Cash Flow — the BCWS curve, and the interest on a contractor's overdraft: 16-Civ-B8 Management of Construction, May 2018, Q5

Question 5: Cash Flow — the BCWS curve, and the 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.

Part (a) — the BCWS curve. BCWS, the budgeted cost of work scheduled (called planned value in current PMBOK usage), is the time-phased baseline budget: the project budget spread over the programme according to when each activity is scheduled to be performed. It is built by loading every activity in the schedule with its budgeted cost, distributing that cost across the activity's duration, and accumulating the result week by week. Plotted cumulatively against time it is the familiar S-curve of Figure 5.1: flat at the start while the site mobilises and only a few low-value activities are open; steep through the middle third, when the maximum number of trades are working concurrently and the expensive structural and mechanical activities run; and flattening again at the end, when the remaining work is finishing, commissioning and deficiency correction, all of which consume calendar time out of proportion to their value. Its purposes are threefold. It is the baseline against which the two other earned-value curves are read — schedule variance $SV = BCWP - BCWS$ and cost variance $CV = BCWP - ACWP$, so a project running behind shows its BCWP curve below the BCWS curve. It is the owner's cash-flow forecast, since progress certificates track the work performed. And it is the contractor's own planning tool, because the slope of the curve at any date is the rate at which resources and money must be available. A BCWS curve that is nearly straight, or that rises steeply from day one, is normally a sign that the cost loading has been spread evenly by default rather than derived from the schedule.

Figure 5.1 — typical BCWS (planned value) curve: cumulative budgeted cost against time, showing the characteristic S shape.

Part (b) — Given. Monthly invoices for work performed, a one-month payment lag, five percent retention held on each certificate and released with the final payment, and a one percent per month financing rate on the contractor's overdraft.

End of month	Invoice (CAD)	Retention held at 5 percent (CAD)	Payment received (CAD)
1	40,000	2,000	—
2	110,000	5,500	38,000
3	160,000	8,000	104,500
4	460,000	23,000	152,000
5	540,000	27,000	437,000
6	710,000	released	513,000
7	—	—	775,500
Total	2,020,000	—	2,020,000

Find. The payment received in each month, the cumulative cost and income curves, the peak overdraft, and the total interest charged on the money the contractor must borrow.

Approach. Build the receipt column from the invoice column by applying the one-month lag and the retention, then roll the overdraft forward month by month, charging one percent on the balance carried into each month before that month's spending and receipts are applied.

Part (b), step 1 — convert invoices into receipts. The invoice raised at the end of month $m$ is paid at the end of month $m+1$ less five percent, so$$R_{m+1} = 0.95\,I_m$$which gives $38{,}000$, $104{,}500$, $152{,}000$, $437{,}000$ and $513{,}000$ at the ends of months 2 to 6. The retention accumulated on the first five invoices is$$\textstyle\sum 0.05\,I_m = 2{,}000 + 5{,}500 + 8{,}000 + 23{,}000 + 27{,}000 = \$65{,}500$$and it is released with the final payment, so month 7 brings $710{,}000 + 65{,}500 = \$775{,}500$. The receipts total $\$2{,}020{,}000$, exactly the invoice total — retention delays money, it does not remove it, and that identity is the first check on the table.
Part (b), step 2 — set up the overdraft recursion. The contractor pays for the work as it is done and is reimbursed a month later, so the shortfall is carried on an overdraft. Charging interest on the balance brought into each month,$$N_m = N_{m-1}(1 + i) + E_m - R_m, \qquad i = 0.01 \text{ per month}$$where $E_m$ is the cost incurred in month $m$ and $R_m$ the cash received. With no separate cost data on the paper, the invoiced value is taken as the cost of the work performed in that month, which is the standard reading of this question.
Part (b), step 3 — roll the overdraft forward. Month 1 carries no opening balance, so no interest, and closes at $\$40{,}000$. Month 2 is charged $0.01 \times 40{,}000 = \$400$ and closes at $40{,}000 + 400 + 110{,}000 - 38{,}000 = \$112{,}400$; month 3 at $0.01 \times 112{,}400 = \$1{,}124.00$ closing at $\$169{,}024.00$; and so on through the table below. The overdraft peaks at the end of month 6:$$N_{\max} = \boxed{\$789{,}366.40 \text{ at the end of month 6}}$$which is 39 percent of the contract value — the number that sizes the contractor's line of credit.
Part (b), step 4 — total the interest. Adding the monthly charges,$$\textstyle\sum I_m = 400 + 1{,}124.00 + 1{,}690.24 + 4{,}787.14 + 5{,}865.01 + 7{,}893.66 = \boxed{\$21{,}760.06}$$The six charges above are each rounded to the cent and so add to $\$21{,}760.05$ as printed; the boxed figure is the total of the unrounded charges, and it is that figure the closing-balance identity must reproduce. Because the receipts exactly repay the costs, the balance left standing after the month-7 payment must be the accumulated financing charge and nothing else — and it is, at $\$21{,}760.06$. That identity is the self-check on the whole recursion. The charge is 1.08 percent of the contract value, which is what the contractor must carry in the markup purely to finance the payment lag and the retention.

Figure 5.2 — cumulative cost and cumulative income. The vertical gap between the curves is the overdraft the contractor must finance; it is widest at the end of month 6 and closes only when the retention is released in month 7.

Overdraft roll-forward at 1 percent per month (CAD)
Month	Cost incurred	Cash received	Interest charged	Closing overdraft
1	40,000	—	0.00	40,000.00
2	110,000	38,000	400.00	112,400.00
3	160,000	104,500	1,124.00	169,024.00
4	460,000	152,000	1,690.24	478,714.24
5	540,000	437,000	4,787.14	586,501.38
6	710,000	513,000	5,865.01	789,366.40
7	—	775,500	7,893.66	21,760.06
Total	2,020,000	2,020,000	21,760.06	21,760.06 (= the interest)

Check: the interest convention and the cost basis. Interest is charged here on the balance brought forward into each month, which is the convention that makes the closing balance equal the total interest exactly. Charging instead on the closing balance of each month raises the total only to $\$21{,}977.66$; the convention should be stated on an exam script either way. The second assumption is that the invoiced value equals the cost of the work in that month, since the paper gives no separate cost column. If the invoices instead carried a ten percent markup, the costs would be about nine percent lower, the overdraft would peak at $\$603{,}366$ and the interest would fall to $\$17{,}536$ — the method is unchanged.

Topic. Earned-value baselines (BCWS) and contractor cash flow: the overdraft created by a payment lag plus retention, and the interest it costs.

Key relations. $SV = BCWP - BCWS$, $CV = BCWP - ACWP$, $CPI = BCWP/ACWP$; receipts $R_{m+1} = (1-r)I_m$ with retention rate $r$; overdraft recursion $N_m = N_{m-1}(1+i) + E_m - R_m$; total financing charge $\sum i\,N_{m-1}$, which equals the closing balance whenever $\sum E_m = \sum R_m$.

Why this works. A construction contract is a lending arrangement in disguise: the contractor buys labour, plant and material this month and is repaid next month, less a slice held back as security. The area between the cumulative cost and cumulative income curves is therefore money the contractor has lent the owner, and the recursion is simply that loan balance rolled forward with interest. Two features of the contract set its size — the payment lag scales the gap with the monthly burn rate, so it bites hardest when production peaks, while retention adds a slowly growing floor that is not released until the end. That is why the peak overdraft here occurs at month 6, when the burn rate is highest and every retention is still held, and why substantial performance and the statutory holdback release provisions matter so much to a contractor's solvency.

Common pitfall. Forgetting that the retention is released at the end, which leaves the accounts unbalanced and destroys the closing-balance check; applying the five percent to the cumulative invoiced total rather than to each certificate; and charging interest in month 1, when nothing has yet been borrowed.

Source. Halpin & Senior, Construction Management, 4th ed., Ch. 14–15 (project cash flow, overdraft profiles and financing); Hendrickson, Project Management for Construction, 2nd ed., Ch. 12 (cost control, monitoring and earned value); PMBOK Guide, 6th ed., §7.4 (control costs, earned-value analysis).

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

Question 5: Cash Flow — the BCWS curve, and the interest on a contractor's overdraft (20 marks)