx2…+bxn+et
Where: y=predicted observation, b=coefficient,
x=independent variable(s), a=constant, e=error term,
t=time period
• Non-linear regression models
ln(yt) =e bxt+et

Regression
• Identifying the contribution of individual
factors when predicting the given value of a
phenomenon
• Simple regression bases the values of y on
the values of x
– Based on the historical relationship between
truck weight and road repairs, we could predict
road expenses based on average truck weights

Regression
• Excel tip: Use the function “forecast” to
find predicted values using simple
regression
• =forecast(x,Y,X)
x = value corresponding to predicted y
Y=range of dependent variables
X=range of independent variables

Public Financial Management combined lecture packet

Public Financial Management combined lecture packet

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Public Financial Management combined lecture packet