07-Str-B2 · May 2017

Question 5 of 6: Cash Flow — the S-curve, overdraft interest and the peak cash requirement

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

Question 5: Cash Flow — the S-curve, overdraft interest and the peak cash requirement (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 typical S-curve

Given and Find. No data: the part asks for a sketch of the cumulative cost-versus-time curve of a typical project and an explanation of why it takes that shape.

The S-curve is the plot of cumulative cost, cumulative work-hours or cumulative percent complete against time, obtained by integrating the period-by-period expenditure of the time-scaled schedule. It takes its name from its shape, which is flat at both ends and steep in the middle. Three phases explain that shape. Early, the project is mobilising: few crews are on site, the work in progress is site establishment, excavation and procurement, and expenditure accrues slowly. In the middle, most trades are working concurrently at full resource, the bulk of the permanent work is being placed, and the expenditure rate reaches its maximum — the curve is at its steepest, and its slope there is the project's peak burn rate, which sets the peak demand on both cash and supervision. Late, the work turns into finishing, testing, commissioning and deficiency correction; the remaining quantities are small, crews demobilise, and the curve flattens as it approaches 100 %. The characteristic long tail is worth noticing on its own account: the last few percent of completion routinely takes a disproportionate share of the calendar because it consists of many small, sequential, inspection-dependent items.

The curve is used in four ways. As a budget baseline, the planned S-curve gives the expected cumulative cost at any date, so plotting the actual curve against it shows immediately whether the project is spending ahead of or behind plan. Combined with earned value it separates the two possible causes: the horizontal gap between the earned-value curve and the planned curve is a schedule variance in time, the vertical gap between earned value and actual cost is a cost variance. As a cash-flow forecast, the contractor's S-curve of cost and the owner's S-curve of payment together give the funding requirement that Question 5(b) quantifies. As a resource forecast, its slope gives the manpower histogram. And as a bid and monitoring tool, a family of S-curves from past projects of the same type gives a normative envelope; an actual curve that leaves the envelope early is a leading indicator that the plan or the resourcing is wrong. A final caution: because the curve is flat at both ends, small deviations early look negligible on the plot even when they represent a large proportional slippage, which is why the S-curve should be read alongside the critical-path schedule and not instead of it.

Part (b) — interest on borrowed money and the peak cash requirement

Given. The printed chart, digitised as described in the disclosure at the top of this paper. All amounts are in thousands of dollars; the financing rate is $i = 1\,\%$ per month.

Find. The total interest charged on the borrowed money over the seven months, the largest amount of cash the contractor must have available at any time, and a brief statement of how a down payment would change both.

[Figure not reproduced: The printed cash-flow diagram redrawn from the digitised readings. The smooth curve is cumulative cash out (the contractor's S-curve of expenditure); the staircase is cumulative payment received, each riser being a monthly progress certificate paid one month in arrears. The vertical gap between them. See the official exam paper.]

Approach. Work month by month down an overdraft table. Interest for a month is charged at 1 % on the overdraft carried into that month; the closing balance is the opening balance plus that interest plus the month's expenditure less the month's receipt. The sum of the interest column is the finance charge, and the largest closing balance is the peak cash requirement.

1. Set up the recursion. Writing $N_t$ for the overdraft at the end of month $t$, $E_t$ for the expenditure in month $t$ and $P_t$ for the payment received in month $t$: $$I_t = i \, N_{t-1}, \qquad N_t = N_{t-1} + I_t + E_t - P_t, \qquad N_0 = 0, \quad i = 0.01$$ Charging interest on the opening balance is the convention used for a construction overdraft, where the bank accrues on the balance outstanding through the period; it is also the conservative reading, since the month's own expenditure is spread through the month rather than incurred on day one.
2. Months 1 to 3 — the shallow start. Nothing is owed at the outset, so the first month attracts no interest and the balance is simply the first month's spend: $$N_1 = 0 + 0 + 4.0 - 0 = 4.0$$ $$I_2 = 0.01(4.0) = 0.040, \qquad N_2 = 4.0 + 0.040 + 7.5 - 4.0 = 7.540$$ $$I_3 = 0.01(7.540) = 0.0754, \qquad N_3 = 7.540 + 0.0754 + 4.0 - 8.5 = 3.115$$ The balance falls in month 3 because the payment for month 2's work, 8.5, exceeds the modest month-3 spend of 4.0.
3. Month 4 — the peak. Month 4 is where the S-curve turns steep: 29.5 of expenditure lands while the certificate being paid is still for month 3's much smaller volume of work. $$I_4 = 0.01(3.115) = 0.0312, \qquad N_4 = 3.115 + 0.0312 + 29.5 - 4.0 = 28.647$$ $$\boxed{N_{\max} = \$28{,}647 \ \text{at the end of month } 4}$$ This is the highest amount of cash needed, and it is the number that determines the size of the credit facility the contractor must arrange before starting the job.
4. Months 5 to 7 — recovery. The large certificate of 31.0 in month 5 pulls the balance back sharply, the balance rises once more in month 6 as the final push of work is executed ahead of its certificate, and the final payment in month 7 clears the account and leaves the contractor in credit: $$I_5 = 0.2865, \qquad N_5 = 28.647 + 0.286 + 9.0 - 31.0 = 6.933$$ $$I_6 = 0.0693, \qquad N_6 = 6.933 + 0.069 + 17.5 - 10.0 = 14.502$$ $$I_7 = 0.1450, \qquad N_7 = 14.502 + 0.145 + 0 - 22.5 = -7.853$$
5. Total interest. Summing the interest column: $$\sum I_t = 0 + 0.040 + 0.0754 + 0.0312 + 0.2865 + 0.0693 + 0.1450 = 0.6474 \ \text{thousand}$$ $$\boxed{\text{interest charged} = \$647}$$ The complete overdraft table is set out below. As a check on the whole calculation, the closing credit balance of 7.853 equals the contract sum less the cost less the interest, $80.0 - 71.5 - 0.647 = 7.853$, so the project's profit is $7,853 after financing — against a gross margin of $8,500, meaning the finance charge consumes about 7.6 % of the profit.

   Month	Opening balance	Interest at 1 %	Expenditure	Payment	Closing balance
   1	0	0	4.0	0	4.000
   2	4.000	0.040	7.5	4.0	7.540
   3	7.540	0.075	4.0	8.5	3.115
   4	3.115	0.031	29.5	4.0	28.647
   5	28.647	0.286	9.0	31.0	6.933
   6	6.933	0.069	17.5	10.0	14.502
   7	14.502	0.145	0	22.5	−7.853
   Total		0.647	71.5	80.0

   All figures in thousands of dollars.
6. Effect of a down payment. A down payment, or mobilisation advance, is a sum paid by the owner at the start of the contract and recovered from later certificates. Because interest is charged on the balance outstanding, money received earlier reduces every subsequent balance by the same amount and therefore reduces the interest on all of them. Taking a 10 % advance, $8,000 received at month 0 and recovered from the final certificate, and re-running the same recursion, the interest falls from $647 to $$\boxed{\sum I_t = \$267 \ \text{with a } 10\,\% \ \text{advance, a saving of } \$380}$$ and the peak overdraft falls from $28,647 to $20,500, so the credit facility needed shrinks by roughly the amount of the advance. Three points complete the discussion. The advance also removes the front-end financing risk that makes small contractors decline large jobs, which is why public owners use it to widen the bidder pool. It is normally secured — by an advance-payment bond or a letter of credit, and recovered by instalments deducted pro rata from progress certificates — because the owner is otherwise unsecured for the advance. And it is only one of several levers on the same quantity: shortening the certification and payment cycle, invoicing promptly and completely, negotiating supplier credit terms that match the payment cycle, and front-end loading the schedule of values all reduce the same overdraft area, while retainage works in the opposite direction by holding back a percentage of every certificate.