The balance sheet is a snapshot of a company’s financial assets, liabilities, and the value of the company to its owner—often referred to as net worth or equity—at a specific point in time. Balance sheets are commonly prepared at the end of each month and at the end of the fiscal year. A typical balance sheet for a construction company using the percentage-of-completion accounting method is shown in Figure 2-2.

The balance sheet is divided into three sections: assets, liabilities, and owner’s equity. The balance sheet reports the values of each of the accounts in the balance sheet portion of the chart of accounts at the time the balance sheet is printed. For example, the amount reported as cash on the balance sheet in Figure 2-2 comes from account number 110 from the chart of accounts shown in Figure 2-1. To prevent the balance sheet from becoming too complicated multiple accounts may be summarized by combining two or more consecutive accounts into a single line on the balance sheet. Other items on the balance sheet may be calculated from other lines on the balance sheet. For example, the Total Current Assets is the sum of the Cash, Accounts Receivable-Trade, Accounts Receivable-Retention, Costs and Profits in Excess of Billings, Notes Receivable, Prepaid Expenses, and Other Current Assets or accounts 110 through 199 on the chart of accounts in Figure 2-1. Not all companies will use all the accounts shown in Figure 2-1. For example, the construction company in Figure 2-2 does not use the inventory account.

On the balance sheet the relationship between assets, liabilities, and equity is as follows:

Asset = Liabilities + Equity     (2-1)

Chart of Accounts
Balance Sheet for Big W Construction


Cost reporting is where the accounting system provides management with the accounting data after the opportunity has passed for management to respond to and correct the problems indicated by the data. When companies wait to enter the cost of their purchases until the bills are received, management does not know if they are under or over budget until the bills are entered, at which time the materials purchased have been delivered to the project and may have been consumed. The extreme case of cost reporting is where companies only look at the costs and profit for each project after the project is finished. Cost reporting is typified by the accounting reports showing where a company has been financially without giving management an opportunity to proactively respond to the data.


Cost control is where the accounting system provides management with the accounting data in time for management to analyze the data and make corrections in a timely manner. Companies that enter material purchase orders and subcontracts, along with their associated costs, into their accounting system as committed costs before issuing the purchase order or subcontract allow management time to address cost overruns before ordering the materials or work. Committed costs are those costs that the company has committed to pay and can be identified before a bill is received for the costs. For example, when a contractor signs a fixed-price subcontract he or she has committed to pay the subcontractor a fixed price once the work has been completed and, short of any change orders, knows what the work is going to cost. Accounting systems that track committed costs give management time to identify the cause of the overrun early on, identify possible solutions, and take corrective action. Cost control is typified by identifying problems early and giving management a chance to proactively address the problem. A lot of money can be saved by addressing pervasive problems—such as excessive waste—early in the project.

If a company’s accounting system is going to allow management to control costs rather than just report costs, the accounting system must have the following key components:

First, the accounting system must have a strong job cost and equipment tracking system. The accounting system should update and report costs, including committed costs and estimated cost at completion on a weekly basis. Having timely, up-to-date costs for the project and the equipment is a must if management is going to manage costs and identify problems early.

Second, the accounting system must utilize the principle of management by exception. It can be easy for managers to get lost in the volumes of data generated by the accounting system. The accounting system should provide reports that allow management to quickly identify problem areas and address the problems. For example, as soon as bills are entered into the accounting system, management should get a report detailing all bills that exceed the amount of their purchase order or subcontract. Problems that are buried in volumes of accounting data are often never addressed because management seldom has time to pour through all of the data to find the problems or if they are found they are often found too late for management to address the problem. Providing reports that flag transactions that fall outside the acceptable limits is a necessity if management is going to control costs. By having reports that flag items that fall outside acceptable limits, management can make addressing these items a priority.

Third, accounting procedures need to be established to ensure that things do not fall through the cracks. These procedures should include things such as who can issue purchase orders and what to do when a bill is received for a purchase order that has not been issued. The procedures should also identify the acceptable limits for different types of transactions. Procedures ensure that the accounting is handled in a
consistent manner and give management confidence in the data that it is using to manage the company.

Finally, the data must be easily and quickly available to management and other employees who are directly responsible for controlling costs. It does little good to collect cost data for use in controlling costs if the data cannot be accessed. Where possible the reports should be automatically prepared by the accounting software. This eliminates the time and effort needed to prepare the reports manually. Additionally, frontline supervisors who are responsible for control costs should readily have access to their costs. Holding supervisors responsible for costs at the end of a job while not giving them access to their costs throughout the project denies them the opportunity to proactively control costs.

The accounting system for many construction companies consists of three different ledgers: the general ledger, the job cost ledger, and the equipment ledger. The general ledger tracks financial data for the entire company and is used to prepare the company’s financial statements and income taxes. The job cost ledger is used to track the financial data for each of the construction projects. The equipment ledger is used to track financial data for heavy equipment and vehicles. All construction companies should have a general ledger and a job cost ledger. Companies with lots of heavy equipment or vehicles should have an equipment ledger.

Managing Cash Flows

Financial managers are responsible for managing the cash flows for the company. Many profitable companies fail because they simply run out of cash and are unable to pay their bills. The duties of a financial manager include the following:

Managing Cash Flows

Matching the use of in-house labor and subcontractors to the cash available for use on a project.
Ensuring that the company has sufficient cash to take on an additional project.
Preparing an income tax projection for the company.
Preparing and updating annual cash flow projections for the company.
Arranging for financing to cover the needs of the construction company.

Managing Costs and Profits

Financial managers are responsible for managing the company’s costs and earning a profit for the company’s owners. Financial managers rely heavily on the reports from the accounting system in their management of costs. Managing the company’s costs and profits includes the following duties:

Managing Costs and Profits

Controlling project costs.
Monitoring project and company profitability.
Setting labor burden markups.
Developing and tracking general overhead budgets.
Setting the minimum profit margin for use in bidding.
Analyzing the profitability of different parts of the company and making the necessary changes to improve profitability.
Monitoring the profitability of different customers and making the necessary marketing changes to improve profitability.

Nominal and Effective Interest Rate Statements

Here we discuss   nominal and effective interest rates, which have the same basic relationship. The difference here is that the concepts of nominal and effective must be used when interest is compounded more than once each year. For example, if an interest rate is expressed as 1% per month, the terms   nominal  and   effective  interest rates must be considered.

To understand and correctly handle effective interest rates is important in engineering practice as well as for individual finances. The interest amounts for loans, mortgages, bonds, and stocks are commonly based upon interest rates compounded more frequently than annually. The engineering economy study must account for these effects. In our own personal fi nances, we manage most cash disbursements and receipts on a nonannual time basis. Again, the effect of compounding more frequently than once per year is present. First, consider a nominal interest rate.

A nominal interest rate r is an interest rate that does not account  for compounding. By definition,

A nominal rate may be calculated for   any time period longer than the time period stated  by using Equation [4.1]. For example, the interest rate of 1.5% per month is the same as each of the following nominal rates.

Note that none of these rates mention anything about compounding of interest; they are all of the form “  r % per time period.” These nominal rates are calculated in the same way that simple rates are calculated using Equation [1.7], that is, interest rate   times  number of periods.

After the nominal rate has been calculated, the   compounding period (CP)  must be in- cluded in the interest rate statement. As an illustration, again consider the nominal rate of 1.5% per month. If we defi ne the CP as 1 month, the nominal rate statement is 18% per year,   compounded monthly,  or 4.5% per quarter,   compounded monthly . Now we can consider an effective interest rate.

An effective interest rate   i  is a rate wherein the  compounding of interest  is taken into account.  Effective rates are commonly expressed on an annual basis as an effective annual rate; however, any time basis may be used.

The most common form of interest rate statement when compounding occurs over time periods  shorter than 1 year is “% per time period, compounded CP-ly,” for example, 10% per year, compounded monthly, or 12% per year, compounded weekly. An effective rate may not always include the compounding period in the statement. If the CP is not mentioned, it is understood to be the same as the time period mentioned with the interest rate. For example, an interest rate of  “1.5% per month” means that interest is compounded each month; that is, CP is 1 month. An equivalent effective rate statement, therefore, is 1.5% per month, compounded monthly.

All of the following are effective interest rate statements because either   they     state they are  effective  or the   compounding period is not mentioned.  In the latter case, the CP is the same as  the time period of the interest rate.

All nominal interest rates can be converted to effective rates. The formula to do this is discussed in the next section.

All interest formulas, factors, tabulated values, and spreadsheet functions must use an effective interest rate to properly account for the time value of money. 

The term   APR (Annual Percentage Rate)  is often stated as the annual interest rate for credit cards, loans, and house mortgages. This is the same as the   nominal rate . An APR of 15% is the same as a nominal 15% per year or a nominal 1.25% on a monthly basis. Also the term   APY (Annual Percentage Yield)  is a commonly stated annual rate of return for investments, certificates of deposit, and saving accounts. This is the same as an   effective rate . The names are different, but the interpretations are identical. As we will learn in the following sections, the effective rate is always greater than or equal to the nominal rate, and similarly APY APR.

Based on these descriptions, there are always three time-based units associated with an interest rate statement.

Interest  period (   t   ) —The period of time over which the interest is expressed. This is the   t   in
the statement of   r % per time period   t , for example, 1%   per month.  The time unit of 1 year is by far the most common. It is assumed when not stated otherwise. 

Compounding  period (CP) —The shortest time unit over which interest is charged or earned.  This is defi ned by the compounding term in the interest rate statement, for example, 8% per  year,   compounded monthly.  If CP is not stated, it is assumed to be the same as the interest period. 

Compounding  frequency  (m) —The number of times that compounding occurs within the  interest period   t.  If the compounding period CP and the time period  t  are the same, the com-pounding frequency is 1, for example, 1%   per month, compounded monthly.   

Consider the (nominal) rate of 8% per year, compounded monthly. It has an interest period  t  of 1 year, a compounding period CP of 1 month, and a compounding frequency   m  of 12 times per  year. A rate of 6% per year, compounded weekly, has  t  = 1 year, CP = 1 week, and   m = 52, based  on the standard of 52 weeks per year.

In previous chapters, all interest rates had   t  and CP values of 1 year, so the compounding frequency was always   m  = 1. This made them all effective rates, because the interest period and compounding period were the same. Now, it will be necessary to express a nominal rate as an  effective rate on the same time base as the compounding period.

An effective rate can be determined from a nominal rate by using the relation

As an illustration, assume  r  = 9% per year, compounded monthly; then   m  = 12. Equation [4.2] is used to obtain the effective rate of 9%   / 12 = 0.75% per month, compounded monthly.

Note that changing the interest period   t  does not alter the compounding period, which is 1 month in this illustration. Therefore,   r = 9% per year, compounded monthly, and   r = 4.5% per 6 months, compounded monthly, are two expression of the same interest rate.

Calculations For Shifted Gradients

Previously, we derived the relation P/G (  P/G ,  i ,  n ) to determine the present worth of the arithmetic gradient series. The   P/G  factor, Equation [2.25], was derived for a present worth in year 0 with the gradient first appearing in year 2.

The present worth of an arithmetic gradient  will always be located two periods  before  the gradient starts. 

Refer to Figure 2–14 as a refresher for the cash flow diagrams.

The relation   A/G (  A/G ,  i ,  n ) was also derived previously. The   A/G  factor in Equation [2.27] performs the equivalence transformation of a gradient only into an   A  series from years 1 through   n  (Figure 2–15). Recall that the base amount must be treated separately. Then the equivalent   P  or   A  values can be summed to obtain the equivalent total present worth  PT  and total  annual series   A/T.

A conventional gradient series starts between periods 1 and 2 of the cash flow sequence. A gradient starting at any other time is called a   shifted gradient .  The n  value in the   P/G  and   A/G  factors for a shifted gradient is determined by renumbering the time scale. The period in which the   gradient first appears is labeled period 2. The n  value for the gradient factor is determined by the renumbered period where the last gradient increase occurs.

Partitioning a cash flow series into the arithmetic gradient series and the remainder of the cash flows can make very clear what the gradient   n  value should be.

It is important to note that the   A/G   factor   cannot  be used to find an equivalent   A  value in periods 1 through   n  for cash flows involving a shifted gradient. Consider the cash flow diagram of Figure 3–11. To find the equivalent annual series in years 1 through 10 for the gradient series only, first find the present worth PG  of the gradient in actual year 5, take this present worth back to year 0, and annualize the present worth for 10 years with the   A/P  factor. If you apply the annual series gradient factor (  A/G ,  i ,5) directly, the gradient is converted into an equivalent annual series over years 6 through 10 only, not years 1 through 10, as requested.

To find the equivalent A series of a shifted gradient through all the n periods, first find the present worth of the gradient at actual time 0, then apply the (A /P,  i, n) factor

Previously, we derived the relation   Pg = A1 (  P /A,g,i,n ) to determine the present worth of a geometric gradient  series, including the initial amount   A1. The factor was derived to find the present worth in year 0, with   A1  in year 1 and the first gradient appearing in year 2. The present worth of a   geometric gradient series  will always be located   two periods before the gradient stars,  and the   initial amount is included  in the resulting present worth. Refer to Figure 2–21 as a refresher for the cash flows.

Equation [2.35] is the formula used for the factor. It is not tabulated.

Decreasing arithmetic and geometric gradients  are common, and they are often   shifted gradient series . That is, the constant gradient is –  G  or the percentage change is –  g  from one period to the next, and the first appearance of the gradient is at some time period (year) other than year 2 of the series. Equivalence computations for present worth   P  and annual worth   A  are basically the  same as discussed previously, except for the following. 

For shifted, decreasing gradients:

•  The base amount A (arithmetic) or initial amount A1 (geometric) is the largest amount in the first year of the series.
•  The gradient amount is subtracted from the previous year’s amount, not added to it.
•  The amount used in the factors is –G for arithmetic and –g for geometric gradient series.
•  The present worth PG or Pg  is located 2 years prior to the appearance of the first gradient; however, a P F factor is necessary to find the present worth in year 0

Figure 3–15 partitions a decreasing arithmetic gradient series with   G = $−100 that is shifted 1 year forward in time.  P/G    occurs in actual year 1, and  PT  is the sum of three components.

Calculations Involving Uniform Series and Randomly Placed Single Amounts

When a cash flow includes both a uniform series and randomly placed single amounts, the procedures are applied to the uniform series and the single-amount formulas are applied to the one-time cash flows. This approach, illustrated in Examples 3.3, is merely a combination of previous ones. For spreadsheet solutions, it is necessary to enter the net cash flows before using the NPV and other functions.


An engineering company in Wyoming that owns 50 hectares of valuable land has decided to lease the mineral rights to a mining company. The primary objective is to obtain long-term income to finance ongoing projects 6 and 16 years from the present time. The engineering company makes a proposal to the mining company that it pay $20,000 per year for 20 years beginning 1 year from now, plus $10,000 six years from now and $15,000 sixteen years from now. If the mining company wants to pay off its lease immediately, how much should it pay now if the investment is to make 16% per year?


The cash flow diagram is shown in Figure 3–6 from the owner’s perspective. Find the present worth of the 20-year uniform series and add it to the present worth of the two one-time amounts to determine   PT,

Note that the $20,000 uniform series starts at the end of year 1, so the   P/A  factor determines the  present worth at year 0. 

When you calculate the   A  value for a cash fl ow series that includes randomly placed single amounts and uniform series,   fi  rst convert everything to a present worth or a future worth. Then you obtain the   A  value by multiplying   P  or   F  by the appropriate   A/P  or   A/F   factor.