Financial Management · Investment appraisal techniques

Net Present Value (NPV) in ACCA FM: Step-by-Step Method

Q: How do I calculate NPV step by step in ACCA FM?

Set up a table by year. Work out inflated revenue and costs, tax, capital allowance savings and working capital changes. Add them to get net cash flow, discount each year at the cost of capital, and subtract the initial investment. Accept if the result is positive.

Q: How do I treat working capital in NPV?

Calculate the working capital needed each year, then take the change from the previous year. An increase is a cash outflow and a decrease is an inflow. Release the entire remaining balance in the final year of the project.

Q: What is the difference between real and nominal cash flows?

Nominal cash flows include the effect of inflation and are the actual amounts received or paid. Real cash flows are in constant, current prices. Use a nominal rate with nominal flows and a real rate with real flows.

Q: How do capital allowances affect NPV?

Capital allowances are not cash flows themselves. They reduce taxable profit, so you include the tax saving (allowance × tax rate) in the year it is received. On disposal, include any balancing allowance or charge in the final year.

Updated 11 October 2026 · Fact-checked

Net present value is the sum of a project's future cash flows discounted at the cost of capital, minus the initial investment. To solve it, list relevant cash flows by year, adjust for inflation, tax, capital allowances and working capital, discount at a consistent rate, and add up. Accept if NPV is positive.

Understand Net Present Value (NPV)

A dollar received in future is worth less than a dollar today. You could invest today's dollar and earn a return. So you cannot add up cash flows from different years. You must first convert each one to its value today. This is discounting.

Net present value (NPV) is the total of all discounted cash flows of a project, including the initial outlay. The discount rate is the company's cost of capital, or a rate that reflects the project's risk. A positive NPV means the project earns more than the required return, so it adds that amount to shareholder wealth. A negative NPV destroys value.

Only relevant cash flows go in. These are future, incremental cash flows caused by the decision. Leave out sunk costs, depreciation (it is not cash), allocated overheads that do not change, and financing costs such as interest. Interest is already covered by the discount rate.

In FM you also adjust for real-world items. Inflation changes the size of cash flows and the discount rate. Tax reduces profits, but capital allowances (tax-allowable depreciation) give tax savings. Working capital is cash tied up in inventory and receivables, less payables. It is paid out when the project needs it and recovered at the end.

The golden rule: match the rate to the cash flows. Nominal (inflated) cash flows use a nominal rate. Real (current price) cash flows use a real rate.

Key rules to remember

Net present value: NPV = Σ [CFt ÷ (1 + r)^t] − initial investment; CFt is the net cash flow in year t and r is the discount rate. Time 0 cash flows are not discounted.
Decision rule: NPV > 0 → accept; NPV < 0 → reject; For mutually exclusive projects, choose the highest positive NPV. With capital rationing, use a profitability index instead.
Inflating a cash flow: Inflated cash flow = current price cash flow × (1 + i)^n; Use the specific inflation rate for each item (sales, costs, wages) if given. n is the number of years from now.
Nominal and real rates (Fisher): (1 + nominal rate) = (1 + real rate) × (1 + inflation rate); Multiply, do not just add the rates. Rearrange to find the real rate: (1 + nominal) ÷ (1 + inflation) − 1.
Tax on operating cash flow: Tax = taxable cash profit × tax rate; Taxable cash profit is revenue less cash costs. Timing is given in the question, often the same year or one year later.
Tax saving from capital allowances: Tax saving = allowance × tax rate; Reducing balance allowance = tax written down value × allowance rate. On disposal, a balancing allowance or charge = written down value − sale proceeds.
Working capital cash flow: Cash flow = −(this year's working capital − last year's working capital); Only the increase is a cash outflow. A decrease is an inflow. All remaining working capital is released at the end of the project.
Annuity factor: Annuity factor = [1 − (1 + r)^−n] ÷ r; Use for equal cash flows in years 1 to n. Tables are given in the exam.

How to solve Net Present Value (NPV) questions

Use the same layout every time. A table with one column per year keeps tax, inflation and working capital from getting mixed up.

1Read the question and note the project life, tax rate and timing of tax, allowance rate, inflation rates, working capital policy and cost of capital. Check whether cash flows are real or nominal.
2Inflate each item that needs it (sales, costs, working capital) to nominal values for each year, using the correct specific rate.
3Calculate operating cash flow each year: revenue less cash costs. Ignore depreciation, sunk costs and interest.
4Calculate tax on operating profit and the tax saving from capital allowances. Include any balancing allowance or charge in the final year, and put each tax item in the year it is paid or saved.
5Calculate working capital: the increase each year is an outflow, and the total balance is recovered in the final year.
6Add up the net cash flow for each year, including the investment at time 0 and any scrap proceeds. Discount at the nominal cost of capital (or the real rate if all flows are real).
7Total the present values to get the NPV. State the decision (accept if positive) and comment briefly on any assumptions or risks.
8 If asked, note limits: forecasts may be unreliable, the rate may change and inflation may differ by item.

Quickest way: Single table, nominal flows, 3-decimal factors

When to use it: Use in Section C when you have inflation, tax and working capital together, and time is short.

Draw one table with years 0 to n across the top. Add rows: sales, costs, tax, allowance saving, working capital, scrap, net cash flow, discount factor, present value.
Fill each row across all years before moving on to the next row. Do not calculate year by year, because that mixes up the items.
For annuities with no inflation, use the annuity factor once instead of discounting each year separately.
If all cash flows are in real terms and inflation is general, discount real flows at the real rate. This avoids inflating every item.
Write the NPV and the decision on a separate line so the marker can find them. Show workings for allowances and working capital in the table, since method marks are available.

Common mistakes in Net Present Value (NPV)

Using a real discount rate with inflated cash flows, or the nominal rate with real cash flows.
The question gives one cost of capital and students use it without checking whether it is a money rate.
Fix: State the basis of the rate and the cash flows first. Convert with (1 + nominal) = (1 + real) × (1 + inflation) so both match.
Including depreciation, interest or sunk costs as cash flows.
Students copy figures from profit statements instead of selecting relevant cash flows.
Fix: Ask: is it future, incremental and cash? If not, leave it out. Show the capital allowance only as a tax saving.
Putting the full working capital balance in as a cash flow each year.
Students forget that only the change in the balance is a cash flow.
Fix: Work out the balance for each year, take the difference, and release the final balance in the last year.
Getting the timing of tax or allowances wrong.
Questions often state tax is paid a year in arrears, and students ignore this.
Fix: Mark each tax item with the year it is paid. Allowances claimed in year 1 give a saving in the year stated, which might be year 2.
Forgetting the balancing allowance or charge on disposal.
Students only calculate the writing down allowances over the project life.
Fix: In the final year, compare scrap proceeds with the tax written down value. The difference gives an extra allowance or a charge.
Treating the time 0 cash flow as if it is discounted, or starting discounting at the wrong year.
Students number years from 1 by habit.
Fix: Time 0 has a factor of 1.000. The first year-end cash flow is discounted one year.

Worked examples

Example 1

A company is considering a machine costing $300,000 now. It will be used for 3 years and sold at the end of year 3 for $100,000. Revenue at current prices is $400,000 a year and inflates at 4% a year. Cash costs at current prices are $220,000 a year and inflate at 5% a year. Tax is 30%, paid in the same year as the profit. Tax allowances are 25% a year on the reducing balance, with a balancing allowance or charge in year 3. Working capital is 10% of each year's revenue, paid at the start of the year and fully recovered at the end of year 3. The nominal cost of capital is 12%. Calculate the NPV and advise. Use factors 0.893, 0.797 and 0.712 and round to the nearest dollar.

Show the solution

Revenue: year 1 = 400,000 × 1.04 = 416,000; year 2 = 432,640; year 3 = 449,946.
Costs: year 1 = 220,000 × 1.05 = 231,000; year 2 = 242,550; year 3 = 254,678.
Net operating cash flow: year 1 = 185,000; year 2 = 190,090; year 3 = 195,268.
Tax at 30%: year 1 = 55,500; year 2 = 57,027; year 3 = 58,580.
Allowances: year 1 = 300,000 × 25% = 75,000 (WDV 225,000); year 2 = 225,000 × 25% = 56,250 (WDV 168,750); year 3 balancing allowance = 168,750 − 100,000 = 68,750.
Tax saved at 30%: year 1 = 22,500; year 2 = 16,875; year 3 = 20,625.
Working capital held for each year (paid at start of year): 41,600 at time 0; 43,264 at time 1; 44,995 at time 2. Cash flows: time 0 = −41,600; time 1 = −1,664; time 2 = −1,731; time 3 = +44,995 recovered.
Net cash flows: time 0 = −300,000 − 41,600 = −341,600. Time 1 = 185,000 − 55,500 + 22,500 − 1,664 = 150,336. Time 2 = 190,090 − 57,027 + 16,875 − 1,731 = 148,207. Time 3 = 195,268 − 58,580 + 20,625 + 100,000 + 44,995 = 302,308.
Present values: time 1 = 150,336 × 0.893 = 134,250; time 2 = 148,207 × 0.797 = 118,121; time 3 = 302,308 × 0.712 = 215,243. Total = 467,614.
NPV = 467,614 − 341,600 = 126,014.

Answer: NPV = $126,014. It is positive, so the project should be accepted on financial grounds, subject to the reliability of the forecasts.

Example 2

A project costs $100,000 now and gives cash flows of $45,000 a year for 3 years at current (year 0) prices. All cash flows inflate at the general rate of 3% a year. The company's nominal (money) cost of capital is 9.18%. Ignore tax. Calculate the NPV using real cash flows and the real discount rate. Annuity factor for 6% over 3 years is 2.673.

Show the solution

Find the real rate: (1 + real) = 1.0918 ÷ 1.03 = 1.06, so the real rate is 6%.
Because every cash flow inflates at the same general rate, the real cash flows can be discounted at the real rate.
Present value of inflows = 45,000 × 2.673 = 120,285.
NPV = 120,285 − 100,000 = 20,285.
Check using nominal flows: 46,350, 47,741 and 49,173 discounted at 9.18% give the same result within rounding, because each real cash flow divided by 1.06^t equals the inflated flow divided by 1.0918^t.

Answer: NPV = $20,285 (approximately). It is positive, so accept the project.

Exam tips

In objective test cases, read the question for the rate type first. Many wrong options come from using the wrong rate or the wrong inflation basis.
Write down what you include and what you exclude in Section C. Marks are given for treating each item correctly, even if a later number is wrong.
If the question gives tax timing (same year or one year later), underline it and apply it to both the tax charge and the allowance savings.
For working capital, always show the balance each year and the change. Do not forget the release in the last year.
Finish with a clear recommendation and one or two sensible comments, such as forecast risk or the effect of inflation. Do not just stop at the number.

Practice questions from Investment appraisal techniques

Net Present Value (NPV) in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Net Present Value (NPV): frequently asked questions

How do I calculate NPV step by step in ACCA FM?

Set up a table by year. Work out inflated revenue and costs, tax, capital allowance savings and working capital changes. Add them to get net cash flow, discount each year at the cost of capital, and subtract the initial investment. Accept if the result is positive.

How do I treat working capital in NPV?

Calculate the working capital needed each year, then take the change from the previous year. An increase is a cash outflow and a decrease is an inflow. Release the entire remaining balance in the final year of the project.

What is the difference between real and nominal cash flows?

Nominal cash flows include the effect of inflation and are the actual amounts received or paid. Real cash flows are in constant, current prices. Use a nominal rate with nominal flows and a real rate with real flows.

How do capital allowances affect NPV?

Capital allowances are not cash flows themselves. They reduce taxable profit, so you include the tax saving (allowance × tax rate) in the year it is received. On disposal, include any balancing allowance or charge in the final year.