the meaning, calculation and interpretation of net present value (NPV)

10.3 Investment Appraisal – Net Present Value (NPV)

Learning Objectives

• Explain why investment appraisal is carried out and the role of NPV within the appraisal process.
• Calculate NPV using the discounted cash‑flow method, including cost of capital, terminal value and sensitivity analysis.
• Interpret NPV results and combine them with qualitative/strategic factors to reach a sound business decision.
• Compare NPV with the basic (non‑discounted) appraisal methods – Pay‑back Period and Accounting Rate of Return (ARR) – and understand their limitations.

10.1 How Investment Appraisal Links to Financial Statements (Syllabus 10.1)

• Cash‑flow forecasts used in NPV calculations are derived from the statement of cash flows (operating, investing and financing activities).
• Depreciation (straight‑line, reducing balance, etc.) appears in the profit and loss account and reduces taxable profit, but it is a non‑cash charge – it is added back when preparing cash‑flow statements.
• Any residual or salvage value at the end of the project is recorded on the balance sheet as a fixed‑asset disposal.

10.2 Impact of Investment Decisions on Ratio Analysis (Syllabus 10.2)

When a project with a positive NPV is accepted, the following ratios are affected:

10.3 Investment Appraisal – Overview

10.3.1 Concept of Investment Appraisal (Syllabus 10.3.1)

Investment appraisal is a systematic evaluation of the expected costs and benefits of a capital project before any cash is spent. It enables a business to:

• Allocate scarce capital to the projects that add the most value.
• Compare alternatives of different sizes, durations and risk profiles.
• Assess whether a project fits the company’s strategic objectives.

10.3.2 Basic (Non‑Discounted) Methods (Syllabus 10.3.2)

Worked Example – Pay‑back & ARR

Assumptions:

• Initial outlay: £100,000
• Annual cash inflows: £30,000 for 5 years
• Depreciation (straight‑line): £20,000 per year
• Tax rate: 0 % (for simplicity)

1. Pay‑back Period
   Cumulative cash flow after each year: £30k, £60k, £90k, £120k. Pay‑back occurs during year 4 → Pay‑back = 4 years.
2. ARR
   
   • Average annual accounting profit = Cash inflow – Depreciation = £30,000 – £20,000 = £10,000.
   • Average investment = (Initial outlay + Residual value) / 2 = (£100,000 + £0) / 2 = £50,000.
   • ARR = (£10,000 / £50,000) × 100 % = 20 %.

10.3.3 Discounted Cash‑Flow Method – Net Present Value (NPV)

Definition (Syllabus 10.3.3)

NPV is the difference between the present value of all expected cash inflows and the present value of all cash outflows associated with a project. A positive NPV indicates that the project is expected to increase the firm’s wealth.

Key Components Required by the Syllabus

• Cost of Capital / Discount Rate (r) – the required rate of return reflecting the risk of the project and the firm’s financing mix.
• Cash‑flow Forecasts (C_t) – include:
  • Initial investment (t = 0, negative cash flow).
  • Operating cash inflows/outflows for each year.
  • Tax effects (depreciation shield, tax payments).
  • Salvage / terminal value at the end of the explicit forecast period.
• Terminal Value – value of cash flows beyond the forecast horizon, usually estimated by a perpetuity growth model: \[ TV = \frac{C_{n+1}}{(r - g)} \] where \(g\) is the assumed long‑term growth rate.
• Sensitivity / Scenario Analysis – testing how NPV changes when key assumptions (r, cash‑flow amounts, growth rate) vary.

Step‑by‑Step NPV Calculation (Syllabus 10.3.4)

1. List all cash flows – include the initial outlay, yearly operating cash flows, tax effects and terminal value.
2. Choose the discount rate – usually the weighted average cost of capital (WACC) or the required rate of return for the project.
3. Discount each cash flow to its present value: \[ PV_t = \frac{C_t}{(1+r)^t} \]
4. Sum the present values – the total is the NPV.
5. Interpret the result using the decision rule (see Section 10.3.5).
6. Perform sensitivity analysis – recalculate NPV with alternative r, cash‑flow levels or growth rates to assess risk.

Example – Full NPV Calculation Including Terminal Value

Assumptions:

• Initial machine cost: £120,000 (t = 0)
• Operating cash inflows: £30,000, £35,000, £40,000, £45,000, £50,000 (t = 1‑5)
• Salvage value at end of year 5: £20,000
• Tax rate: 20 %
• Depreciation (straight‑line, 5 years): £24,000 per year → tax shield = 0.20 × £24,000 = £4,800 each year.
• Discount rate (WACC): 10 % (r = 0.10)

Because NPV ≈ £27,600 > 0, the project should be accepted.

Decision Rule (Syllabus 10.3.5)

• NPV > 0 – Accept; the project adds net wealth.
• NPV = 0 – The project earns exactly the required return; decision may depend on strategic or qualitative considerations.
• NPV < 0 – Reject; the project would destroy value.
• For mutually exclusive projects, choose the one with the highest positive NPV.

Limitations of NPV and How to Overcome Them (Syllabus 10.3.6)

Qualitative / Strategic Factors (Syllabus 10.3.7)

When NPV is close to zero, these qualitative considerations can tip the decision one way or the other.

10.4 Comparison of All Three Appraisal Methods (Syllabus 10.4)

10.5 Links to Other Syllabus Areas

• Risk Management (10.5) – Sensitivity and scenario analysis for NPV are practical applications of risk assessment.
• Finance & Accounting (10.5.1) – Determining the discount rate uses the cost of capital, which is covered in the finance section.
• Business Strategy (10.5.2) – Selecting projects based on NPV supports strategic goals such as market expansion, diversification or sustainability.

10.6 Summary Checklist – Calculating & Using NPV

1. Identify every cash inflow and outflow, including tax effects, depreciation shields, and terminal value.
2. Determine an appropriate discount rate (WACC or required return).
3. Discount each cash flow to its present value using \(\frac{C_t}{(1+r)^t}\).
4. Sum all discounted values – this is the NPV.
5. Apply the decision rule: Accept if NPV > 0; reject if NPV ≤ 0.
6. If NPV is borderline, weigh qualitative/strategic factors and perform sensitivity analysis.