Profitability Analysis

Project profitability is judged by discounting future cash flows to the present: a positive net present value at the required rate of return means acceptance, and the internal rate of return is the discount rate that makes NPV zero.

Key formulas & points

Skim these first — then read the full notes below.

  • Accept a project if NPV > 0 at the required rate of return
  • IRR must exceed the cost of capital; non-conventional cash flows can give multiple IRRs
  • Depreciation and the tax shield affect after-tax cash flow

Topic details

Introduction

This topic evaluates whether an investment pays. You build an after-tax cash-flow table including depreciation, discount the flows to net present value, compute the internal rate of return, and compare simple and discounted payback periods to rank alternatives against the company’s cost of capital.

Key relations & formulas

NPV=ΣCFt(1+i)tI0NPV = Σ \frac{CF_{t}}{(1 + i)}^t - I_{0}
(net present value)
NPV=0ati=IRRNPV = 0 at i = IRR
(internal rate of return)
Payback=I0annualnetcashflowPayback = \frac{I_{0}}{annual} net cash flow
(simple, undiscounted)

Notation and sign conventions

Relation 1 —
NPV=ΣCFt/NPV = Σ CF_{t}/
NPV=ΣCFt(1+i)tI0NPV = Σ \frac{CF_{t}}{(1 + i)}^t - I_{0}
(net present value)
Write this relation with symbols exactly as in Peters Timmerhaus Plant Design — Standard reference before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.
Relation 2 —
NPV=0ati=IRRNPV = 0 at i = IRR
NPV=0ati=IRRNPV = 0 at i = IRR
(internal rate of return)
Write this relation with symbols exactly as in Peters Timmerhaus Plant Design — Standard reference before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.
Relation 3 —
Payback=I0annualnetcashflowPayback = \frac{I_{0}}{annual} net cash flow
Payback=I0annualnetcashflowPayback = \frac{I_{0}}{annual} net cash flow
(simple, undiscounted)
Write this relation with symbols exactly as in Peters Timmerhaus Plant Design — Standard reference before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.

Concept in depth

Money has time value, so a rupee earned next year is worth less than one today; discounting at the required return puts all cash flows on a common basis. A positive NPV means the project earns more than the hurdle rate and creates value, while the IRR expresses that return as a single percentage for comparison. Depreciation matters not as a cash flow itself but through the tax shield it provides, raising after-tax cash flow in early years. Simple payback ignores time value and is only a screening tool; NPV is the decisive criterion when projects compete for limited capital.

Assumptions and validity limits

State assumptions explicitly before using any relation for profitability analysis — steady state, uniform properties, linear elastic material, ideal gas, incompressible flow, etc., as applicable.
Wrong assumptions invalidate the entire solution even when the formula is correct. In Plant Design & Economics viva and GATE descriptive questions, listing valid assumptions often earns separate marks.

Step-by-step problem approach

1. Read the question and list given data with SI units (common in Plant Design & Economics papers).
2. Draw a neat labelled diagram where applicable — examiners in Indian universities award diagram marks even when arithmetic slips.
3. Identify which relation from this topic applies to profitability analysis.
4. Use equation 1:
NPV=ΣCFt/NPV = Σ CF_{t}/
.
5. Use equation 2:
NPV=0ati=IRRNPV = 0 at i = IRR
.
6. Substitute values, compute, and verify units and sign (direction).
7. State conclusion in one line — e.g. safe/unsafe, stable/unstable, feasible/infeasible.

Applications & exam relevance

Profitability Analysis appears in project feasibility studies. In Indian chemical curricula this topic is tested because it connects theory to PFD, costing, and profitability.
GATE and semester exams often combine profitability analysis with earlier units — revise prerequisites before attempting mixed problems.
Industry interview panels sometimes ask: "Where did you use profitability analysis?" — answer with a lab, mini-project, or plant visit example if possible.

Common mistakes in exams

Students discount pre-tax instead of after-tax cash flows, treat depreciation as a cash outflow, and rely on simple payback (ignoring the time value of money) for the final decision. Overlooking multiple IRRs with non-conventional cash flows is a subtler error.

Quick revision checklist

Before attempting profitability analysis problems, confirm you can:
1. Accept a project if NPV > 0 at the required rate of return
2. IRR must exceed the cost of capital; non-conventional cash flows can give multiple IRRs
3. Depreciation and the tax shield affect after-tax cash flow
Revise the solved examples in Peters Timmerhaus Plant Design — Standard reference and one previous-year GATE or university paper for this unit.

Worked examples

Try the problem first — open the solution when you are ready to check.

Two-year NPV

Problem

An investment of ₹100 returns ₹60 at year 1 and ₹70 at year 2. At i = 10%, find the NPV.

Solution

NPV = 60/1.1 + 70/1.21 − 100 = 54.55 + 57.85 − 100 = 12.40. Positive NPV means the project clears the 10% hurdle and should be accepted.

Conceptual check — Profitability Analysis

Problem

In a Plant Design & Economics semester or GATE paper you are asked: "State the main assumption, the governing relation, and one practical consequence of profitability analysis." What should a complete answer include?

Exams & GATE

Use after-tax cash flow in NPV — see the economic-analysis chapter.

📖 Standard books (India)

  • Peters Timmerhaus Plant DesignStandard reference

    Read: Syllabus unit

    Referenced in Indian B.Tech syllabus