ACCA MA & FMA — Management Accounting

The MA formula sheet,
actually explained

Nine formulas. Three tables. Every one with a live calculator you can type your own numbers into.

You get these formulas in the exam. Everybody does. Knowing the formula was never the hard part — knowing which number goes where is.

The same sheet is used for FMA in Foundations, so this page covers both.

Start with regression

What's on the sheet

MA is the most generous of all the papers — nine formulas and three tables. It is also the paper where the sheet covers the smallest share of what is actually examined.

1 · Regression 2 · Correlation 3 · EOQ 4 · EBQ 5–8 · Mean, SD, variance, CV 9 · Expected value The 3 tables What it doesn't give you
Area 1 of 4

Regression analysis

Splitting a mixed cost into fixed and variable parts — properly, rather than with high-low.

Formula 1

The regression equation

As given in the ACCA examy = a + bx
a = (Σy)/n − b(Σx)/n
b = [ nΣxy − ΣxΣy ] ÷ [ nΣx² − (Σx)² ]

What each bit is

  • y — total cost
  • x — activity level
  • a — fixed cost (the intercept)
  • b — variable cost per unit (the gradient)
  • n — number of pairs

Live calculator

b — variable cost per unit—
a — fixed cost—
The line—

Worked example

Six months. n = 6, Σx = 1,350 units, Σy = $13,250, Σxy = 3,262,500, Σx² = 347,500.

  1. b = [(6×3,262,500) − (1,350×13,250)] ÷ [(6×347,500) − 1,350²] = 1,687,500 ÷ 262,500 = $6.43
  2. a = (13,250÷6) − 6.4286×(1,350÷6) = $761.90
  3. y = 761.90 + 6.43x

Where the marks go

  • Σx² is not (Σx)². Square each x then add, versus add then square. The formula uses both, one in each half of the denominator. This costs more marks than anything else on the sheet.
  • Find b first. The formula for a contains b.
  • a is fixed cost, b is variable cost per unit. The wrong way round gives an answer that looks tidy and scores nothing.
  • Regression beats high-low because it uses every observation rather than two. If asked to compare, that is the point to make.
Sense check: b should look like a plausible cost per unit and a should be positive. A negative fixed cost means a term has been swapped.
Formula 2

The correlation coefficient

As given in the ACCA examr = [ nΣxy − ΣxΣy ] ÷ √{ [ nΣx² − (Σx)² ] [ nΣy² − (Σy)² ] }

What each bit is

  • r — strength and direction of a linear relationship, −1 to +1
  • r² — the proportion of variation in y explained by variation in x

Live calculator

r—
r²—
In words—

Worked example

  1. Top: 1,687,500
  2. Brackets: 262,500 and 10,872,500
  3. Bottom: √(262,500 × 10,872,500) = 1,689,388
  4. r = 0.999 — very strong positive correlation

Where the marks go

  • The square root covers both brackets, not just the first.
  • r² needs saying in words. r = 0.9 means 81% of the variation in cost is explained by the variation in activity.
  • Correlation is not causation, and a strong r says nothing about extrapolating beyond the observed range.
Sense check: r must land between −1 and +1. Outside that, a sum of squares is mis-keyed or the square root has been lost.
Area 2 of 4

Inventory control

Two formulas that look almost identical and are used in completely different situations.

Formula 3

Economic order quantity

As given in the ACCA examEOQ = √( 2CoD ÷ Ch )

What each bit is

  • Co — cost of placing one order
  • D — annual demand in units
  • Ch — cost of holding one unit for a year

Live calculator

EOQ—
Orders per year—
Annual ordering cost—
Annual holding cost—
Total inventory cost—

Worked example

Order cost $40, annual demand 18,000 units, holding cost $4 a unit a year.

  1. EOQ = √(2 × 40 × 18,000 ÷ 4) = √360,000 = 600 units
  2. Orders a year: 18,000 ÷ 600 = 30
  3. Ordering cost: 30 × $40 = $1,200
  4. Holding cost: (600÷2) × $4 = $1,200

The two costs are equal — that is what "economic" means, and it is the fastest way to check your answer.

Where the marks go

  • Holding cost is per unit per year. If the question gives it as a percentage of purchase price, convert first — 10% of a $40 item is $4.
  • Average inventory is EOQ ÷ 2, not EOQ. Holding cost applies to the average, ordering cost to the number of orders.
  • At the EOQ, ordering cost equals holding cost. If yours don't match, the answer is wrong — a free check worth taking every time.
  • Purchase cost is irrelevant unless there are bulk discounts, in which case EOQ is only the starting point and each discount level must be tested.
Sense check: EOQ should be a sensible fraction of annual demand. If it comes out larger than D, a term is inverted.
Formula 4

Economic batch quantity

As given in the ACCA examEBQ = √( 2CoD ÷ Ch(1 − D/R) )

What each bit is

  • D — annual demand
  • R — annual production (replenishment) rate
  • (1 − D/R) — the adjustment for stock building up gradually rather than all at once

Live calculator

1 − D/R—
EBQ—
EOQ if made all at once (for comparison)—
Maximum inventory level—

Worked example

Setup cost $100, demand 20,000 a year, holding $2, production rate 50,000 a year.

  1. 1 − D/R = 1 − (20,000÷50,000) = 0.6
  2. EBQ = √(2 × 100 × 20,000 ÷ (2 × 0.6)) = √3,333,333 = 1,826 units

Larger than the plain EOQ of 1,414, because stock never all arrives at once.

Where the marks go

  • Use EBQ when goods are produced, EOQ when they are bought in. The giveaway is a production or replenishment rate in the question.
  • R must exceed D. If it doesn't, the company cannot meet its own demand and the formula breaks — check you have not swapped them.
  • Maximum inventory is EBQ × (1 − D/R), not EBQ, because stock is being used while it is being made.
Sense check: EBQ is always larger than the EOQ for the same figures. If yours is smaller, the bracket has gone in upside down.
Area 3 of 4

Averages, spread and risk

Four formulas that come as a set, plus the one that turns a spread into a decision.

Formulas 5–8

Mean, standard deviation, variance and CV

As given in the ACCA exam̄x = Σx ÷ n   or   Σfx ÷ Σf
σ = √( Σ(x − ̄x)² ÷ n )
Variance = σ²
CV = σ ÷ ̄x

What each bit is

  • ̄x — the arithmetic mean
  • σ — standard deviation, the spread around the mean
  • Variance — simply σ squared
  • CV — relative risk: spread expressed as a proportion of the mean

Live calculator — enter up to six values

n (values entered)—
Mean ̄x—
Standard deviation σ—
Variance σ²—
Coefficient of variation—

Worked example

Values 12, 15, 18, 22, 25.

  1. Mean: 92 ÷ 5 = 18.4
  2. Squared deviations: 40.96 + 11.56 + 0.16 + 12.96 + 43.56 = 109.2
  3. σ = √(109.2 ÷ 5) = 4.67
  4. Variance = 4.67² = 21.84  ·  CV = 4.67 ÷ 18.4 = 0.254

Where the marks go

  • Divide by n, not n − 1. ACCA uses the population formula at MA.
  • Variance and standard deviation are not interchangeable. Variance is in squared units and cannot be compared to the mean; σ can.
  • CV is what lets you compare risk across differently sized projects. A $10,000 spread means something different on a $20,000 project than on a $2m one — that comparison is where the marks are.
  • With a frequency distribution use the Σf versions, and remember Σf is the total frequency, not the number of rows.
Sense check: σ should be smaller than the range of your data and comfortably smaller than the mean for most exam figures. A σ larger than the range is arithmetic gone wrong.
Formula 9

Expected value

As given in the ACCA examEV = Σpx

What each bit is

  • p — the probability of each outcome, as a decimal
  • x — the value of that outcome
  • EV — the long-run average. Risk neutral.

Live calculator — three outcomes

Probabilities total—
Expected value—

Worked example

  1. (0.30 × 50,000) = 15,000
  2. (0.50 × 25,000) = 12,500
  3. (0.20 × −10,000) = −2,000
  4. EV = $25,500

Note that $25,500 is an outcome that cannot actually happen.

Where the marks go

  • Probabilities must total 1. If they don't, an outcome has been missed.
  • Losses go in negative. Dropping the minus sign is the most common error here.
  • EV only makes sense for repeated decisions. For a one-off it is a number that will never occur — say so, it is worth a mark.
Sense check: The EV must sit between the smallest and largest outcomes. If it doesn't, a probability or a sign is wrong.
Area 4 of 4

The three tables

MA gets one more than FM does — the standard normal distribution comes with it.

Provided

The three maths tables

As given in the ACCA examPresent value of $1  →  1 ÷ (1 + r)n
Annuity, years 1 to n  →  [ 1 − (1 + r)−n ] ÷ r
Standard normal distribution

What each bit is

  • Present value table — a single sum received in year n
  • Annuity table — an equal amount each year for n years
  • Normal distribution table — the proportion of a normal distribution between the mean and z standard deviations

Live calculator

PV factor—
Annuity factor—
PV of the single sum—
PV of the annuity—
Area from mean to z—

Worked example

10% for 5 years, $100,000 a year.

  1. PV factor year 5: 1 ÷ 1.1⁵ = 0.621
  2. Annuity factor years 1–5: (1 − 1.1⁻⁵) ÷ 0.10 = 3.791
  3. PV of $100,000 a year for 5 years: 100,000 × 3.791 = $379,100

Where the marks go

  • Annuity factors start in year 1. For a flow starting later, take the factor for the full span and subtract the years before it starts.
  • The perpetuity factor is not in the tables — 1 ÷ r. Learn it.
  • The normal table gives the area from the mean to z, so for "more than z" subtract from 0.5, and for a two-tailed range double it. Sketching the curve takes ten seconds and prevents most errors.
  • Tables round to three decimals, your calculator doesn't. Small differences are accepted.
Sense check: A PV factor is always between 0 and 1 and falls as n rises. An annuity factor rises with n but can never exceed 1 ÷ r.
The bit nobody tells you

What the sheet doesn't give you

Nine formulas are provided. The MA syllabus needs a great deal more, and every one of these comes out of your own head.

  1. The high-low method — still examined, still not given.
  2. Overhead absorption rates, plus under- and over-absorption.
  3. Marginal versus absorption profit and the reconciliation between them.
  4. Breakeven point, C/S ratio, margin of safety and target profit.
  5. Every variance — material, labour, variable and fixed overhead, sales.
  6. Equivalent units and the treatment of normal and abnormal losses.
  7. Labour turnover, plus the efficiency, capacity and activity ratios.
  8. Inventory control levels — reorder level, maximum and minimum. EOQ is given; these are not.
  9. Time series — moving averages and seasonal variations, additive and multiplicative.
  10. Index numbers, base changes and deflation.
  11. NPV, IRR and payback. The discount tables are given; the methods are not.
  12. ROI, residual income and the basic performance ratios.

Knowing it isn't the same as scoring it

Every formula above turns up in real MA questions. Go and meet them where the marks are.

Practise MA questions