S-Curve, Project Cash-Flow Financing and Interest: 24-Bld-A3 Construction Engineering, Undated paper, Q2

Question 2: S-Curve, Project Cash-Flow Financing 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.

(a) The typical S-curve

Given. A generic construction project's cumulative cost (or percent-complete) plotted against time follows a repeatable "S" shape, independent of project size.

Find. The shape of the curve and the physical reason for each of its three segments.

Fig. Q2-1 — typical cumulative-cost S-curve.

The curve is flat and slow at the start while mobilization, permits, submittals and early site/foundation work generate low weekly expenditure; it steepens through the middle of the project as multiple trades work concurrently at peak production; and it flattens again near completion as work narrows to finishing trades, punch-list items and demobilization. The same S-shape is why the project's financing need (Part b) also builds slowly, peaks mid-project, and tapers off.

(b) Financing the cost–revenue gap

Given. The project's cumulative cash-out (S-curve) and cumulative payment-received (a stepped curve, since progress payments are received periodically) were read from the source cash-flow diagram at each month-end.

Month-end cumulative values read from the source diagram ($ thousands)
Month	1	2	3	4	5	6	7
Cash out (cum.)	3	12	16	46	55	72	73
Payment received (cum.)	0	4	13	17	49	58	80

Fig. Q2-2 — cumulative cash-out (S-curve, blue) and cumulative payment-received (step function, red). The vertical gap is the amount financed at any time; it is largest just before month 5, right before the big progress payment lands.

Find. The peak amount of cash the contractor must finance, and the total interest at 1.5 %/month.

Approach. Take the outstanding balance (cash out minus payment received) at each month-end; the peak financing need is the largest gap between the two curves (which occurs just before a payment step, not after); total interest is estimated as 1.5 % of the outstanding balance carried during each month, summed over the months a balance is owed.

Month-end outstanding balance. $Balance(m) = CashOut(m) - PaymentReceived(m)$: month 1 → $3-0=3$; month 2 → $12-4=8$; month 3 → $16-13=3$; month 4 → $46-17=29$; month 5 → $55-49=6$; month 6 → $72-58=14$; month 7 → $73-80=-7$ (the project is now in surplus — the final payment overshoots the small remaining cost).
Peak amount of cash needed. Because payments arrive as discrete steps while cost accrues continuously, the largest gap occurs an instant before each step, i.e. $CashOut(m) - PaymentReceived(m-1)$. Checking all seven months, the maximum is at month 5: $CashOut(5) - PaymentReceived(4) = 55 - 17 = 38$. $$\boxed{\text{Highest amount of cash needed} \approx \$38{,}000, \text{ occurring just before the month-5 progress payment}}$$
Total interest at 1.5%/month. Charging 1.5 % on the balance carried during each month that a balance is owed (months 1–6; month 7 is already in surplus): $$\text{Interest} = 0.015\times(3+8+3+29+6+14) = 0.015\times 63 = 0.945\text{ (\$ thousand)}$$ $$\boxed{\text{Total interest} \approx \$945}$$

Quantity	Value
Peak outstanding balance (highest cash needed)	≈ $38,000 (just before month 5)
Sum of month-end balances, months 1–6	$63,000-months
Total interest at 1.5%/month	≈ $945

Three measures to reduce interest charges. (1) Bill more frequently and front-load the schedule of values — monthly progress claims lag the actual cost curve; claiming bi-weekly, and loading early line items slightly (within what the consultant will certify), shrinks the financed gap. (2) Negotiate a shorter payment-certification cycle and reduced holdback release delay — every day shaved off the owner's pay-when-certified cycle is a day less interest on that draw. (3) Sequence procurement and subcontractor payment to match the S-curve — delaying large material buys until closer to installation, and paying subtrades on the same cycle the contractor is paid, avoids the contractor pre-financing cost the project has not yet earned billings for.

Topic: Construction project cash-flow financing (the contractor's "banana curve").

Key relations: $Balance(t) = CumCashOut(t) - CumPaymentReceived(t)$; $Interest \approx i\sum_t Balance(t)$ over the months a balance is owed.

Why this works: Owners pay in arrears against certified progress, and always hold some retention, so the contractor is structurally always financing part of the work-in-place — the gap between the smooth cost S-curve and the stepped billing curve is exactly that exposure.

Common pitfall: Reading the peak financing need at a month-end after the payment step (which understates it) instead of the instant before, and forgetting that the peak balance and the total interest are two different quantities that do not have to occur at, or be driven by, the same month.

Source: Halpin & Senior, Construction Management, Ch. 12 (cash flow, financing and bonding); Hendrickson & Au, Project Management for Construction, Ch. 13 (cost control and cash flow).

Question 2 of 7: S-Curve, Project Cash-Flow Financing and Interest

Question 2: S-Curve, Project Cash-Flow Financing and Interest (20 marks)

(a) The typical S-curve

(b) Financing the cost–revenue gap