ACCA Applied Skills · Financial Management

Allowing for inflation and taxation in DCF: formula sheet

Full chapter guide

Key formulas

Fisher formula: (1 + i) = (1 + r) × (1 + h); i = money (nominal) rate, r = real rate, h = general inflation rate. Use decimals.
Money rate from real rate: i = (1 + r) × (1 + h) − 1; Use this when you have a real rate and inflation and need the rate for money cash flows.
Real rate from money rate: r = (1 + i) ÷ (1 + h) − 1; Use this when you have a money rate such as WACC and need to discount real cash flows.
Inflating a cash flow: Money cash flow in year n = current price cash flow × (1 + inflation)^n; Use the inflation rate that applies to that specific cash flow. Year 1 is inflated by one year.
Consistency rule: Money cash flows ÷ money rate; real cash flows ÷ real rate; Never discount money flows at a real rate or real flows at a money rate.
Inflating a cash flow: Money cash flow in year n = current-price cash flow × (1 + i)ⁿ; Use the specific rate i for that item. If the base is 'year 1 prices', inflate only from year 1, so the exponent is n − 1.
Fisher relationship: (1 + money rate) = (1 + real rate) × (1 + general inflation rate); Multiply the factors. Do not simply add the rates. Rearrange to find the real rate or inflation rate.
Money method rule: Money (inflated) cash flows ÷ money discount rate; Required whenever cash flows have different specific inflation rates.
Real method rule: Real (current-price) cash flows ÷ real discount rate; Valid only if every cash flow rises at the general inflation rate.
Net cash flow: Net cash flow = inflated receipts − inflated payments; Inflate each line separately first, then net them. Netting first hides different inflation rates.
Tax on operating cash flow: Tax = Operating cash flow × tax rate; This is the simple version. It applies when you work with cash flows and allowances separately. Tax on profits is a cash outflow. A tax-allowable loss may give relief if the question says so.
Tax saved on allowance: Tax saving = TAD × tax rate; The allowance is not a cash flow. Only the tax saving goes into the NPV.
Reducing balance TAD: TAD = allowance rate × opening WDV; closing WDV = opening WDV − TAD; The rate is given in the question. Check when the first allowance is claimed. Often it is year 1 for an asset bought at time 0.
Straight line TAD: TAD per year = (cost − residual value) ÷ number of years; Use the tax life given in the question, not the accounting life, if they differ.
Balancing allowance or charge: WDV at disposal − sale proceeds. Positive = balancing allowance. Negative = balancing charge.; Claim it in the year of disposal. Then work out the tax effect: amount × tax rate.
Tax timing: Tax paid in year n + 1 = tax on profits of year n (if one year in arrears); The last year's tax is paid in the year after the project ends. Show it as a separate cash flow.
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.

Quick revision

Fisher: (1 + money rate) = (1 + real rate) × (1 + inflation).
Nominal cash flows use the nominal discount rate. Real cash flows use the real rate.
Inflate each cash flow at its own specific rate if given. Otherwise use the general rate.
Inflated flow = base flow × (1 + i)^n, where n is the number of years from now.
Tax is charged on taxable profit, not on cash flow. Capital allowances reduce taxable profit.
Capital allowances are not cash flows. Only the tax saved on them is a cash flow.
Follow the question's tax timing: same year or one year later. Move all tax flows the same way.
Ignore depreciation, financing costs and sunk costs. Include opportunity costs and relevant incremental costs.
Working capital cash flow equals the increase or decrease in the balance each year.
Recover working capital at the end of the project unless told otherwise.
Discount the net cash flow of each year, add the results, and accept if NPV is positive.
Finish Section C answers with a clear recommendation and any key assumption.

Common mistakes

Discounting money cash flows at a real rate (or real flows at a money rate). Fix: Label every cash flow and every rate as real or money before calculating. Match them.
Adding inflation to the real rate instead of using the Fisher formula. Fix: Multiply the (1 + r) and (1 + h) terms, then subtract 1. For example, 5% real and 3% inflation gives 8.15%, not 8%.
Discounting inflated cash flows at the real rate (or real cash flows at the money rate). Fix: Label each rate and each cash flow as 'real' or 'money' before calculating. Methods must match.
Applying general inflation to every cash flow when specific rates are given. Fix: Underline every rate in the question and assign it to an item. Use general inflation only for items with no specific rate.
Deducting accounting depreciation when working out tax Fix: Ignore accounting depreciation. It is non-cash. Use only the TAD method that the question states.
Putting the allowance itself in the cash flows instead of the tax saved Fix: Multiply every TAD and balancing allowance by the tax rate. Only that saving belongs in the NPV.
Discounting nominal cash flows at the real cost of capital, or real cash flows at a money rate. 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. Fix: Leave accounting depreciation out completely. Use only the tax-allowable depreciation given in the question as a deduction for tax.

Exam tips

Look for the words 'current prices', 'real terms', 'in today's money' or 'money terms'. They tell you the basis of the cash flows.
In Section B and Section A objective questions, the Fisher calculation is often the whole question. Use a calculator, keep decimals and watch the rounding of the options.
Because objective questions are all or nothing, check whether the question asks for the money rate, the real rate or the NPV before you start.
In Section C, show the inflation step clearly in your workings, so you earn method marks even if a number slips.
If different cash flows have different specific inflation rates, inflate each at its own rate, but discount all at the money rate.
Look at the wording: 'at current prices', 'in money terms', 'real cost of capital'. This tells you what must be inflated and which rate to use.
If specific rates differ, go straight to the money method and set out a clear year-by-year table. Markers give credit for clear working even if one figure is wrong.
In objective questions, check the method matches the rate first. Many wrong options come from mixing real flows with a money rate.