Financial Management · Allowing for inflation and taxation in DCF

Combined NPV with Inflation, Tax and Working Capital in ACCA FM

Updated 11 October 2026 · Fact-checked

A combined NPV question asks you to inflate each cash flow at its own rate, deduct tax on taxable profit, add tax saved by capital allowances, and include inflated working capital changes. You then discount the nominal after-tax cash flows at the nominal after-tax cost of capital and sum them.

Understand Combined NPV with Inflation, Tax and Working Capital

A full DCF question is several small calculations joined in one layout. Each piece is simple. The marks go to doing them in the right order and not mixing real and nominal figures.

Inflation. Cash flows in the question are usually given at current prices. You inflate them to the money you will actually receive or pay. Sales, costs and working capital each may have their own inflation rate. When you inflate the cash flows, you discount at the nominal (money) cost of capital. You cannot discount inflated flows at a real rate.

Tax. Tax is a cash flow, so it goes in the layout. You tax the operating cash flow less the tax-allowable depreciation (capital allowances). Depreciation in the accounts is ignored. Capital allowances are not cash. They matter only because they cut the tax you pay. Check the timing the question gives: tax paid in the same year, or one year in arrears.

Working capital. A project ties up cash in inventory and receivables, net of payables. That money goes out before the sales arrive and comes back at the end. Because prices rise, the working capital needed rises as well. Only the increase each year is a cash flow. At the end of the project the full balance is released. Working capital is not tax-allowable.

Discounting. The finished cash flows are after-tax, nominal figures. You discount them at an after-tax nominal cost of capital. If you are given a real rate, convert it first. Then NPV is the sum of the present values. IRR is found by trying two discount rates and interpolating.

Key rules to remember

Inflating a cash flow: Future cash flow = current-price cash flow × (1 + i)ⁿ; Use the rate that applies to that item. Sales, costs and working capital can inflate at different rates. n is the number of years from the date the current price applies to.
Fisher relationship: (1 + money rate) = (1 + real rate) × (1 + inflation rate); Use it to convert a real cost of capital to a nominal one. If cash flows have different inflation rates, inflate them and use the money rate.
Tax on operating cash flow: Tax = (operating cash flow − tax-allowable depreciation) × tax rate; A negative figure gives a tax saving only if the question says losses can be relieved against other profits. Follow the question's timing for payment.
Tax saved by capital allowances: Tax saving = capital allowance × tax rate; You can show it as a separate line. Or you can deduct the allowance inside the taxable profit line, as long as you do not count it twice.
Working capital cash flow: Cash flow in year t = −(WC required at start of year t+1 − WC required at start of year t); Use inflated balances. The final release at the end of the project is a positive flow equal to the balance then held.
NPV: NPV = Σ [after-tax nominal cash flow ÷ (1 + r)ⁿ], r = nominal after-tax cost of capital; Accept the project if NPV is above zero.
IRR by interpolation: IRR ≈ L + [NPV at L ÷ (NPV at L − NPV at H)] × (H − L); L is the lower rate, H the higher rate. Choose rates that give one positive and one negative NPV.

How to solve Combined NPV with Inflation, Tax and Working Capital questions

Use the same layout every time. Build it left to right across the years, with one row for each item. Keep tax and working capital as separate rows so you can check them.

1Read the question for tax timing, the tax rate, how allowances are given, the inflation rates, the working capital rule and the cost of capital. Underline whether the rates are real or nominal.
2Draw columns for year 0 up to the final year. List the rows: sales, operating costs, net operating cash flow, tax, capital expenditure, working capital and net cash flow.
3Inflate sales and costs separately, using each item's own rate. Check whether the year 1 figure needs one year of inflation. It usually does if prices are quoted at today's level.
4Calculate tax. Take the net operating cash flow less capital allowances, then multiply by the tax rate. Put the tax in the year it is paid. Add scrap value effects and any balancing allowance in the final year if the question gives them.
5Calculate the inflated working capital required each year. Find the change from the previous year. Show an outflow for increases and release the whole balance at the end.
6Add the rows to get the net nominal after-tax cash flow for each year. Discount it using the nominal after-tax cost of capital. Convert a real rate with the Fisher relationship first.
7Sum the present values to get the NPV. State your decision. If asked for IRR, find the NPV at a second rate and interpolate.
8Check your rows once: no depreciation in cash flow, allowances not counted twice, working capital recovered and nominal rate used.

Quickest way: One-grid method for Section C

When to use it: Use it when the question asks for a full NPV and you have about 30 to 35 minutes for 20 marks. It saves writing out each workings table in full.

Make one grid with a row for each cash flow item. Put workings at the bottom, not on separate pages.
Work out the inflation factors once, such as 1.03, 1.0609 and 1.0927. Reuse them for every row that has the same rate.
Calculate tax as one figure: (net operating cash flow − allowance) × tax rate. This is faster than finding tax on operating cash flow and tax saved on allowances separately.
Find the working capital balance in each year by multiplying that year's inflated sales by the percentage given. Then take differences in a single line.
Round to the nearest whole currency unit but keep the layout clear. Use the discount factors from the tables in the exam. Then show the NPV and a one-line recommendation.

Common mistakes in Combined NPV with Inflation, Tax and Working Capital

Discounting nominal cash flows at the real cost of capital, or real cash flows at a money rate.
Questions often give a rate without saying which type it is, and students rush the first step.
Fix: Decide first whether you inflate. If you inflate, the rate must be nominal. Convert a real rate with (1 + m) = (1 + r)(1 + i) before you start discounting.
Including accounting depreciation as a cash flow or as a tax deduction.
Students see depreciation in the question and treat it like any other cost.
Fix: Leave accounting depreciation out completely. Use only the tax-allowable depreciation given in the question as a deduction for tax.
Treating the whole working capital balance as a cash flow each year.
It is easy to confuse the balance held with the change in the balance.
Fix: List the balance for each year, then take the difference. Only the increase is an outflow. At the end, release the full balance as an inflow.
Not inflating working capital, or inflating it from the wrong base year.
Students inflate sales and costs but then use the current price working capital figure.
Fix: Work out working capital from inflated sales, or inflate the working capital requirement at the stated rate. Do it in the same way for every year.
Putting tax in the wrong year.
Some questions use tax paid in the same year and others one year in arrears. Students apply the same pattern to both.
Fix: Underline the timing statement and label the tax row with the year the cash leaves. With a one-year lag, the final year's tax falls one year after the project ends.
Counting the capital allowance tax saving twice.
Students deduct the allowance in the tax calculation and also add a separate tax saving row.
Fix: Choose one method. Either deduct the allowance inside the taxable profit, or compute tax on operating cash flow alone and add allowance × tax rate as a separate saving. Never do both.

Worked examples

Example 1

A company is considering a three-year project. Equipment costs $600,000 now and has no scrap value. Tax-allowable depreciation is $200,000 a year for three years. Sales at current prices are $500,000 a year and inflate at 3% a year. Cash operating costs at current prices are $200,000 a year and inflate at 5% a year. Year 1 figures are the current prices inflated by one year. Working capital must equal 10% of that year's sales, is paid at the start of the year and is fully recovered at the end of year 3. Tax is 30% and is paid in the year the profit arises. The nominal after-tax cost of capital is 10%. Calculate the NPV.

Show the solution

Inflate sales: year 1 = 500,000 × 1.03 = 515,000. Year 2 = 500,000 × 1.0609 = 530,450. Year 3 = 500,000 × 1.092727 = 546,364.
Inflate costs: year 1 = 200,000 × 1.05 = 210,000. Year 2 = 200,000 × 1.1025 = 220,500. Year 3 = 200,000 × 1.157625 = 231,525.
Net operating cash flow: year 1 = 305,000. Year 2 = 309,950. Year 3 = 546,364 − 231,525 = 314,839.
Tax: taxable profit is operating cash flow less 200,000. Year 1 = 105,000, tax 31,500. Year 2 = 109,950, tax 32,985. Year 3 = 114,839, tax 34,452.
Working capital balances: 10% of sales gives 51,500 for year 1, 53,045 for year 2 and 54,636 for year 3. Cash flows: year 0 = −51,500, year 1 = −1,545 (53,045 − 51,500), year 2 = −1,591 (54,636 − 53,045), year 3 = +54,636 (release).
Net cash flows: year 0 = −600,000 − 51,500 = −651,500. Year 1 = 305,000 − 31,500 − 1,545 = 271,955. Year 2 = 309,950 − 32,985 − 1,591 = 275,374. Year 3 = 314,839 − 34,452 + 54,636 = 335,023.
Discount at 10% using factors 0.909, 0.826 and 0.751: year 1 = 247,207, year 2 = 227,459, year 3 = 251,602. Total PV = 726,268.
NPV = 726,268 − 651,500 = 74,768.

Answer: NPV is about $74,768, positive at 10%, so the project should be accepted on financial grounds.

Example 2

Using the net after-tax cash flows from the previous example (year 0 = −651,500; year 1 = 271,955; year 2 = 275,374; year 3 = 335,023) and an NPV of $74,768 at 10%, estimate the IRR by using 20% as the second discount rate.

Show the solution

Discount at 20% using factors 0.833, 0.694 and 0.579.
Year 1 = 271,955 × 0.833 = 226,539. Year 2 = 275,374 × 0.694 = 191,110. Year 3 = 335,023 × 0.579 = 193,978.
Total PV at 20% = 611,627. NPV at 20% = 611,627 − 651,500 = −39,873.
The NPV changes sign between 10% and 20%, so interpolate: IRR ≈ 10 + [74,768 ÷ (74,768 + 39,873)] × (20 − 10).
74,768 ÷ 114,641 = 0.652, so IRR ≈ 10 + 6.52 = 16.5%.
Compare with the cost of capital of 10%. The IRR is higher, which agrees with the positive NPV.

Answer: IRR is approximately 16.5%, above the 10% cost of capital, so the project is acceptable. This is an estimate because interpolation assumes a straight line between two rates.

Exam tips

Draw the layout first and fill rows one at a time. Markers give credit for correct method even if one earlier figure is wrong, so keep each row visible.
Underline the words that tell you whether rates are real or nominal, whether tax is in arrears and whether working capital is recovered. These three details change the answer most often.
Show inflation factors and the working capital workings clearly. Even a small slip is then easier to follow for follow-through marks.
In the objective test cases, one question may ask only for a single year's tax or working capital flow. Do just that line carefully rather than the whole NPV.
Finish with a decision and one caveat, such as sensitivity to the inflation rates or the tax timing, if the question asks for comment.

Practice questions from Allowing for inflation and taxation in DCF

Combined NPV with Inflation, Tax and Working Capital: frequently asked questions

How do you deal with working capital in an NPV with inflation?

Work out the working capital needed each year using inflated figures. Then take the change from the previous year. An increase is an outflow and a decrease is an inflow. At the end of the project, release the full balance as an inflow.

Should I discount after-tax cash flows using the after-tax cost of capital?

Yes. After-tax cash flows should be discounted at a cost of capital that is also after tax. In FM questions the rate given is usually already the after-tax figure, so use it as stated. If the question gives separate before-tax and after-tax rates, choose the after-tax one.

Do I inflate cash flows when I have a real cost of capital?

There are two consistent options. You can inflate the flows and discount at the nominal rate. Or you can leave the flows at current prices and discount at the real rate. Do not mix them, and the first option is needed when items inflate at different rates.

How do capital allowances affect the NPV?

They are not cash flows, but they reduce taxable profit. Multiply each year's allowance by the tax rate to find the tax saved. Include that saving in the year the tax payment is reduced, following the timing the question gives.