Investment Appraisal: Net Present Value

The payback period and ARR are useful but fundamentally flawed because they ignore the time value of money. A pound received today is worth more than a pound received in five years' time — because today's pound can be invested to earn a return, and because inflation erodes the purchasing power of future money. Net present value (NPV) addresses this weakness by discounting future cash flows to their present-day value. NPV is widely regarded as the most theoretically sound method of investment appraisal.

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The Time Value of Money

The concept is straightforward: money received sooner is worth more than the same amount received later. There are three reasons for this:

Reason	Explanation
Opportunity cost	Money received today can be invested to earn a return — delaying receipt means forgoing that return
Inflation	Rising prices reduce the purchasing power of future money — £100 in five years will buy less than £100 today
Risk	The further into the future a cash flow falls, the greater the uncertainty that it will actually materialise

Example

If the interest rate is 10%, £100 invested today will be worth £110 in one year. Conversely, £110 received in one year is worth only £100 in today's terms. We say that the present value of £110 received in one year, at a 10% discount rate, is £100.

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Discount Factors

To convert future cash flows into present values, we use discount factors. A discount factor tells you what £1 received in a future year is worth today, given a particular discount rate.

Discount Factor Formula

Discount Factor = 1 ÷ (1 + r)^n

Where:

• r = the discount rate (expressed as a decimal, e.g. 10% = 0.10)
• n = the number of years in the future

Discount Factor Table (10% Discount Rate)

Year	Discount Factor (10%)
0	1.000
1	0.909
2	0.826
3	0.751
4	0.683
5	0.621

This table tells us that £1 received in Year 3, at a 10% discount rate, has a present value of £0.751 — or equivalently, £1,000 received in Year 3 has a present value of £751.

In exams, discount factors are always provided in the question. You do not need to calculate them from the formula — you need to apply them correctly.

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Calculating Net Present Value

Method

1. List the expected net cash flows for each year of the project (including the initial investment in Year 0)
2. Multiply each cash flow by the discount factor for that year to obtain its present value
3. Sum all present values — the total is the net present value (NPV)

Decision Rule

• NPV > 0 (positive): The project is expected to generate a return above the discount rate — accept the project
• NPV = 0: The project generates a return exactly equal to the discount rate — the firm is indifferent
• NPV < 0 (negative): The project is expected to generate a return below the discount rate — reject the project

When comparing multiple projects, the project with the highest positive NPV is preferred.

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Worked Example 1

A business invests £200,000 in a project. The discount rate is 10%. Expected net cash flows are:

Year	Net Cash Flow (£)	Discount Factor (10%)	Present Value (£)
0	(200,000)	1.000	(200,000)
1	60,000	0.909	54,540
2	60,000	0.826	49,560
3	80,000	0.751	60,080
4	80,000	0.683	54,640
5	40,000	0.621	24,840
NPV			43,660

The NPV is £43,660 (positive). This means the project is expected to generate a return greater than 10%, and the investment should be accepted.

Interpretation: In today's money, the project generates £43,660 more than it costs. The business is £43,660 better off in present value terms by undertaking the project than by investing the money at 10%.

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Worked Example 2: Comparing Two Projects

A business must choose between two mutually exclusive projects. The discount rate is 8%.

Discount factors at 8%:

Year	Discount Factor (8%)
0	1.000
1	0.926
2	0.857
3	0.794

Project A — Initial investment: £100,000