Question 5 of 6: Cash Flow

Question 5: Cash Flow (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 S-curve. An S-curve is the plot of cumulative expenditure, work-hours or physical progress against elapsed time. Its name comes from its shape, and the shape comes from the rate at which resources can be brought to bear.

Three phases are visible. Early in the job the site is being established, submittals and shop drawings are in review, permits are being closed out and only a few trades are mobilised, so the cumulative curve rises slowly. In the middle period the maximum number of crews is deployed on work that is well defined and repetitive, and expenditure per unit time is at its highest and roughly constant, giving the steep and nearly straight central section. Towards the end, trades demobilise progressively while the remaining work — commissioning, snagging, testing, documentation and handover — is labour-light and slow to close out, so the curve flattens and approaches the contract value asymptotically. The practical value of the curve is as a control instrument: the planned S-curve derived from the accepted programme becomes the budgeted cost of work scheduled, the actual expenditure curve plotted against it exposes over- and under-spend at a glance, and a third curve of earned value between them separates a schedule problem from a cost problem. A curve that is steeper than planned early on usually signals front-end loading in the payment schedule rather than genuine progress, and a curve that fails to flatten near the end is a reliable warning that closeout has been underestimated.

Given. The chart gives two cumulative curves over a seven-month project: a smooth cash-out curve for money the contractor spends and a stepped curve for payments received, read to the nearest half thousand dollars as follows. The financing rate is 1% per month.

Find. The interest charged on the money the contractor has to borrow over the life of the job, the largest amount of cash the contractor must have available at any one time, and the effect of a down payment on both.

Approach. Difference each cumulative curve to get the cost incurred and the payment received in each month, run a monthly overdraft account in which interest at 1% is charged on the balance outstanding at the end of the month and rolled into that balance, then read the total interest as the sum of the monthly charges and the cash requirement as the largest closing balance.

1. Difference the two curves. The monthly cost is \(c_t = C_t - C_{t-1}\) and the monthly receipt is \(p_t = P_t - P_{t-1}\); for example month 4 shows \(45{,}000 - 15{,}500 = \$29{,}500\) spent against \(17{,}500 - 13{,}000 = \$4{,}500\) received, which is where the job gets into difficulty. The full set appears in the table below.
2. Run the overdraft account. The balance owed at the end of month \(t\) before interest is $$B_t = N_{t-1} + c_t - p_t$$ and interest is charged on it at \(r = 0.01\) and added to the debt, so the closing balance is \(N_t = B_t (1 + r)\) whenever \(B_t\) is positive. Month 1 therefore closes at \(4{,}000 \times 1.01 = \$4{,}040\), month 2 at \((4{,}040 + 7{,}000 - 4{,}500) \times 1.01 = \$6{,}605.40\), and so on.
3. Total the interest. Summing the monthly charges over the six months in which the account is overdrawn: $$I = 40.00 + 65.40 + 26.05 + 276.31 + 64.08 + 144.72 = \boxed{\$616.56}$$ Month 7 opens with a debt of $14,616.56 and closes $7,383.44 in credit once the final payment of $22,500 arrives, so no interest is charged in that month.
4. Read the peak cash requirement. The largest closing balance is the end of month 4, immediately after the heaviest month of expenditure and before the large month-5 receipt: $$N_{\max} = N_4 = \boxed{\$27{,}907.77 \approx \$28{,}000}$$ This, not the total contract value, is the number that sizes the overdraft facility or the working capital the contractor must commit to the job.

Two things are worth noticing about the result. The interest is small in absolute terms, about $617 against a gross margin of $8,000 on the job ($81,500 received against $73,500 spent), but it is close to 8% of that margin. Re-running the account with the month-5 payment delayed by a single month raises the interest to $934.71 and the peak exposure to $38,286.85, so a one-month slip in certification costs about $318 and adds more than $10,000 to the facility required. The other is that the peak requirement is driven almost entirely by a single month: the $29,500 spent in month 4 against $4,500 received is what creates the $27,900 exposure.

How a down payment reduces the interest charge. A down payment, mobilisation payment or advance against materials is money received at or before the start of the work, so it displaces borrowing at the very point where the borrowing is deepest and lasts longest. It shifts the whole payment curve upward and to the left, which reduces the shaded area in Figure 7 in two ways at once: the peak overdraft falls by the amount of the advance, and every month's balance falls with it, so the interest — which is the rate multiplied by the area under the balance curve — falls roughly in proportion. On this job a $15,000 mobilisation payment received at month zero and recovered out of the final certificate removes $15,000 from every subsequent balance. The account then stays in credit until month 4 and is overdrawn in that month alone, so the interest falls from $616.56 to $125.00 and the facility required drops from about $28,000 to $12,625.00. The same effect can be obtained less dramatically by negotiating shorter payment periods and reduced holdback, by front-loading the schedule of values within the limits of honest measurement, and by aligning supplier payment terms with the owner's payment cycle so that the contractor is not financing both ends. From the owner's side the advance is not free — it transfers the financing cost, and it is normally secured by a labour and material payment bond or by an advance-payment guarantee for exactly that reason.