Money maths: interest, cash flow, retainage and sales tax

Construction is financed work. Contractors pay for labor, materials and equipment weeks or months before they are paid, owners borrow to fund projects, and payment rules hold back part of every invoice until the work is finished. The mathematics of money, interest, escalation, cash flow, retained amounts and sales taxes, therefore affects every project's profit as much as the mathematics of quantities. This lesson works through simple and compound interest, escalation of costs over time, the time value of money, progress payments with holdback or retainage, the cash flow gap that contractors must finance, and the sales taxes that apply to construction. It explains the arithmetic and the main rules; it is not legal, tax or accounting advice, and the rules change, so always confirm current requirements for a specific project.

Simple and compound interest

Interest is the price of borrowing money. Simple interest is calculated only on the original amount, the principal. Compound interest is calculated on the principal plus interest already earned or charged, so it grows faster. Construction loans, lines of credit and late-payment interest are usually compounded monthly or daily, while short-term calculations are often done with simple interest for convenience.

In the simple interest formula, P is the principal, r the annual rate and t the time in years. In the compound formula, F is the future amount, i the rate per compounding period and n the number of periods. An annual rate of 7.2 % compounded monthly has a monthly rate of 0.6 %. The effective annual rate, the true yearly cost after compounding, is (1 + i)ⁿ − 1 over one year, which for 0.6 % monthly is 1.006¹² − 1 = 7.44 %.

Escalation

An estimate prepared today prices labor and materials at today's costs, but much of the work will be bought months or years later. Escalation is the expected increase in costs over that time, applied as a compound rate. Estimators usually escalate to the midpoint of construction, or to the expected purchase date of major items, because spending is spread across the construction period. Escalation rates come from cost indices, supplier forecasts and economic data, and can vary sharply by material and region.

The time value of money

A dollar received later is worth less than a dollar today, because today's dollar could earn interest in the meantime. The present value of a future amount discounts it back to today at an interest rate, called the discount rate. Present value explains why holdback or retainage costs contractors money even when it is eventually paid in full, and why owners compare options with different payment timing using discounted values rather than raw totals.

Progress payments

Most construction contracts pay monthly for work completed (Lesson 2). The contractor submits an application for payment showing the value of work done to date, often with materials stored on site, less previous payments and less a retained percentage. The owner or the owner's consultant certifies the amount, and the owner pays within the contract or statutory period. The contractor then pays its subcontractors their shares, and so on down the chain.

In the United States, the retained amount is called retainage. It is set by the contract and, on public work, by statute. Retainage is commonly 5 to 10 % of each progress payment; many contracts reduce it to 5 % or stop retaining once the work is 50 % complete. On federal contracts, the Federal Acquisition Regulation allows retainage of up to 10 % only when progress is unsatisfactory, and the federal Prompt Payment Act requires prime contractors to pay subcontractors within 7 days of receiving payment. Most states have prompt payment acts for public work, and many for private work, with payment deadlines, interest on late payments and limits on retainage, such as a 5 % cap on many public projects. Rules differ by state and by public or private work, so check the governing statute and the contract.

The cash flow gap

A contractor's costs are incurred as the work is done, but income arrives later: invoices are submitted at month end, certified, paid weeks later and reduced by the retained amount. The difference between cumulative costs and cumulative receipts is the contractor's negative cash position, which must be financed from working capital or borrowing. Plotting cumulative costs and cumulative receipts over time produces two S-shaped curves, with the gap between them showing the money the contractor has tied up in the project.

Sales taxes on construction

In the United States, sales tax is imposed by states and many local governments, at combined rates that vary from zero in a few states to over 10 % in some cities. Most states treat construction contractors who install materials into real property as the consumers of those materials: the contractor pays sales or use tax when buying the materials and recovers it through its contract price, and does not charge sales tax on the contract. Some states instead tax the contract or certain services, some allow resale treatment for certain contract types, and exemptions for tax-exempt owners such as government agencies vary. Use tax applies when materials are bought tax-free out of state and used in a taxing state. Confirm the rules for each state and project with current guidance or a tax adviser.

Whatever the system, two arithmetic rules from Lesson 2 apply. Tax is calculated on the taxable amount, so check what the base includes. And to remove tax from a tax-inclusive total, divide by one plus the rate rather than subtracting the rate.

Putting it together

These calculations interact. Escalation raises the costs that are financed; slow payment and retained amounts lengthen the financing period; interest rates set its cost; and sales taxes change what materials really cost. A contractor deciding whether to bid a project with slow-paying owners or high retainage, or an owner deciding whether to release retained money early in exchange for a lower price, can compare options by putting each cash flow on a timeline and discounting it to a present value. Spreadsheets, covered in Lesson 12, make that comparison quick and transparent.