07-Str-B2 · May 2018

Question 5 of 6: Cash Flow — the BCWS curve, and interest on a contractor's overdraft

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

Notes on this paper

Paper format: National Exams, May 2018 — 07-Str-B2 Management of Construction. Three hours, closed book, one approved Casio or Sharp calculator permitted. Six questions of equal value (20 marks each); any five constitute a complete paper and only the first five that appear in the answer book are marked. All six are worked below so the paper serves as a complete revision set whichever five a candidate elects.

Reference texts: Hegazy, T., Computer-Based Construction Project Management (Prentice Hall) — precedence (activity-on-node) networks with start-to-start lags, forward and backward passes, total and free float, the late bar chart, and contractor cash-flow and overdraft analysis; these chapters carry Questions 1 and 5. Hendrickson, C. & Au, T., Project Management for Construction (2nd ed., Carnegie Mellon) — Chapter 5 (cost estimation and unit-cost data), Chapter 8 (bidding and contract award), Chapter 10 (fundamental scheduling procedures), Chapter 11 (advanced scheduling with lags) and Chapter 12 (cost control and financing of constructed facilities). Halpin, D.W. & Senior, B.A., Construction Management (4th ed., Wiley) — quantity take-off, crew productivity, bidding strategy, bonding and construction safety management. Peurifoy, R.L. & Schexnayder, C.J., Construction Planning, Equipment and Methods (9th ed., McGraw-Hill) — excavation production and the physical determinants of backhoe daily output, behind Question 2. R.S. Means, Building Construction Cost Data (annual) — the anatomy of a unit-price line: crew, daily output, unit, and bare material / labour / equipment / total columns. Sullivan, W.G., Wicks, E.M. & Koelling, C.P., Engineering Economy (17th ed., Pearson) — Chapters 5 and 6, present-worth analysis and the repeatability (least common multiple of lives) assumption for alternatives with unequal lives, used in Question 4. Canadian Construction Documents Committee, CCDC 2 — Stipulated Price Contract (2020), CCDC 220 Bid Bond, CCDC 221 Performance Bond and CCDC 222 Labour and Material Payment Bond, with the BC Builders Lien Act holdback provisions and the Master Municipal Construction Documents (MMCD) — the Canadian tendering and payment machinery behind Questions 3 and 5. WorkSafeBC Occupational Health and Safety Regulation (Parts 8, 11, 12, 13, 18 and 33), CSA Z259 fall-protection and CSA Z94.4 respirator series, and the Transportation Association of Canada Manual of Uniform Traffic Control Devices for Canada — the Canadian rule set behind Question 6.

Check — how the two printed figures on page 2 were read. Network (Question 1): nine activity boxes with seven links — A → D carrying the printed SS = 3 lag (the line leaves A's top-left corner, runs across the top of the sheet and drops into D's top-left corner), then D → H, B → E, B → F, C → G, F → I and G → I, all finish-to-start with zero lag. No further arrows are drawn; A, B and C are the only start activities and E, H and I the only finish activities. Foundation plan (Question 2): an 80 m × 70 m rectangle with a rectangular notch 25 m deep cut into the top edge, one internal trench running the full width 20 m up from the bottom (the 50 m and 20 m dimensions meet on it), and one internal trench dropping from the bottom of the notch to that line. The notch width is not dimensioned on the paper, and Step 1 below shows the total trench length does not depend on it, so nothing is assumed. All plan dimensions are taken as trench centrelines; reading them instead to the outside face of the trench would shorten the total by about 1.6 per cent and change no conclusion.

Question 5: Cash Flow — the BCWS curve, and interest on a contractor's overdraft (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.

(a) The BCWS curve

BCWS — the budgeted cost of work scheduled, now more often called planned value — is the cumulative budget for the work the baseline schedule says should have been performed by any given date. It is obtained by loading each activity in the CPM schedule with its budget, spreading that budget across the activity's duration, and accumulating the result month by month from the project start to the budget at completion.

Typical BCWS (planned value) curve. The slope at any point is the planned monthly expenditure, so the S shape reflects the build-up, peak and run-down of crews on site.

The characteristic shape is an S: shallow at the beginning, steep through the middle, and flattening again at the end. That shape is a direct consequence of how construction resources build up. In the opening period only a few activities are open — mobilisation, site set-up, survey, early excavation — so few crews are on site and the spend rate is low. As the work opens out, many activities run in parallel at full crew strength and the monthly spend reaches its maximum, which is the steep central portion; the slope of the curve at any point is the planned monthly expenditure, so the middle of the project is where the owner's financing requirement is growing fastest. Towards the end the remaining work is finishing trades, testing, commissioning and deficiency correction, carried out by small crews at low value, so the curve flattens and asymptotes to the budget at completion.

Its practical use is as the baseline against which the other two earned-value curves are read. Plotting BCWP (budgeted cost of work performed, or earned value) below BCWS at a reporting date shows the project is behind schedule by that value, and the schedule variance is $SV=BCWP-BCWS$; plotting ACWP (actual cost of work performed) above BCWP shows a cost overrun, $CV=BCWP-ACWP$. Because the BCWS curve is derived from the schedule, an early-start version and a late-start version can be drawn, and the envelope between them is the float the project holds in cash terms. Its second use is financing: the owner reads the curve to arrange draw-downs, and the contractor uses the same shape, shifted by the payment lag, to size the working capital required — which is exactly the calculation part (b) asks for.

(b) Interest on the contractor's overdraft

Given. Six monthly invoices of $40,000, $110,000, $160,000, $460,000, $540,000 and $710,000 at the ends of months 1 to 6; each invoice paid at the end of the following month less 5 per cent retention; all retention released with the final payment at the end of month 7; overdraft interest 1 per cent per month.

Find. The payment received each month, the running overdraft, the peak cash requirement, and the total interest charged over the project.

Approach. Take the invoice for each month as the value of work done in that month and therefore as the cash the contractor has already had to spend, schedule the receipts one month in arrears net of retention, and roll a monthly overdraft balance forward with interest charged on the opening balance.

Build the receipt schedule. The invoice raised at the end of month $t$ is paid at the end of month $t+1$ with five per cent held back, so $P_{t+1}=0.95\,E_t$ for $t=1\ldots6$. The withheld amounts accumulate to $$R=0.05\sum_{t=1}^{6}E_t=0.05\times2{,}020{,}000=\$101{,}000$$ and are released with the month-7 payment, which is therefore $0.95(710{,}000)+101{,}000=\$775{,}500$. Nothing is received in month 1, which matches the dash printed in the table.
Set up the overdraft recursion. Interest is charged on the balance the contractor carried into the month, so with $i=0.01$ per month, $$N_t=N_{t-1}(1+i)+E_t-P_t,\qquad N_0=0$$ where $E_t$ is the cash out during month $t$ and $P_t$ the cash in at its end. Interest accrued in month $t$ is $I_t=i\,N_{t-1}$, which is zero in month 1 because the contractor starts with no borrowing.
Roll the table forward. Month 1: $N_1=0+40{,}000-0=\$40{,}000$. Month 2: $I_2=0.01(40{,}000)=\$400$ and $N_2=40{,}400+110{,}000-38{,}000=\$112{,}400$. Month 3: $I_3=\$1{,}124$ and $N_3=113{,}524+160{,}000-104{,}500=\$169{,}024$. Month 4: $I_4=\$1{,}690$ and $N_4=170{,}714+460{,}000-152{,}000=\$478{,}714$. Month 5: $I_5=\$4{,}787$ and $N_5=483{,}501+540{,}000-437{,}000=\$586{,}501$. Month 6: $I_6=\$5{,}865$ and $N_6=592{,}366+710{,}000-513{,}000=\$789{,}366$.
Identify the peak cash requirement. The balance rises monotonically to the end of month 6, immediately before the final payment lands: $$N_{\max}=\boxed{\$789{,}366\ \text{at the end of month }6}$$ This is the working capital the contractor must have arranged — an overdraft facility, a line of credit or equity — before starting, and it is nearly 40 per cent of the whole contract value.
Close out month 7 and total the interest. In month 7 no further work is done, interest of $I_7=0.01(789{,}366)=\$7{,}894$ accrues and the final payment of $775,500 arrives: $$N_7=797{,}260-775{,}500=\$21{,}760$$ Summing the monthly charges gives the same figure, $$\sum I_t=0+400+1{,}124+1{,}690+4{,}787+5{,}865+7{,}894=\boxed{\$21{,}760\ \text{total interest}}$$
Check the result against the closing balance. Total cash out over the project is $2,020,000 and total cash received is $0.95(2{,}020{,}000)+101{,}000=\$2{,}020{,}000$ — identical, because retention is withheld and then released in full. The closing balance must therefore be exactly the accumulated interest, and it is: $21,760 by both routes. That agreement is the arithmetic check on the whole table, and it is worth writing down in the exam because it catches a single mis-keyed row instantly.

Contractor's cash-flow curves. The cumulative cash-out staircase always leads the cumulative cash-in staircase; the vertical gap between them is the money the contractor is financing, and it peaks at the end of month 6 immediately before the final payment.

Check — how the invoice column is read. The table pairs an invoice at month $t$ with a receipt at month $t+1$, and both columns are per-month amounts rather than running totals; the six invoices are therefore the monthly amounts and sum to $2,020,000 of certified work. The paper gives no mark-up, so the contractor's cash outflow during a month is taken equal to the value invoiced for that month's work, which is the standard simplification when only a billing schedule is supplied. This makes the interest a pure financing loss with no profit to offset it — the closing balance equalling the accumulated interest confirms the two totals cancel exactly. If a mark-up were known, the outflows would be reduced accordingly and both the peak overdraft and the interest would fall. Read instead as a running (cumulative) total, the column would imply monthly work of $40,000, 70,000, 50,000, 300,000, 80,000 and 170,000, a peak overdraft of about $309,700 and total interest of about $7,894; the per-month reading is adopted because the column is headed simply “Invoice” and each invoice is paid in its own right the following month.

Question 5(b) — monthly cash position, all amounts in dollars
End of month	Cash out (work done)	Cash in (payment)	Interest charged	Overdraft balance
1	40,000	—	0	40,000
2	110,000	38,000	400	112,400
3	160,000	104,500	1,124	169,024
4	460,000	152,000	1,690	478,714
5	540,000	437,000	4,787	586,501
6	710,000	513,000	5,865	789,366
7	—	775,500	7,894	21,760
Total	2,020,000	2,020,000	21,760	peak 789,366

Topic. The earned-value baseline curve, and contractor cash-flow analysis with a payment lag, retention and overdraft interest.

Key relations. BCWS is the schedule-loaded cumulative budget, with $SV=BCWP-BCWS$ and $CV=BCWP-ACWP$. Payment schedule $P_{t+1}=(1-r)E_t$ with retention $R=r\sum E_t$ released at completion. Overdraft roll-forward $N_t=N_{t-1}(1+i)+E_t-P_t$, interest $I_t=i\,N_{t-1}$, and the closing check $N_{\text{final}}=\sum I_t$ when total receipts equal total disbursements.

Why this works. A contractor is paid for work already performed, so the cash-out curve always leads the cash-in curve, and the vertical gap between them at any date is the money the contractor has funded from its own resources. Retention widens that gap by a further five per cent for the whole project life, and the one-month certification lag shifts the whole receipt curve to the right, so the two mechanisms compound. Charging interest on the opening balance rather than the closing one is the conservative and conventional treatment because the money is drawn at the start of the period in which the work is done. The identity between the closing balance and the summed interest is not a coincidence: when receipts and disbursements are equal in total, the only money left owing is what the financing itself cost.

Common pitfall. Candidates commonly forget that retention is withheld from every payment and released only once, and so pay 95 per cent in month 7 as well without adding the accumulated holdback — which leaves a phantom $101,000 shortfall. Others charge interest on the closing balance, or take the peak overdraft as the largest single monthly outflow rather than the largest cumulative gap. On part (a), a frequent error is drawing the BCWS curve as a straight line, which implies uniform monthly spend and misses the whole point of the question.

Source. Hegazy, Computer-Based Construction Project Management, chapters on project cash flow, the S-curve and earned-value progress measurement; Hendrickson & Au, Project Management for Construction, Chapter 7 (financing of constructed facilities) and Chapter 12 (cost control, monitoring and accounting); CCDC 2 (2020) Part 5 and the BC Builders Lien Act holdback provisions for the Canadian retention rules.

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