Question 2 of 6: Cost Estimation

Question 2: Cost Estimation (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 five components of total capital investment

The total capital investment (TCI) of a plant is the sum of the fixed capital that buys the physical installation and the working capital that keeps it running; the five categories named in the question map onto that split as follows:

• (i) Battery-limits investment. The capital for the processing units inside the plant's defined boundary ("inside battery limits", ISBL) — reactors, columns, exchangers, pumps and their installation. It is the core, directly productive investment and normally the largest single block, so it anchors every factored cost estimate.
• (ii) Utility investment. The capital for on-site utility generation and distribution — steam boilers, cooling water, refrigeration, power, instrument air. Without it the process units cannot run; its size depends on how much utility is bought over the fence versus generated in-house.
• (iii) Off-site investment. The "outside battery limits" (OSBL) facilities that support production but sit outside the process boundary — storage, tank farms, roads, buildings, effluent treatment, site preparation. It is essential to a workable plant and is easy to underestimate in early estimates.
• (iv) Engineering fees. The cost of process and detailed engineering, design, drafting, project management and the constructor's overhead and profit. It is an indirect but unavoidable fixed-capital cost, typically taken as a percentage of the direct plant cost.
• (v) Working capital. The money tied up in operating the plant once built — raw-material and product inventories, cash for wages and payables, accounts receivable. Unlike the fixed-capital items it is recovered at the end of the project life, but it must be financed throughout and so is part of the TCI.

Items (i)–(iv) together make up the fixed-capital investment (FCI); adding (v) gives the total capital investment, $\text{TCI}=\text{FCI}+\text{WC}$. Distinguishing them matters because depreciation is charged on the fixed capital only, whereas working capital is returned intact.

(b) Selling price for a turnover ratio of 1.0

Given. Total capital investment $\text{TCI}=\$50{,}000{,}000$; working capital $\text{WC}=\$1{,}000{,}000$; capacity $=24$ t/day; operating time $=360$ days/yr; target turnover ratio $=1.0$.

Find. The selling price per kilogram of cement.

Approach. Peters & Timmerhaus define the turnover ratio as gross annual sales divided by the fixed-capital investment; so first strip working capital out of the TCI to get the FCI, set annual sales equal to the turnover ratio times FCI, then divide those sales by the annual production in kilograms.

1. Fixed-capital investment. Working capital is not part of the fixed plant, so $$\text{FCI} = \text{TCI} - \text{WC} = \$50\text{M} - \$1\text{M} = \boxed{\$49\text{ million}}$$
2. Required gross annual sales. The turnover ratio is $\text{TR}=\dfrac{\text{annual sales}}{\text{FCI}}$, so for $\text{TR}=1.0$ $$\text{Sales} = \text{TR}\times\text{FCI} = 1.0\times\$49\text{M} = \$49\text{ million/yr}$$
3. Annual production. At 24 t/day for 360 days, $$\dot m = 24\ \tfrac{\text{t}}{\text{day}}\times360\ \tfrac{\text{day}}{\text{yr}} = 8640\ \tfrac{\text{t}}{\text{yr}} = 8{,}640{,}000\ \tfrac{\text{kg}}{\text{yr}}$$
4. Selling price. Dividing the required sales by the production, $$P = \frac{\text{Sales}}{\dot m} = \frac{\$49{,}000{,}000}{8{,}640{,}000\ \text{kg}} = \boxed{\$5.67\text{/kg}}$$ The cement must sell for about $\$5.67$ per kilogram to return a turnover ratio of one.