Saturday, May 10, 2008

Present Value

The present value of a sum of money to be received at a future date is determined by discounting the future value at the interest rate that the money could earn over the period.

Starting with the future value equation:

FV = PV ( 1 + i ) t

where

FV = future value
PV = present value
i = annual interest rate

we see that the present value is given by:

PV =

FV

( 1 + i ) t

The term 1 / ( 1 + i ) t is known as the discount factor.

If both the future value and present value are known, one can solve for the time or the interest rate using one of the techniques discussed in future value calculations.

Present Value of Multiple Future Cash Payments

When there is more than a single cash payment at a future date, the present value is calculated by taking the present values of the individual cash payments and summing them. It is helpful to draw a time line depicting the timing of the cash payments:

Time Line

0

1

2

3

PV

C1

C2

C3

In this model, the cash payment at each date may be either an inflow or an outflow; the direction is designated by the sign. The present value of the above cash flow is:

PV = C1 / ( 1 + i ) + C2 / ( 1 + i )2 + C3 / ( 1 + i )3


Discount Factor Table

The discount factor 1 / ( 1 + i ) t may be calculated for a range of time periods and interest rates and tabulated for quick reference.

Table of Discount Factors

t \ i

1%

2%

3%

4%

5%

6%

7%

8%

9%

10%

1

0.990

0.980

0.971

0.962

0.952

0.943

0.935

0.926

0.917

0.909

2

0.980

0.961

0.943

0.925

0.907

0.890

0.873

0.857

0.842

0.826

3

0.971

0.942

0.915

0.889

0.864

0.840

0.816

0.794

0.772

0.751

4

0.961

0.924

0.888

0.855

0.823

0.792

0.763

0.735

0.708

0.683

5

0.951

0.906

0.863

0.822

0.784

0.747

0.713

0.681

0.650

0.621

6

0.942

0.888

0.837

0.790

0.746

0.705

0.666

0.630

0.596

0.564

7

0.933

0.871

0.813

0.760

0.711

0.665

0.623

0.583

0.547

0.513

8

0.923

0.853

0.789

0.731

0.677

0.627

0.582

0.540

0.502

0.467

9

0.914

0.837

0.766

0.703

0.645

0.592

0.544

0.500

0.460

0.424

10

0.905

0.820

0.744

0.676

0.614

0.558

0.508

0.463

0.422

0.386

11

0.896

0.804

0.722

0.650

0.585

0.527

0.475

0.429

0.388

0.350

12

0.887

0.788

0.701

0.625

0.557

0.497

0.444

0.397

0.356

0.319

13

0.879

0.773

0.681

0.601

0.530

0.469

0.415

0.368

0.326

0.290

14

0.870

0.758

0.661

0.577

0.505

0.442

0.388

0.340

0.299

0.263

15

0.861

0.743

0.642

0.555

0.481

0.417

0.362

0.315

0.275

0.239

Future Value

The future value of a sum of money invested at interest rate i for one year is given by:

FV = PV ( 1 + i )

where

FV = future value
PV = present value
i = annual interest rate

If the resulting principal and interest are re-invested a second year at the same interest rate, the future value is given by:

FV = PV ( 1 + i ) ( 1 + i )

In general, the future value of a sum of money invested for t years with the interest credited and re-invested at the end of each year is:

FV = PV ( 1 + i ) t


Solving for Required Interest Rate or Time

Given a present sum of money and a desired future value, one can determine either the interest rate required to attain the future value given the time span, or the time required to reach the future value at a given interest rate. Because solving for the interest rate or time is slightly more difficult than solving for future value, there are a few methods for arriving at a solution:

  1. Iteration - by calculating the future value for different values of interest rate or time, one gradually can converge on the solution.

  2. Financial calculator or spreadsheet - use built-in functions to instantly calculate the solution.

  3. Interest rate table - by using a table such as the one at the end of this page, one quickly can find a value of interest rate or time that is close to the solution.

  4. Algebraic solution - mathematically calculating the exact solution.

Algebraic Solution

Beginning with the future value equation and given a fixed time period, one can solve for the required interest rate as follows.

FV = PV ( 1 + i ) t

Dividing each side by PV and raising each side to the power of 1/t:

( FV / PV ) 1/t = 1 + i

The required interest rate then is given by:

i = ( FV / PV ) 1/t - 1

To solve for the required time to reach a future value at a specified interest rate, again start with the equation for future value:

FV = PV ( 1 + i ) t

Taking the logarithm (natural log or common log) of each side:

log FV = log [ PV ( 1 + i ) t ]

Relying on the properties of logarithms, the expression can be rearranged as follows:

log FV = log PV + t log ( 1 + i )

Solving for t:

t =

log ( FV / PV )

log ( 1 + i )



Interest Factor Table

The term ( 1 + i ) t is the future value interest factor and may be calculated for an array of time periods and interest rates to construct a table as shown below:


Table of Future Value Interest Factors

t \ i

1%

2%

3%

4%

5%

6%

7%

8%

9%

10%

1

1.010

1.020

1.030

1.040

1.050

1.060

1.070

1.080

1.090

1.100

2

1.020

1.040

1.061

1.082

1.103

1.124

1.145

1.166

1.188

1.210

3

1.030

1.061

1.093

1.125

1.158

1.191

1.225

1.260

1.295

1.331

4

1.041

1.082

1.126

1.170

1.216

1.262

1.311

1.360

1.412

1.464

5

1.051

1.104

1.159

1.217

1.276

1.338

1.403

1.469

1.539

1.611

6

1.062

1.126

1.194

1.265

1.340

1.419

1.501

1.587

1.677

1.772

7

1.072

1.149

1.230

1.316

1.407

1.504

1.606

1.714

1.828

1.949

8

1.083

1.172

1.267

1.369

1.477

1.594

1.718

1.851

1.993

2.144

9

1.094

1.195

1.305

1.423

1.551

1.689

1.838

1.999

2.172

2.358

10

1.105

1.219

1.344

1.480

1.629

1.791

1.967

2.159

2.367

2.594

11

1.116

1.243

1.384

1.539

1.710

1.898

2.105

2.332

2.580

2.853

12

1.127

1.268

1.426

1.601

1.796

2.012

2.252

2.518

2.813

3.138

13

1.138

1.294

1.469

1.665

1.886

2.133

2.410

2.720

3.066

3.452

14

1.149

1.319

1.513

1.732

1.980

2.261

2.579

2.937

3.342

3.797

15

1.161

1.346

1.558

1.801

2.079

2.397

2.759

3.172

3.642

4.177

Wednesday, May 7, 2008

Chart of Accounts

The chart of accounts is a listing of all the accounts in the general ledger, each account accompanied by a reference number. To set up a chart of accounts, one first needs to define the various accounts to be used by the business. Each account should have a number to identify it. For very small businesses, three digits may suffice for the account number, though more digits are highly desirable in order to allow for new accounts to be added as the business grows. With more digits, new accounts can be added while maintaining the logical order. Complex businesses may have thousands of accounts and require longer account reference numbers. It is worthwhile to put thought into assigning the account numbers in a logical way, and to follow any specific industry standards. An example of how the digits might be coded is shown in this list:

Account Numbering

1000 - 1999: asset accounts
2000 - 2999: liability accounts
3000 - 3999: equity accounts
4000 - 4999: revenue accounts
5000 - 5999: cost of goods sold
6000 - 6999: expense accounts
7000 - 7999: other revenue (for example, interest income)
8000 - 8999: other expense (for example, income taxes)

By separating each account by several numbers, many new accounts can be added between any two while maintaining the logical order.

Defining Accounts

Different types of businesses will have different accounts. For example, to report the cost of goods sold a manufacturing business will have accounts for its various manufacturing costs whereas a retailer will have accounts for the purchase of its stock merchandise. Many industry associations publish recommended charts of accounts for their respective industries in order to establish a consistent standard of comparison among firms in their industry. Accounting software packages often come with a selection of predefined account charts for various types of businesses.

There is a trade-off between simplicity and the ability to make historical comparisons. Initially keeping the number of accounts to a minimum has the advantage of making the accounting system simple. Starting with a small number of accounts, as certain accounts acquired significant balances they would be split into smaller, more specific accounts. However, following this strategy makes it more difficult to generate consistent historical comparisons. For example, if the accounting system is set up with a miscellaneous expense account that later is broken into more detailed accounts, it then would be difficult to compare those detailed expenses with past expenses of the same type. In this respect, there is an advantage in organizing the chart of accounts with a higher initial level of detail.

Some accounts must be included due to tax reporting requirements. For example, in the U.S. the IRS requires that travel, entertainment, advertising, and several other expenses be tracked in individual accounts. One should check the appropriate tax regulations and generate a complete list of such required accounts.

Other accounts should be set up according to vendor. If the business has more than one checking account, for example, the chart of accounts might include an account for each of them.

Account Order

Balance sheet accounts tend to follow a standard that lists the most liquid assets first. Revenue and expense accounts tend to follow the standard of first listing the items most closely related to the operations of the business. For example, sales would be listed before non-operating income. In some cases, part or all of the expense accounts simply are listed in alphabetical order.

Sample Chart of Accounts

The following is an example of some of the accounts that might be included in a chart of accounts.

Sample Chart of Accounts

Asset Accounts

Current Assets


1000

Petty Cash
1010Cash on Hand (e.g. in cash registers)
1020Regular Checking Account
1030Payroll Checking Account
1040Savings Account
1050Special Account
1060Investments - Money Market
1070Investments - Certificates of Deposit
1100Accounts Receivable
1140Other Receivables
1150Allowance for Doubtful Accounts
1200Raw Materials Inventory
1205Supplies Inventory
1210Work in Progress Inventory
1215Finished Goods Inventory - Product #1
1220Finished Goods Inventory - Product #2
1230Finished Goods Inventory - Product #3
1400Prepaid Expenses
1410Employee Advances
1420Notes Receivable - Current
1430Prepaid Interest
1470Other Current Assets

Fixed Assets


1500

Furniture and Fixtures
1510Equipment
1520Vehicles
1530Other Depreciable Property
1540Leasehold Improvements
1550Buildings
1560Building Improvements
1690Land
1700Accumulated Depreciation, Furniture and Fixtures
1710Accumulated Depreciation, Equipment
1720Accumulated Depreciation, Vehicles
1730Accumulated Depreciation, Other
1740Accumulated Depreciation, Leasehold
1750Accumulated Depreciation, Buildings
1760Accumulated Depreciation, Building Improvements

Other Assets


1900

Deposits
1910Organization Costs
1915Accumulated Amortization, Organization Costs
1920Notes Receivable, Non-current
1990Other Non-current Assets

Liability Accounts

Current Liabilities


2000

Accounts Payable
2300Accrued Expenses
2310Sales Tax Payable
2320Wages Payable
2330401-K Deductions Payable
2335Health Insurance Payable
2340Federal Payroll Taxes Payable
2350FUTA Tax Payable
2360State Payroll Taxes Payable
2370SUTA Payable
2380Local Payroll Taxes Payable
2390Income Taxes Payable
2400Other Taxes Payable
2410Employee Benefits Payable
2420Current Portion of Long-term Debt
2440Deposits from Customers
2480Other Current Liabilities

Long-term Liabilities


2700

Notes Payable
2702Land Payable
2704Equipment Payable
2706Vehicles Payable
2708Bank Loans Payable
2710Deferred Revenue
2740Other Long-term Liabilities

Equity Accounts


3010

Stated Capital
3020Capital Surplus
3030Retained Earnings

Revenue Accounts


4000

Product #1 Sales
4020Product #2 Sales
4040Product #3 Sales
4060Interest Income
4080Other Income
4540Finance Charge Income
4550Shipping Charges Reimbursed
4800Sales Returns and Allowances
4900Sales Discounts

Cost of Goods Sold


5000

Product #1 Cost
5010Product #2 Cost
5020Product #3 Cost
5050Raw Material Purchases
5100Direct Labor Costs
5150Indirect Labor Costs
5200Heat and Power
5250Commissions
5300Miscellaneous Factory Costs
5700Cost of Goods Sold, Salaries and Wages
5730Cost of Goods Sold, Contract Labor
5750Cost of Goods Sold, Freight
5800Cost of Goods Sold, Other
5850Inventory Adjustments
5900Purchase Returns and Allowances
5950Purchase Discounts

Expenses


6000

Default Purchase Expense
6010Advertising Expense
6050Amortization Expense
6100Auto Expenses
6150Bad Debt Expense
6200Bank Fees
6250Cash Over and Short
6300Charitable Contributions Expense
6350Commissions and Fees Expense
6400Depreciation Expense
6450Dues and Subscriptions Expense
6500Employee Benefit Expense, Health Insurance
6510Employee Benefit Expense, Pension Plans
6520Employee Benefit Expense, Profit Sharing Plan
6530Employee Benefit Expense, Other
6550Freight Expense
6600Gifts Expense
6650Income Tax Expense, Federal
6660Income Tax Expense, State
6670Income Tax Expense, Local
6700Insurance Expense, Product Liability
6710Insurance Expense, Vehicle
6750Interest Expense
6800Laundry and Dry Cleaning Expense
6850Legal and Professional Expense
6900Licenses Expense
6950Loss on NSF Checks
7000Maintenance Expense
7050Meals and Entertainment Expense
7100Office Expense
7200Payroll Tax Expense
7250Penalties and Fines Expense
7300Other Taxes
7350Postage Expense
7400Rent or Lease Expense
7450Repair and Maintenance Expense, Office
7460Repair and Maintenance Expense, Vehicle
7550Supplies Expense, Office
7600Telephone Expense
7620Training Expense
7650Travel Expense
7700Salaries Expense, Officers
7750Wages Expense
7800Utilities Expense
8900Other Expense
9000Gain/Loss on Sale of Assets