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.

(i) Working capital and turnover ratio

Working capital is the additional money, over and above the fixed-capital investment in physical plant, that a company must have on hand to operate the plant. It funds the raw-materials and product inventories, the goods in process, the accounts receivable (product shipped but not yet paid for), the cash for wages and supplies, and the accounts payable and taxes. Unlike fixed capital, working capital is not consumed or depreciated: it is tied up while the plant runs and is recovered in full at the end of the project life. The total capital investment is the sum of the fixed-capital investment and the working capital, so here the fixed-capital investment is $\$5{,}000{,}000-\$750{,}000=\$4{,}250{,}000$.

The turnover ratio is a rapid economic yardstick defined as the ratio of gross annual sales to the fixed-capital investment, $\text{turnover ratio}=\dfrac{\text{gross annual sales}}{\text{fixed-capital investment}}$. Its reciprocal is the capital ratio. A high turnover ratio means each dollar of plant generates many dollars of sales per year (typical of high-throughput, low-value bulk chemicals); a low ratio is characteristic of capital-intensive, high-value products. It is used for order-of-magnitude estimates of either the sales a given investment should support or the investment a target sales figure requires.

Given.

Find. (ii) the annual production capacity in tonnes/year, and (iii) the unit selling price of product ($/tonne) consistent with a turnover ratio of 0.8.

Approach. Convert the daily rate to an annual tonnage using the actual on-stream days, obtain the fixed-capital investment by removing working capital from the total, use the turnover-ratio definition to get gross annual sales, and divide sales by annual production to get the unit price.

1. (ii) On-stream days and annual production. The plant runs every day of the year except the two maintenance shutdowns: $$t_\text{op}=365-2(10)=345\ \text{days/yr}$$ $$\dot m_\text{yr}=\left(32\ \tfrac{\text{t}}{\text{day}}\right)(345\ \text{day})=\boxed{11{,}040\ \text{t/yr}}$$ The annual production capacity is 11,040 metric tonnes per year.
2. Fixed-capital investment. Working capital is separated from the total capital to leave the fixed-capital investment that the turnover ratio is based on: $$C_{FC}=C_T-C_{WC}=\$5{,}000{,}000-\$750{,}000=\$4{,}250{,}000$$
3. Gross annual sales from the turnover ratio. Rearranging the definition $\text{turnover ratio}=\text{sales}/C_{FC}$: $$S=(\text{turnover ratio})\,C_{FC}=(0.8)(\$4{,}250{,}000)=\$3{,}400{,}000\ \text{per year}$$
4. (iii) Unit selling price. Gross annual sales divided by annual production gives the price per tonne: $$P_\text{unit}=\frac{S}{\dot m_\text{yr}}=\frac{\$3{,}400{,}000}{11{,}040\ \text{t}}=\boxed{\$308\ \text{/t}}\quad(\$307.97\text{/t}\approx\$0.308\text{/kg})$$ Each tonne of product must sell for about $308 (31 cents per kilogram) for the plant to hit a turnover ratio of 0.8.