In simple terms
A friendly intro before the formal notes — no formulas yet.
Money today vs tomorrow
£1 today is worth more than £1 in five years because it can be invested to earn return. NPV discounts future cash flows to today's value and subtracts the initial investment.
Someone offers you $100 now or $110 in two years. If your bank pays 8% interest, $100 now grows to about $116 — so the delayed $110 is actually the worse deal. Discounting makes future money comparable to today.
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Discount factor = 1 ÷ (1 + r)^n (or use exam tables).
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Present value (PV) = net cash flow × discount factor.
- 3
NPV = sum of PVs − initial investment.
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Accept the project if NPV > 0 (at the given cost of capital).
Explore the concept
Use the live diagram and synced steps — play it or tap a step card to walk through.
The cash flows An investment is money out now for money back later: the cost in year 0, then a forecast net cash flow for each year of the project’s life.
1 more simulation for this topic — run them in the Simulations section below
Simulations
Every simulation here runs the real model — try the steps on a card, then check what you see against the notes.
1 simulation
- GeoGebra9609 10.3.3
Simple vs compound interest
Sliders P, R, T and n set the sum invested, the interest rate, the years and the compounding periods; blue bars are simple interest, orange is the compounding.
Try this
- Drag T from 1 to 10 and watch the orange part of each bar grow faster every year.
- Drag R down towards 10: the bars shrink and the gap between blue and orange narrows.
- Read a bar backwards: its height is what P grows into, so that future sum is worth only P today.
Look for Discounting is compounding run in reverse. The higher the rate and the later the year, the more a future cash flow shrinks when it is brought back to present value, which is why discount factors fall year by year.
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Key formulas
Tap any symbol to reveal exactly what it means and its units.
Tap a symbol — great for exam definitions
At a glance — side by side
Compare key properties side by side — ideal for exam contrasts.
Comparison of NPV and ARR Investment Appraisal Methods
| Feature | Net Present Value (NPV) | Accounting Rate of Return (ARR) |
|---|---|---|
| Primary Focus | Cash flows, which are seen as a more objective measure of investment return. | Accounting profit, which can be subject to manipulation and non-cash items like depreciation. |
| Time Value of Money | Yes, this is a core strength. It discounts future cash flows to their present value. | No, it is completely ignored. Profit in Year 1 is treated as equal in value to profit in Year 5. |
| Decision Rule | Accept if NPV is positive. Provides an absolute value (£) of expected value creation. | Accept if ARR > target rate. Provides a relative percentage return. |
| Link to Shareholder Value | Direct link. A positive NPV project is forecast to increase shareholder wealth. | Indirect link. Higher profit may lead to higher share price, but the link is less direct than with NPV. |
| Complexity | More complex to calculate and can be harder for non-financial managers to understand. | Relatively simple to calculate and is easily understood as a percentage return. |
Primary Focus
Net Present Value (NPV)
Accounting Rate of Return (ARR)
Time Value of Money
Net Present Value (NPV)
Accounting Rate of Return (ARR)
Decision Rule
Net Present Value (NPV)
Accounting Rate of Return (ARR)
Link to Shareholder Value
Net Present Value (NPV)
Accounting Rate of Return (ARR)
Complexity
Net Present Value (NPV)
Accounting Rate of Return (ARR)
Full topic notes
Formal explanation with the rigour you need for the exam.
The Foundation: The Time Value of Money
The entire principle of discounted cash flow is built upon the concept of the time value of money. This fundamental idea states that a sum of money received today is worth more than the identical sum received in the future. There are two primary reasons for this. Firstly, money available now can be invested to earn a return, meaning it can grow over time – this is its opportunity cost. Secondly, inflation erodes the purchasing power of money, so £100 in five years will buy fewer goods and services than £100 today. Therefore, to make a valid comparison between an initial investment cost (a present value) and future earnings (future values), we must first discount the future cash flows to find their equivalent value in today's terms.
Money is more valuable now than in the future due to its potential to earn interest (opportunity cost).
Inflation reduces the future purchasing power of money.
The time value of money concept is essential for comparing cash flows that occur at different points in time.
Investment appraisal methods that ignore this concept, such as Payback and ARR, can be misleading.
The Mechanism: Discounting and Discount Factors
Discounting is the process of calculating the present value of a future cash flow. It is essentially the reverse of calculating compound interest. To do this, we use a discount rate, which represents the minimum required rate of return on an investment, often reflecting the business's cost of capital or the return available from alternative investments of similar risk. The formula for a discount factor is 1 ÷ (1 + r)^n, where 'r' is the discount rate and 'n' is the number of years. In an exam, you will typically be provided with a table of discount factors. To find the present value of a future cash flow, you simply multiply the cash flow by the appropriate discount factor for that year and that rate. A higher discount rate signifies greater risk or higher opportunity cost, leading to a lower present value.
Discounting converts future cash flows into their present-day value.
The discount rate reflects the opportunity cost and risk of an investment.
Present Value (PV) = Future Cash Flow × Discount Factor.
Higher discount rates are used for riskier projects, which lowers their calculated present values.
The Calculation: Step-by-Step Net Present Value (NPV)
Calculating the Net Present Value involves a clear, methodical process. First, identify the initial investment cost, which is the cash outflow at Year 0. Next, forecast the net cash flows (inflows minus outflows) for each year of the project's life. Then, using the given discount rate and a discount factor table, calculate the present value of each year's net cash flow by multiplying the cash flow by its corresponding discount factor. Remember, the Year 0 outflow is already a present value and is not discounted. After discounting all future cash flows, sum these present values together. Finally, subtract the initial investment (the Year 0 outflow) from the total sum of the discounted future cash flows. The resulting figure is the Net Present Value.
Step 1: Identify initial investment (Year 0) and annual net cash flows.
Step 2: Multiply each future net cash flow by the correct discount factor to find its Present Value (PV).
Step 3: Sum the PVs of all future cash flows.
Step 4: NPV = Total PV of future cash flows - Initial Investment.
The Decision: Interpreting NPV and Making Choices
The NPV calculation provides a clear, financially-grounded decision rule. If the NPV is positive, the project is forecast to generate returns that exceed the required rate of return (the discount rate). This means it is expected to add value to the business and increase shareholder wealth, and should therefore be accepted. If the NPV is negative, the project is forecast to earn less than the required rate of return, effectively destroying business value, and should be rejected. An NPV of zero indicates the project will earn exactly the required rate of return, making it financially acceptable but not adding any extra value. When comparing two or more mutually exclusive projects, the one with the highest positive NPV should be chosen, as it is expected to generate the most value for the business.
Positive NPV: Accept the project; it is expected to be profitable above the minimum required return.
Negative NPV: Reject the project; it is not expected to meet the minimum required return.
NPV of Zero: The project is borderline acceptable, meeting the target return exactly.
For mutually exclusive projects, select the one with the highest positive NPV.
In evaluation questions, always state that while NPV is a powerful quantitative tool, a final investment decision should also consider qualitative factors. For example, a project with a lower NPV might be chosen if it enhances the company's ethical reputation, improves employee skills, or aligns better with long-term strategic goals. Showing this balanced view demonstrates a higher level of understanding.
Discounting cash flows
Discount factor (year ) =
Present value = Net cash flow × Discount factor
NPV =
The cost of capital (discount rate) reflects the firm's required return given risk and financing costs. Cash flows in Year 0 are usually not discounted (initial investment). Years 1, 2, 3… each have their own factor.
NPV vs payback and ARR
NPV +: Time value of money; all cash flows; wealth-maximisation criterion.
NPV −: Needs reliable forecasts and appropriate discount rate; less intuitive for non-finance managers.
Methods may conflict — e.g. short payback but negative NPV; explain which dominates and why.
Show all columns (Year, CF, DF, PV) even if the mark scheme only checks NPV — method marks are common. Round consistently (usually to nearest
Worked examples
See the formulas applied — reveal one step at a time, like the exam.
Project costs $100 000 now. Net cash flows: Year 1 $40 000, Year 2 $45 000, Year 3 $50 000. Cost of capital 10%.
Discount factors: Y1 0.909, Y2 0.826, Y3 0.751.
Calculate NPV and advise.
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Year Net CF DF @ 10% PV 0 (100 000) 1.000 (100 000) 1 40 000 0.909 36 360 2 45 000 0.826 37 170 3 50 000 0.751 37 550
Project X NPV = +$8 000. Project Y NPV = +$12 000. Only one can be chosen (mutually exclusive). Which should the firm select?
- 1
Both have positive NPV, but only one can proceed.
How it all connects
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Glossary
Key terms for this topic — skim now; the Check step will test them.
- cost of capital
The cost of capital (discount rate) reflects the firm's required return given risk and financing costs.
- Year 0
Cash flows in Year 0 are usually not discounted (initial investment).
- Time value of money
Money received sooner is worth more because it can earn a return; future cash must be discounted.
- Discount factor formula
DF = 1 ÷ (1 + r)^n where r = cost of capital (decimal) and n = year.
- NPV formula
NPV = Σ (PV of net cash flows) − Initial investment.
- NPV decision rule
Accept if NPV > 0; reject if NPV < 0; indifferent if NPV = 0.
- NPV preferred over
NPV accounts for timing and size of all cash flows; payback ignores both after recovery and time value.
- Mutually exclusive
Choose the project with the higher NPV (if both positive and only one can be done).
- Negative NPV meaning
Project earns less than the required return — destroys shareholder value at that discount rate.
Sort it out
One statement at a time, say which heading it belongs under. Every statement comes from this lesson’s side-by-side comparison.
Indirect link. Higher profit may lead to higher share price, but the link is less direct than with NPV.
Quick check
Write your answer first, then compare it with the model one — the gap is what you would have lost.
Teach it back
If you can explain it simply, you own it — gaps here are marks you’d lose.
Teach it back
Explain this topic as if teaching a friend. We name the gaps an examiner would still dock.
Revision flashcards
Guess first, then flip — retrieval beats re-reading.
Key takeaways
Review these before you close the topic — retrieval beats re-reading.
Money is more valuable now than in the future due to its potential to earn interest (opportunity cost).
Inflation reduces the future purchasing power of money.
The time value of money concept is essential for comparing cash flows that occur at different points in time.
Investment appraisal methods that ignore this concept, such as Payback and ARR, can be misleading.
Practice — then mark it
The whole point: a real Cambridge question, marked mark-by-mark.
Mark an NPV question
Mark an NPV question
Extra simulations & links
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Frequently asked
Checkpoint
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Reading it isn’t knowing it — prove it.
Before you move on: do Mark an NPV question on paper, snap a photo, and get examiner-style feedback on exactly where you win and lose marks.
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