# The economics of a chemical plant: costs, prices and profit: Profitability: does the project earn its capital back?

Source page: https://www.materialinsights.org/learn/chemicals/plant-economics-costs-and-profit/p5/

[Understanding Chemicals](https://www.materialinsights.org/learn/chemicals/) / [Module 3: The economics of a chemical plant: costs, prices and profit](https://www.materialinsights.org/learn/chemicals/plant-economics-costs-and-profit/) Part 5 of 5

## Profitability: does the project earn its capital back?

Markets give revenue and the estimates give costs; profitability evaluation brings them together over the life of the plant. Brennan's method is the cash flow table: money out during construction, money in during operation, tax in between, then discounting to allow for the time value of money. This part builds the measures, works through his sulphuric acid example, and identifies which inputs matter most.

### 5.1 Return on investment is quick, but cash flow is the real test

The simplest measure is return on investment (ROI): annual operating profit divided by total investment, that is, annual sales revenue minus annual operating cost, divided by fixed plus working capital. Brennan suggests about 20% a year as the threshold for a moderate-risk project with a 10-15 year life.

His hydrogen comparison shows ROI exposing capital intensity. Coal is the cheaper feedstock, but the coal plant needs $657 million of capital against $284 million for gas. Annual profits are similar, so ROI is 18.0% for gas and 8.5% for coal.

ROI ignores timing, the build-up of sales, tax and inflation. Cash flow analysis captures them. Cash flow is the net money into or out of the project each year: capital spending, extra working capital and tax are outflows; operating income and recovered working capital are inflows. Depreciation is not a cash flow, but the tax depreciation allowance is deducted before tax is worked out, so it lowers the tax paid.

Brennan's Example 5.1 is a 100,000 t a year plant for an imaginary product, Magidrop, costing $50 million in year 1. Sales are 70,000 t, then 85,000 t, then 100,000 t a year at $1,000/t, with variable costs of $700/t and fixed costs of $8 million a year. Tax is 40%, with tax depreciation of 10% a year. At full output the plant earns $22 million before tax, pays $6.8 million in tax and keeps $15.2 million. Example 5.2 adds working capital at 20% of sales: $14 million at start-up, rising to $20 million, all recovered in year 12.

Data Hydrogen from natural gas or coal: a simple ROI comparison

| Item ($ million a year unless stated) | Natural gas | Coal |
|---|---|---|
| Plant capacity (t a year) | 118,000 | 118,000 |
| Total fixed capital ($ million) | 284 | 657 |
| Raw materials | 88.0 | 33.3 |
| Utilities | 14.1 | 42.1 |
| Fixed costs | 18.7 | 45.0 |
| Nonmanufacturing costs | 9.0 | 12.3 |
| Total operating cost | 129.8 | 132.7 |
| Hydrogen sales | 138.0 | 138.0 |
| By-product steam sales | 42.8 | 50.6 |
| Annual profit | 51.0 | 55.9 |
| Return on investment | 18.0% | 8.5% |

Approximate teaching figures; external environmental costs excluded.
 Source: Brennan (2020), Ch 5 Evaluation of project profitability, pdf p. 132 (Table 5.2)  Case

#### Why better new plants often do not replace old ones

Brennan's Example 6.4 compares keeping a waste treatment plant (Project A), already paid for and earning $0.4 million a year after tax, with scrapping it for a new process (Project B) costing $1.6 million and earning $0.8 million a year, over the 7 years of market left. The $2.0 million originally spent on A is sunk and plays no part. B returns 63% a year on its new capital, yet at a 15% discount rate A's NPV is $1.66 million and B's $1.59 million. Old, paid-for plants are hard to displace.

- Brennan (2020), Ch 5 Evaluation of project profitability · pdf pp. 131-137, 157-158
- Brennan (2020), Ch 6 Some examples in process economics · pdf pp. 163-164

### 5.2 Discounting turns a cash profile into payback, NPV and IRR

Money has earning power, so a dollar next year is worth less than a dollar now. The present value of a cash flow C received in t years at interest rate i is C/(1 + i)^t. Net present value (NPV) is the sum of the present values of all the project's cash flows, normally after tax. A positive NPV means the project beats investing the money at rate i. The discount rate that makes NPV zero is the discounted cash flow rate of return (DCFR), also called the internal rate of return (IRR). The project is profitable if its IRR exceeds the cost of capital.

For Magidrop with working capital, the cumulative cash flow bottoms at -$64 million and ends at +$93.9 million. Payback of the fixed capital, counted from start-up, takes about 3.2 years. At a 10% cost of capital the NPV is $21.9 million, and the IRR is 16.6%.

NPVs can be added across the parts of a large project, such as a cracker and its derivative plants; IRRs cannot. When projects compete, the one with the higher IRR can have the lower NPV at the actual cost of capital, and NPV should then decide.

Inflation must be handled consistently: nominal cash flows with a nominal rate, or real cash flows with a real rate. If Magidrop's prices, costs and capital escalate at 9-12% a year while consumer prices rise 10%, and the nominal cost of capital is 16% (5.5% real), the NPV falls from $54.1 million with inflation ignored to $9.2 million, with a real IRR of 9.8%. Tax depreciation stays fixed in money terms while everything else inflates, and costs are assumed to rise faster than price.

Data Magidrop (Example 5.3): NPV at different discount rates

| Discount rate (% a year) | NPV ($ million) |
|---|---|
| 0 | 93.9 |
| 5 | 49.4 |
| 10 | 21.9 |
| 12.5 | 12.1 |
| 15 | 4.3 |
| 16.6 (IRR) | 0 |
| 17.5 | -2.0 |
| 20 | -7.1 |

At 0% the NPV equals the final cumulative cash flow. Negative signs restored from the context of Brennan's Fig. 5.3.
 Source: Brennan (2020), Ch 5 Evaluation of project profitability, pdf pp. 140-143 (Tables 5.5-5.7)  In the data

#### Debt raises returns, and risk

Brennan extends the inflation case to 50% loan funding at 16% interest, repaid over 10 years. Interest is tax-deductible, so returns to the equity holders rise: the real DCFR goes from 9.8% to 17.9% and the NPV from $9.2 million to $16.9 million. The price is financial risk, greatest at the lowest point of the cumulative cash profile, when an overrun or slow market can leave interest unpaid. Brennan evaluates projects first without financing, then adds it.

- Brennan (2020), Ch 5 Evaluation of project profitability · pdf pp. 138-155

### 5.3 Worked example: a sulphur-burning sulphuric acid plant

Brennan's Example 6.8 pulls the methods together. A company plans a single-stream plant making 150,000 t a year of 98% sulphuric acid from sulphur. Burning sulphur and converting sulphur dioxide both release heat, so the plant exports steam and electricity. Fixed capital is $38.2 million IBL plus $9.5 million OBL, $47.7 million in all, built in one year and run for 15. Acid sells at $100 a tonne.

Variable cost per tonne: sulphur, 0.32 t at $80, is $25.6 and cooling water, 70 m3 at 12 cents, is $8.4. Against these the plant earns credits of $20.0 for 0.2 MWh of electricity at $100/MWh and $7.2 for 0.6 t of steam at $12/t. Net variable cost is only $6.8 a tonne. Fixed costs are $2.0 million for labour and plant overheads, $2.8 million for maintenance, insurance and property taxes, and $0.4 million for administration: $5.2 million a year, or $34.7 a tonne. Cash operating cost is about $41.5 a tonne against a $100 price. Here fixed costs dominate, and energy credits almost cancel the raw material.

Working capital comes to about $2 million. Sales build from 100,000 t to 120,000 t and then 150,000 t. With 30% tax and tax depreciation of 10% a year, the plant at full output earns $8.78 million a year before tax and about $7.6 million after tax while depreciation lasts, falling to $6.1 million once the plant is fully written down.

The total outlay of about $49 million is recovered only in the eighth year of operation. At a 10% cost of capital Brennan's NPV is $2.9 million after 15 years of operation, and he classes the project as only marginally profitable.

Process flowchart Sulphur-burning contact plant for sulphuric acid (Brennan's Example 6.8) Inputs **Sulphur**0.32 t per t acid, at $80/t **Dried air**for combustion and conversion **Cooling water**70 m3 per t acid, at 12 cents/m3 Process steps 1 **Sulphur burner**

S + O2 → SO2; molten sulphur burned in dried air, gas leaves at 1,000-1,200 C with 10-12% SO2
 2 **Waste heat boilers**

Cool the gas to 420-440 C, raising steam; surplus steam and electricity are exported
 3 **Converter (vanadium catalyst, usually 4 beds)**

2SO2 + O2 → 2SO3 at 410-440 C; heat removed between beds
 4 **Absorption towers (double absorption)**

SO3 absorbed in 98% acid at 60-80 C; SO3 + H2O → H2SO4; overall conversion 99.5-99.8%
 Outputs **Sulphuric acid 98%**1 t (150,000 t a year), sold at $100/t **Exported electricity**0.2 MWh per t acid, credit $20/t **Exported steam**0.6 t per t acid, credit $7.2/t

Quantities and prices from Brennan; process steps and conditions from Kent (2012) Ch 25. Net variable cost $6.8/t; cash operating cost about $41.5/t.
 Source: Brennan (2020), Ch 6 Example 6.8; Kent (2012), Ch 25 Sulfur and Sulfuric Acid, Brennan pdf pp. 174-177; Kent pdf pp. 1013, 1016  Worked example

#### Checking the arithmetic

Brennan's printed cost table gives a total of $6.82 million a year ($45.5/t), but its own items sum to $6.22 million ($41.5/t), and his cash flows use the lower figure (15.0 - 1.02 - 5.2 = $8.78 million). His NPV table also adds the working capital increments in years 2 and 3 instead of subtracting them. Correcting the sign gives an NPV of about $1.7 million and an IRR of about 10.6%, against a 10% cost of capital. The conclusion stands: the project barely earns its cost of capital.

- Brennan (2020), Ch 6 Some examples in process economics · pdf pp. 174-177
- Kent (2012), Ch 25 Sulfur and Sulfuric Acid · pdf pp. 1013, 1016

### 5.4 Sensitivity analysis points to price and volume first, then capital

Every input to a cash flow is a forecast. Sensitivity analysis varies them one at a time, typically by 10% in the adverse direction, and records the effect on NPV or IRR. Brennan's illustrative project has a base IRR of 22.1%. A 10% lower selling price cuts it by 4.9 points, 10% lower sales volume by 3.6, 10% higher capital by 2.5, 10% higher variable costs by 1.8 and 10% higher fixed costs by 1.7. Brennan notes that this pattern is common in chemical projects.

The reason is leverage. Price acts on the whole of revenue, while any one cost acts only on its own share. In the acid plant, a 10% fall in price takes $1.5 million a year from a pre-tax cash flow of $8.78 million, a cut of 17%, which would turn a marginal project negative.

What-if tests, such as a six-month start-up delay, add realism. Decision trees and Monte Carlo simulation go further, though Brennan observes that few companies use them and fewer still audit forecasts afterwards.

Scale changes the picture for the acid plant. With b = 0.6, capital is $37.4 million at 100,000 t a year and $109.6 million at 600,000 t. Holding labour and overheads near $2.0-2.4 million and scaling maintenance with capital, cash cost is about $52.8/t at 100,000 t, $41.5/t at 150,000 t and about $22/t at 600,000 t (Brennan prints $16, but his own items, 6.8 + 15.3, give $22), before depreciation of roughly $25, $21 and $12 a tonne. For a fixed-cost plant, size is a powerful lever. Brennan also advises checking that a project's cash cost would sit in the lowest quarter of the world cost curve.

Data Sensitivity of an illustrative project's IRR to 10% adverse changes

| Case | IRR (%) | Change from base (points) |
|---|---|---|
| Base case | 22.1 | 0 |
| 10% lower product selling price | 16.2 | -4.9 |
| 10% lower product sales volume | 18.5 | -3.6 |
| 10% higher capital investment | 19.6 | -2.5 |
| 10% higher variable operating costs | 20.3 | -1.8 |
| 10% higher fixed operating costs | 20.4 | -1.7 |

Rows reordered from most to least influential.
 Source: Brennan (2020), Ch 5 Evaluation of project profitability, pdf p. 156 (Table 5.11)  Common misreading

#### A single base case is not an answer

Brennan warns that risk assessment always involves judgement, and that people matter. A team committed to a project may play down its risks, while an excessively gloomy view will see any project rejected. The base-case NPV is one point in a range. What a board needs is the range, the few inputs that drive it, and actions that can narrow it: more market development, a changed project definition, or experienced people to carry it out.

- Brennan (2020), Ch 5 Evaluation of project profitability · pdf pp. 153-158
- Brennan (2020), Ch 6 Some examples in process economics · pdf pp. 176-177

### See it in the table
[H₂O Water](https://www.materialinsights.org/commodities/water/)[H2SO4 Sulphuric acid](https://www.materialinsights.org/chemicals/sulphuric_acid/)[H2 Hydrogen](https://www.materialinsights.org/chemicals/hydrogen/)

### Check your understanding

Brennan's hydrogen plants earn similar annual profits. Why does the coal plant's ROI (8.5%) fall so far below the gas plant's (18.0%)?
 ROI divides profit by investment. $55.9 million on $657 million is 8.5%; $51.0 million on $284 million is 18.0%. Cheap feedstock does not rescue a project that needs more than twice the capital.

Magidrop's NPV is $21.9 million at 10% and zero at 16.6%. What does this tell you?
 16.6% is the IRR, the rate at which discounted inflows exactly balance outflows. Any cost of capital below it gives a positive NPV.

In Brennan's sensitivity table, which 10% adverse change hurts the IRR most?
 A lower price cuts the IRR from 22.1% to 16.2%, nearly 5 points, because price acts on the whole of revenue. Capital costs 2.5 points and operating costs under 2.

[← Part 4: Operating cost: what each tonne costs to make](https://www.materialinsights.org/learn/chemicals/plant-economics-costs-and-profit/p4/)[Mark read · Wrap-up →](https://www.materialinsights.org/learn/chemicals/plant-economics-costs-and-profit/review/)

## Other sections

- [Module overview](https://www.materialinsights.org/learn/chemicals/plant-economics-costs-and-profit/index.md)
- [What makes the process industries different](https://www.materialinsights.org/learn/chemicals/plant-economics-costs-and-profit/p1/index.md)
- [Markets: sizing demand and forecasting price](https://www.materialinsights.org/learn/chemicals/plant-economics-costs-and-profit/p2/index.md)
- [Capital cost: what the plant costs to build](https://www.materialinsights.org/learn/chemicals/plant-economics-costs-and-profit/p3/index.md)
- [Operating cost: what each tonne costs to make](https://www.materialinsights.org/learn/chemicals/plant-economics-costs-and-profit/p4/index.md)
- [Key terms, quiz and sources](https://www.materialinsights.org/learn/chemicals/plant-economics-costs-and-profit/review/index.md)