ACCA Applied Knowledge · Management Accounting

Asset budgeting and investment appraisal: formula sheet

Full chapter guide

Key formulas

Capital expenditure test: Spend creates, improves or extends a non-current asset, or gets it ready for use → capital; Benefit lasts beyond the current period. Record as an asset and depreciate.
Revenue expenditure test: Spend runs the business or maintains an asset in its existing condition → revenue; Charged to profit or loss in the period. Repairs and maintenance are revenue.
Cost of a non-current asset: Purchase price + delivery + installation + testing + legal fees to acquire (less trade discounts); All costs needed to bring the asset to its location and working condition are capital.
Investment process stages: Objectives → identify opportunities → screen and appraise → approve and fund → implement → monitor and review; Learn the order. Questions often ask which stage an activity belongs to.
Payback period (even cash flows): Payback = Initial investment ÷ Annual net cash inflow; Use only when the inflows are the same each year. The answer is in years.
Payback period (uneven cash flows): Payback = Last full year before recovery + (Unrecovered cost at start of next year ÷ Cash flow in that year); Assumes cash flows arrive evenly through the year. Build a cumulative cash flow line first.
Decision rule: Accept if payback ≤ target payback; choose the shortest when comparing; Payback is a screening tool. It does not measure profitability.
Years to months: Months = Decimal part of a year × 12; For example, 0.5 years is 6 months.
ARR (initial investment basis): ARR = average annual accounting profit ÷ initial investment × 100%; Use when the question says initial investment or gives no other instruction and the syllabus basis is clear.
ARR (average investment basis): ARR = average annual accounting profit ÷ average investment × 100%; Use when the question asks for average investment.
Average investment: Average investment = (initial cost + residual value) ÷ 2; If residual value is nil, this is half of the initial cost.
Average annual profit: Average annual profit = (total cash inflows − total depreciation − other non-cash items) ÷ number of years; Total depreciation = initial cost − residual value. Equivalent to total profit ÷ years.
Annual depreciation (straight line): (cost − residual value) ÷ useful life; Needed to turn cash flows into profits.
Decision rule: Accept if ARR ≥ target return; with alternatives, choose the highest ARR; Only valid if all figures use the same basis.
Future value (compounding): FV = PV × (1 + r)^n; r is the rate per period as a decimal; n is the number of periods.
Present value (discounting): PV = FV ÷ (1 + r)^n; Same as FV × 1 ÷ (1 + r)^n. The term 1 ÷ (1 + r)^n is the discount factor.
Annuity present value: PV = annual cash flow × annuity factor; Annuity factor = [1 − (1 + r)^−n] ÷ r. It assumes the first cash flow arrives at the end of year 1.
Perpetuity present value: PV = annual cash flow ÷ r; Assumes the first cash flow is one year from now and flows continue forever.
Growing perpetuity: PV = cash flow in year 1 ÷ (r − g); Only valid when r is greater than g. Use it only if the question gives growth.
Net present value: NPV = Σ [Cash flow in year t × discount factor for year t] − initial investment; Treat Year 0 cash flows with a discount factor of 1.0. Outflows are negative, inflows are positive.
Discount factor: DF = 1 ÷ (1 + r)^n; r is the cost of capital as a decimal and n is the year. In the exam, discount factor tables are normally provided, so you rarely compute this by hand.
Annuity factor for a constant cash flow: Present value = annual cash flow × annuity factor (n years, r%); Use only when the same cash flow occurs every year. The annuity factor is the sum of the discount factors for those years.
Decision rule: NPV > 0 accept; NPV < 0 reject; NPV = 0 indifferent; For mutually exclusive projects, choose the one with the highest positive NPV.
Working capital cash flow: Cash flow = −(closing requirement − opening requirement); An increase in the requirement is an outflow. A decrease, including the final release, is an inflow.
IRR interpolation formula: IRR = L + [NPV at L ÷ (NPV at L − NPV at H)] × (H − L); L is the lower rate (positive NPV). H is the higher rate (negative NPV). Subtracting a negative NPV means you add the two NPVs ignoring signs.
Definition of IRR: IRR = the discount rate where NPV = 0; It is the break-even cost of capital for the project.
Decision rule: Accept if IRR > cost of capital; reject if IRR < cost of capital; This applies to a single project with conventional cash flows (outflow first, then inflows).
Annuity shortcut for level cash flows: Annuity factor = initial investment ÷ annual cash inflow; Find this factor in the annuity table on the row for the project life. The matching rate is the IRR.
Present value of a cash flow: PV = cash flow × 1 ÷ (1 + r)^n; r is the cost of capital as a decimal and n is the year. In the exam you normally use the discount factor from the tables given.
Discounted payback period: DPP = last full year before recovery + (unrecovered investment ÷ PV of cash flow in the recovery year); Use cumulative present values. This assumes cash arrives evenly through the recovery year.
Net present value: NPV = Σ PV of cash inflows − initial investment; Accept if NPV is greater than zero. Among mutually exclusive projects, choose the highest positive NPV.
Internal rate of return (interpolation): IRR = a + [NPV at a ÷ (NPV at a − NPV at b)] × (b − a); a is the lower rate and b the higher rate. Accept if IRR is greater than the cost of capital.
Payback period: Payback = last full year before recovery + (unrecovered investment ÷ cash flow in the recovery year); Undiscounted. With equal annual inflows, payback = investment ÷ annual inflow.
Accounting rate of return: ARR = average annual accounting profit ÷ average investment × 100%; Average investment is (initial investment + residual value) ÷ 2. Some questions use initial investment instead, so follow the question wording.

Quick revision

Capital expenditure buys or improves non-current assets; revenue expenditure covers day-to-day running costs.
Payback is the time taken to recover the initial investment from cash flows. It ignores cash flows after payback and the time value of money.
ARR = average annual accounting profit ÷ investment × 100%. The investment can be initial or average, so follow the question.
Average investment = (initial investment + residual value) ÷ 2.
Discounting converts future cash flows into present values using the cost of capital.
NPV = sum of discounted cash inflows − initial outlay. Accept the project if NPV is positive.
Include only relevant cash flows: future, incremental and cash. Ignore depreciation and sunk costs.
IRR is the discount rate at which NPV equals zero. Accept if IRR exceeds the cost of capital.
IRR by interpolation = A% + [NPV at A ÷ (NPV at A − NPV at B)] × (B − A)%.
Discounted payback uses discounted cash flows, so it is always longer than simple payback.
NPV is generally preferred because it uses the time value of money and shows the increase in wealth.

Common mistakes

Treating a large repair as capital expenditure Fix: Judge by nature, not size. Repairs that restore an asset to its previous condition are revenue.
Treating depreciation as capital expenditure Fix: Depreciation is an expense charged to profit or loss each period. It is revenue, and not a cash spend.
Including depreciation as a cash outflow or deducting it from inflows. Fix: Payback uses cash only. Add depreciation back if you start from profit, or ignore it if cash flows are given.
Dividing by the wrong year's cash flow when finding the fraction. Fix: Divide the unrecovered balance by the cash flow of the year in which payback occurs.
Using cash flow instead of profit Fix: Always deduct depreciation from cash inflows before averaging. ARR is an accounting measure.
Deducting depreciation using the full cost Fix: Depreciation is cost minus residual value. Write it down before you start.
Using the wrong table year, for example year 4 instead of year 3. Fix: Write the year next to each cash flow before looking up the factor, and read the row label twice.
Discounting year 0 cash flows. Fix: Cash flows happening now have a factor of 1.000. Do not discount them.
Including depreciation as a cash flow. Fix: Depreciation is not a cash flow. Remove it. Use the actual cash paid for the asset at Year 0 instead.
Treating the whole working capital balance as the cash flow each year. Fix: Work out the increase or decrease each year. Show the increase as an outflow and recover the total at the end of the project, if the question says it is released.

Exam tips

Classify by nature of the spend, not by its size or how often it occurs.
Always add costs of getting an asset ready for use into the capital figure.
In multiple response questions, check how many answers you must select before choosing.
For process questions, remember that post-completion review is the final stage.
In number entry questions, split the total into capital and revenue first, then answer only what is asked.
Check first whether cash flows are even or uneven. This decides the method in seconds.
In number entry questions, check the units asked for (years, months, decimals) and the decimal places required.
Advantages and limitations are common in multiple response questions. Remember: simple, favours liquidity and lower risk, but ignores time value of money, later cash flows and profitability.