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Investment appraisal: discounted cash flow and net present value

Edexcel IAL Business · WBS13 Business decisions and strategy

Money received in the future is worth less than the same amount today. Net present value (NPV), the discounted cash flow method in the specification, adjusts future cash flows for this before comparing them with the cost.

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The time value of money

$100 today is worth more than $100 in three years, because:

money today can be invested to earn interest (opportunity cost);
inflation reduces what future money will buy;
future cash is uncertain.

So future cash flows are discounted back to their present value (PV) using a discount rate, usually based on the interest rate or the firm's target return.

Discount factors

Present value = future cash flow x discount factor. The discount factor for year n at rate r is 1 / (1 + r)ⁿ. In WBS13 you are not expected to work the factors out: the extract supplies the figures you need. In the October 2023 paper (Question 1(b), the first WBS13 NPV question), the mark scheme's working starts from the total of the discounted cash flows given by Extract C: NPV = total discounted cash flows - initial cost = GBP21,635 - GBP10,000 = GBP11,635. An answer of 11,635 without the GBP sign and without working scored 3 out of 4. Knowing where the factors come from still helps you check them. At 10%:

Year	1	2	3	4	5
Discount factor at 10%	0.909	0.826	0.751	0.683	0.621

1 / 1.1, 1 / 1.1 squared, and so on, to 3 decimal places.

Calculating NPV

NPV = total present value of net cash inflows - initial cost.

Example: the project costing $200,000 with net cash flows $50,000, $60,000, $70,000, $60,000, $40,000 at 10%:

Year	Net cash flow ($)	Discount factor	Present value ($)
0	(200,000)	1.000	(200,000)
1	50,000	0.909	45,450
2	60,000	0.826	49,560
3	70,000	0.751	52,570
4	60,000	0.683	40,980
5	40,000	0.621	24,840
		NPV	13,400

NPV = 213,400 - 200,000 = $13,400.

Interpreting NPV and its limitations

Positive NPV: the project earns more than the discount rate, so it adds value; on financial grounds, accept.
Negative NPV: it earns less than the discount rate; reject on financial grounds.
When comparing projects of similar size, prefer the higher NPV.

Here NPV is +$13,400, so the project is worthwhile at 10%. Notice how discounting cuts the value of the later cash flows.

Strengths: takes account of the time value of money and all cash flows.

Limitations: harder to calculate and explain; the choice of discount rate is a judgement and changes the answer (a higher rate gives a lower NPV); still relies on forecasts; ignores qualitative factors; does not show the size of the investment, so a large and a small project are hard to compare.

Worked example

A project costs $100,000 and will produce net cash flows of $40,000 a year for 3 years. Using discount factors at 8% of 0.926, 0.857, 0.794, calculate the NPV and advise.

PVs: 40,000 x 0.926 = 37,040; 40,000 x 0.857 = 34,280; 40,000 x 0.794 = 31,760.
Total PV = 103,080.
NPV = 103,080 - 100,000 = $3,080.
Positive but small, so the project only just beats an 8% return; a small fall in cash flows would make it negative, so qualitative factors and risk should decide.

Answer: NPV = +$3,080: marginally worthwhile.

Key idea: Discount future cash flows to present value (cash flow x discount factor). NPV = total PV of inflows - initial cost. Positive NPV: accept on financial grounds. A higher discount rate lowers NPV.

Check yourself

Using a 10% discount factor of 0.826 for year 2, calculate the present value of $50,000 received in year 2.
Show answer
$41300. 50,000 x 0.826 = $41,300.
A project costs $200,000. Net cash flows for years 1 to 5 are $50,000, $60,000, $70,000, $60,000, $40,000. Discount factors at 10% are 0.909, 0.826, 0.751, 0.683, 0.621. Calculate the NPV.
Show answer
$13400. PVs: 45,450, 49,560, 52,570, 40,980, 24,840; total 213,400; NPV = 213,400 - 200,000 = $13,400.
A machine costs $90,000 and gives net cash flows of $40,000, $30,000, $25,000, $20,000 in years 1 to 4. Discount factors at 12% are 0.893, 0.797, 0.712, 0.636. Calculate the NPV.
Show answer
$150. PVs: 35,720, 23,910, 17,800, 12,720; total 90,150; NPV = 90,150 - 90,000 = $150.
October 2023 WBS13: the total discounted cash flows of a new milkshake machine over five years were GBP21,635 and its initial cost was GBP10,000. Calculate the NPV.
Show answer
GBP11635. NPV = total discounted cash flows - initial cost = 21,635 - 10,000 = GBP11,635.
A project has a negative NPV at the firm's discount rate. What does this mean?
- It will make a loss in every year
- Its payback period is more than five years
- Its ARR must be negative
- It earns a return below the discount rate, so it should be rejected on financial grounds
Show answer
It earns a return below the discount rate, so it should be rejected on financial grounds. Negative NPV means the discounted inflows do not cover the cost.
If the discount rate used rises from 8% to 12%, the NPV of a project will
- rise
- fall
- stay the same
- become exactly zero
Show answer
fall. Higher rates give smaller discount factors and lower present values.
What is the main advantage of NPV over payback and ARR?
- It is the simplest to calculate
- It does not need forecasts
- It includes qualitative factors
- It takes account of the time value of money
Show answer
It takes account of the time value of money. Discounting values later cash less than earlier cash.
Explain why $10,000 received in four years' time is worth less than $10,000 today.
Show answer
Money today could be invested to earn interest, inflation reduces the value of future money, and future cash is uncertain, so the future amount has a lower present value.. Give at least one reason: interest forgone, inflation or risk.

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Last updated 8 November 2026. Spotted a mistake? Tell us.