Wrap Rate and Indirect Rates

Wrap Rate and Indirect Rates

Wrap Rate and Indirect Rates: Pools, Bases and the Price of a Labour Hour

What the tool computes

A contractor that sells labour to the U.S. Government prices each direct hour at its raw rate plus a share of every indirect cost of the business. The Federal Acquisition Regulation (FAR Part 31) requires those indirect costs to be gathered in logical pools and allocated on bases that reflect the benefit the contracts receive; the Cost Accounting Standards (48 CFR 9904) add rules for some pools, among them that an indirect cost pool be homogeneous, its activities sharing the same beneficial or causal relationship to the cost objectives (9904.418-50(b)); the Defense Contract Audit Agency publishes model schedules that show the arithmetic. The tool builds the pools of a small services firm from its annual budget, divides each by its base, and prints the rates, the wrap rate (the price of one dollar of direct labour), the loaded hourly rate of each labour category, a task price in three contract forms, the sensitivity of the wrap rate to utilisation, the year-end true-up and the uncompensated-overtime rate. Money is a plain number in one currency; rates are entered in percent.

Hours and labour

A full-time year is 2,080 paid hours. Paid time off, holidays and sick leave are paid but not worked: their pay is a fringe cost, and the rest are the productive hours, H_prod = 2,080 − leave. Each category's productive time splits by its utilisation u into direct hours, charged to contracts, and non-billable hours, which go to the pool named on its line (overhead for technical staff between assignments and their supervision, G&A for management and administration). Direct labour is DL = Σ n r u H_prod (n headcount, r raw rate). Labour of independent research and development and of bid and proposal work (IR&D / B&P) is taken out of the overhead categories' non-billable labour.

Fringe rate

The fringe pool holds the leave pay, the employer payroll taxes, health insurance, retirement and other benefits. On a total-labour base every productive labour dollar carries the same fringe rate, f = pool / (direct + non-billable + IR&D / B&P labour), and the fringe on non-billable labour follows that labour into the overhead and G&A pools. On a direct-labour base the whole pool is recovered on direct labour, f = pool / DL.

Overhead rate

The overhead pool holds the non-billable labour of the overhead categories (with its fringe on a total-labour fringe base) and the allowable overhead expenses: rent, utilities, software, depreciation, supplies. Its base is the direct labour, with or without fringe, of the contracts and of the IR&D / B&P projects, because those projects must carry their share of overhead (FAR 31.205-18; DCAAM 7641.90, Schedule E, note 1). The rate is o = pool / base. When part of the direct labour is performed at customer sites a second, off-site pool with its own expenses and a share of the supervision gives a lower off-site rate; the single blended rate is printed for comparison.

Material handling

Purchasing, receiving and subcontract administration may be pooled and allocated on direct materials, or on materials and subcontracts: m = pool / base.

G&A rate and the cost input base

The G&A pool holds the allowable general and administrative expenses, the non-billable labour of the G&A categories, and the IR&D / B&P costs: their labour, the overhead on that labour at the billed rate, and their other costs. FAR 31.205-18 allocates IR&D and B&P on the same base as G&A, and the DCAA model schedules carry them in the G&A pool. The base is one of the three cost input bases of 48 CFR 9904.410-50(d): total cost input (all costs except G&A: direct labour with fringe, overhead, materials, subcontracts, other direct costs, material handling), value-added cost input (total cost input less materials and subcontracts, for a business where those would distort the allocation), or a single element (direct labour dollars). The rate is g = pool / base.

Unallowable costs (FAR 31.205: interest, entertainment, contributions, bad debts, lobbying, alcoholic beverages and others) are excluded from the pools and so from the price. They are not removed from a base: FAR 31.203(d) requires every item that belongs in a base to bear its share of indirect cost whether or not it is allowable. The overhead in the cost input base is therefore the general-ledger overhead (allowable plus unallowable) less the overhead on IR&D / B&P labour at the general-ledger rate, exactly as Schedule E of the DCAA model incurred cost proposal computes it; the G&A that the unallowable overhead draws is not recovered, and the tool prints it.

Wrap rate

The wrap rate W is the price of one dollar of direct labour. Its form follows the structure. With overhead on direct labour plus fringe and G&A on a cost input base the factors multiply:

W = (1 + f)(1 + o)(1 + g)(1 + p)

with p the fee or profit rate. With overhead on direct labour dollars the labour burdens add, (1 + f + o)(1 + g)(1 + p); with a single-element G&A base the G&A rate adds as well, (1 + f + o + g)(1 + p) or ((1 + f)(1 + o) + g)(1 + p). The same rates can therefore describe very different prices, and two firms' rates can only be compared through their wrap rates. The billing rate of a category is its raw rate times W, and the table of loaded rates shows each step.

Facilities capital cost of money

Cost of money is an imputed cost of the capital tied up in facilities (48 CFR 9904.414; FAR 31.205-10). For each pool the cost-of-money rate set by the Secretary of the Treasury is multiplied by the net book value of the facilities allocated to the pool and divided by the pool's allocation base, which gives a factor per unit of base (Form CASB-CMF); a contract's cost of money is the factor times its share of the base. The cost of money on IR&D / B&P labour moves to the G&A pool, as in Schedule F of the DCAA model. For a fiscal year that spans two published rates the rates are weighted by months. Cost of money is added to the price after the fee, which is not computed on it (FAR 15.404-4(c)(3)).

Task price and contract types

The task's labour (hours by category at the raw rates), materials, subcontracts and other direct costs are burdened in the order of the structure: fringe, overhead, material handling, G&A, then fee and cost of money. The result is shown three ways. Cost-plus-fixed-fee (FAR 16.306): an estimated cost, reimbursed at actual allowable cost, and a fee fixed at award; FAR 15.404-4(c)(4)(i) limits that fee to 10 % of the estimated cost (15 % for experimental, developmental or research work). Firm-fixed-price: the same total as one price. Time-and-materials (FAR 16.601): fixed hourly rates that include wages, overhead, G&A and profit, which are the raw rates times the wrap rate rounded to the cent, with materials, subcontracts and other direct costs at cost with their indirect costs and no fee, so the time-and-materials price is lower by the fee on those costs.

Utilisation, break-even and the overhead budget

Scaling every utilisation by a factor k moves hours between direct labour and the pools: a lower k shrinks the base and swells the overhead and G&A pools, so the wrap rate rises steeply as utilisation falls. The chart plots W against the company utilisation (direct hours / productive hours) up to the point where the busiest category is fully billable or the non-billable overhead labour has shrunk to the budgeted IR&D / B&P labour. The break-even utilisation is the utilisation at which W equals the entered target, found by bisection, since W falls steadily with k. The inverse problem holds utilisation at the budget and solves for the overhead expense budget that gives the target wrap rate; when even a zero budget leaves W above the target, the tool says so.

Year-end true-up

Cost-reimbursement contracts are billed during the year at provisional billing rates and adjusted to the final rates after the year (FAR 42.704). The tool treats its budget rates as the billing rates, forms the actual rates from the entered actual pools and bases, and burdens the cost-type direct costs of the year with each set. The difference is the amount to be claimed from, or credited to, the Government. The effect of each rate is taken in sequence (fringe, overhead, material handling, G&A) so that the four effects add up to the total; a different order would divide the total differently among the rates but not change it.

Uncompensated overtime

When salaried staff are proposed at more than 40 hours a week, FAR 52.237-10 requires the adjusted hourly rate: the rate for a 40-hour week times 40, divided by the hours proposed (20.00 × 40 / 45 = 17.78 in the clause). Under total-time accounting the salary is distributed over all hours worked (DCAA Contract Audit Manual 6-410.4 lists the acceptable methods). The tool prints the adjusted raw and billing rates and the task price at them, holding the indirect rates at their budget values; in a firm that works such hours all year the bases and the rates themselves would be set on the total hours.

Checks

The library reproduces the two models printed in DCAAM 7641.90. Model incurred cost proposal (Figure 12): overhead 510,610 / 656,824 = 77.74 %, G&A 271,022 / 3,151,320 = 8.60 %, cost-of-money rate 5.156 % with factors 0.01558 and 0.00067, and the rates applied contract by contract in Schedule H. Model proposal (Figure 4): overhead 56.7 %, material handling 5.0 %, G&A 8.0 % on a total cost input of 3,994,060, and the price build-up 478,563 of labour to 1,032,065. An independent numpy and scipy script recomputes the default firm, seven structure variants, a two-pool case, the utilisation curve, the inverse problems and twenty random companies.

Default case

The default is an illustrative twelve-person engineering services firm, not a published example: 1,832 productive hours, 71.42 % utilisation, direct labour 794,208.64; fringe 38.66 % on total labour, overhead 27.24 % on direct labour plus fringe, material handling 3.00 %, G&A 26.75 % on total cost input, 8 % fee; wrap rate 2.4151 (2.4214 with cost of money). A task of 1,660 hours with 45,000 of other direct costs prices at 260,058.01 as cost-plus-fixed-fee or firm-fixed-price and 255,388.53 as time-and-materials. A target wrap rate of 2.30 needs 75.08 % utilisation, or an overhead expense budget of 103,402.94 in place of 185,000.

Limits

• One business unit, one fiscal year, at most two overhead pools; no service centres, no home-office allocation, no separate IR&D / B&P base.
• Whether a cost is allowable, and which base is equitable, are determinations under FAR Part 31 and the Cost Accounting Standards that the tool does not make; it applies the amounts and bases entered.
• The profit objective of a negotiated contract is set by FAR 15.404-4 and, in the Department of Defense, by the weighted guidelines (DD Form 1547); the tool applies an entered rate.
• The Treasury rate and the payroll-tax percentage are entered values; the defaults are illustrative.