Project Control — expense S-curve, owner payments, overdraft and interest: 16-Civ-B8 Management of Construction, December 2018, Q3

Question 3: Project Control — expense S-curve, owner payments, overdraft and interest (20 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Given. The cumulative budgeted expense of a six-month project, read off the printed S-curve, together with the commercial terms that govern how money comes back in.

Given data — cumulative budget and commercial terms
Item	Value
Cumulative budgeted expense, months 1 to 6	$29,000; $40,000; $54,000; $86,000; $112,000; $127,000
Contractor's markup on cost	10 %
Owner's retention (holdback)	5 % of each progress claim, released with the last payment
Owner's payment delay	1 month after the month in which the work is done
Interest on borrowed money	12 % per annum, i.e. 1 % per month
Project duration	6 months of work; final payment in month 7

Find. (a) the cumulative expense curve plotted against the cumulative owner payments actually received; (b) the total interest chargeable on the money the contractor must borrow, and the overdraft limit the contractor must arrange.

Approach. Differentiate the cumulative budget to get each month's expense, apply the markup to obtain the monthly invoice, withhold the retention and shift each payment one month to obtain the receipts, then run a month-by-month cash ledger charging interest on the balance brought forward.

Recover the monthly expenses from the cumulative curve. The S-curve is cumulative, so each month's spend is the first difference: $$e_m = C_m - C_{m-1}$$ which gives $29,000, $11,000, $14,000, $32,000, $26,000 and $15,000 for months 1 to 6, summing to $127,000. The shape is the ordinary S: a heavy mobilisation month, a quiet pair of months while the work is set up, the steep central months 4 and 5 when production peaks, and a tapering finish.
Convert expense to the value of work billed. The contractor claims cost plus a 10 % markup, so the monthly invoice is $$b_m = e_m\,(1+0.10)$$ giving $31,900, $12,100, $15,400, $35,200, $28,600 and $16,500. The contract value is therefore $$V = 127{,}000 \times 1.10 = \$139{,}700$$ of which $12,700 is the gross markup the contractor expects to keep before financing costs.
Apply the retention and the payment delay. The owner holds back 5 % of every claim and pays the remaining 95 % one month in arrears, so the cash arriving in month $m$ is $$r_m = 0.95\,b_{m-1}$$ The accumulated holdback, $$R = 0.05 \times 139{,}700 = \$6{,}985$$ is released with the final payment. Month 1 therefore brings in nothing at all, months 2 to 6 bring in $30,305, $11,495, $14,630, $33,440 and $27,170, and month 7 brings $15,675 of final progress payment plus the $6,985 holdback, that is $22,660. The receipts total $139,700, matching the contract value exactly — the check that the retention has been released and nothing has been double-counted.

Figure 3.1 — (a) the required plot: cumulative expenses (the given budget S-curve), the cumulative value of work billed at cost plus 10 % markup, and the cumulative owner payments actually received. The vertical gap between the expense curve and the receipt curve is the money the contractor must finance; it is widest at the end of month 4.

Run the cash ledger. Interest is charged on the balance brought forward from the previous month, and then the month's expenses go out and the month's receipt comes in: $$B_m = B_{m-1} - I_m - e_m + r_m,\qquad I_m = i\,\max\left(0,\,-B_{m-1}\right),\qquad i = \frac{12\%}{12} = 1\%\ \text{per month}$$ where the interest term applies only while the balance is negative. Month 1 opens at zero, so no interest is charged; the balance closes at −$29,000. Month 2 is charged 1 % of $29,000, that is $290, spends $11,000 and receives $30,305, closing at −$9,985. Continuing month by month produces the ledger below.

Contractor's cash ledger — all figures in dollars
Month	Balance b/f	Interest at 1 %	Expense	Owner payment	Balance c/f
1	0.00	0.00	29,000	0	−29,000.00
2	−29,000.00	290.00	11,000	30,305.00	−9,985.00
3	−9,985.00	99.85	14,000	11,495.00	−12,589.85
4	−12,589.85	125.90	32,000	14,630.00	−30,085.75
5	−30,085.75	300.86	26,000	33,440.00	−22,946.61
6	−22,946.61	229.47	15,000	27,170.00	−11,006.07
7	−11,006.07	110.06	0	22,660.00	+11,543.87
Total	—	1,156.13	127,000	139,700.00	—

(b) Interest chargeable and the overdraft limit. Summing the interest column, $$\sum I = 290.00+99.85+125.90+300.86+229.47+110.06=\boxed{\$1{,}156.13}$$ (The ledger is carried at full precision and only displayed to the cent, so adding the six rounded charges exactly as printed gives $1,156.14; the exact total is $1,156.13 and that is the figure the closing identity below uses. A one-cent rounding residue in a compounded column is normal and is not an error — but it is worth stating rather than leaving a reader to find it.) The deepest point of the ledger, at the end of month 4, sets the facility the contractor must have in place: $$\boxed{\text{Overdraft limit required} \approx \$30{,}100}$$ The ledger proves itself. Receipts exceed expenses by exactly the markup, $12,700, so the balance standing after the final payment must equal the markup less the financing cost: $$11{,}543.87 = 12{,}700.00 - 1{,}156.13 \;\checkmark$$ Financing has therefore consumed 9.1 % of the gross markup, leaving a net profit of $11,543.87 on a $139,700 contract — about 8.3 % of the contract value.
Interpret the result for practice. Two features of the profile matter more than the arithmetic. The peak overdraft of $30,086 occurs at the end of month 4, not at the end of the job, because month 4 is the heaviest spending month while the receipt arriving in it is only 95 % of the very light month-3 invoice; the contractor must arrange the facility before that month, not discover the need during it. And the 5 % holdback does not reduce what the contractor is ultimately paid — it only delays it — yet that delay costs real money: re-running the same ledger with no retention gives $977.20 of interest and a $29,000 peak, so the holdback adds about $179 of interest and $1,086 to the required facility.

Figure 3.2 — closing cash balance at the end of each month. The deepest bar, −$30,085.75 at the end of month 4, is the overdraft limit that must be arranged; the account only turns positive when the holdback is released in month 7.

Check: assumptions stated explicitly. (i) The printed curve is read as the contractor's budgeted expense, so the markup is added to it to obtain what the owner is billed; the alternative reading, in which the curve is already the contract value, would make the expenses $127,000/1.10 and reduce every figure by about 9 %. The question's own wording, "the S-curve of expenses against the expected owner payments", supports the reading used. (ii) Expenses are treated as paid at the end of each month and interest is charged on the balance brought forward, which is the convention that makes the closing balance equal markup less interest exactly. (iii) The final payment, including release of the holdback, is taken in month 7, one month after the last month of work, consistent with the stated one-month delay.

Final results — Question 3
Quantity	Result
Total expense (cost)	$127,000
Contract value (cost + 10 % markup)	$139,700
Retention held and released in month 7	$6,985
Owner payments, months 2 to 7	$30,305; $11,495; $14,630; $33,440; $27,170; $22,660
Interest chargeable on borrowed money	$1,156.13
Overdraft limit required	$30,085.75, at the end of month 4 (arrange about $32,000)
Net cash after the final payment	$11,543.87 = $12,700 markup − $1,156.13 interest
Financing cost as a share of markup	9.1 %

Topic. Contractor cash flow and project financing: the expense S-curve, progress billing with markup and holdback, and the overdraft profile.

Key relations. Monthly expense $e_m = C_m - C_{m-1}$; monthly claim $b_m = e_m(1+\text{markup})$; receipt $r_m = (1-\text{retention})\,b_{m-1}$ with the accumulated retention released at the end; ledger $B_m = B_{m-1} - i\max(0,\,-B_{m-1}) - e_m + r_m$; peak overdraft $= -\min_m B_m$; and the closing identity, final balance $=$ total markup $-$ total interest.

Why this works. A contractor is a lender to the owner for the duration of the job. Work is performed and paid for before it is claimed, the claim is assessed and paid a month later, and part of it is held back until the end — so the cash line always sits below the cost line, and the vertical distance between the two is money the contractor has borrowed. Charging interest on the balance brought forward reproduces exactly what a bank does with an operating line, and the closing identity is what makes the whole ledger auditable: because receipts eventually total the contract value and expenses total the cost, whatever remains after the last payment must be the markup less the interest, to the cent. If it is not, an entry has been mis-timed.

Common pitfall. Treating the holdback as lost revenue rather than delayed revenue — it is paid in full at the end, and its true cost is only the interest on the delay. A second is placing the peak overdraft at the end of the job: the deepest point is set by the mismatch between the heaviest spending month and the light receipt that happens to arrive in it, which here is month 4, well before completion. A third is forgetting that the delay applies to the whole claim, so month 1 generates no cash at all and the first month is always financed in full.

Source. Halpin & Senior, Construction Management, 4th ed., Ch. 15–16 (Project Cash Flow, Financing); Hendrickson, Project Management for Construction, 2nd ed., Ch. 12 (Cost Control, Monitoring and Accounting).

Question 3 of 6: Project Control — expense S-curve, owner payments, overdraft and interest

Question 3: Project Control — expense S-curve, owner payments, overdraft and interest (20 marks)