CMA Final · Cost and Management Audit

Audit of Different Service Organisations: formula sheet

Full chapter guide

Key formulas

Capacity utilisation: Capacity utilisation (%) = Actual service units ÷ Available capacity units × 100; Use the same unit for both, for example passenger-km or bed-days. Low utilisation signals idle capacity cost.
Cost per service unit: Cost per unit = Total cost of the service ÷ Number of service units; Total cost must be only the cost of that service. Do not mix in costs of other services.
Occupancy rate: Occupancy (%) = Units occupied ÷ Units available × 100; Applies to rooms, beds and seats. Count available units for the full period.
Idle capacity: Idle capacity = Available capacity − Actual units used; Report it as a cost of unused capacity, not as a cost of the service delivered.
Composite unit: Composite unit = Quantity × Distance (or time), such as tonne-km or passenger-km; Used when a single measure does not capture the service, as in transport.
Cost per occupied bed-day: Total cost of the ward or hospital ÷ Number of occupied bed-days; Use occupied bed-days, not available bed-days, unless the question asks for cost on capacity.
Bed occupancy rate: Occupied bed-days ÷ Available bed-days × 100; Available bed-days = number of beds × days in the period.
Average length of stay: Total inpatient days ÷ Number of patients discharged; Check whether the question counts deaths and transfers as discharges.
Cost per unit of other centres: Cost of centre ÷ Units of service (per test, per scan, per theatre hour, per meal, per kg of linen); The unit must match what the centre actually delivers.
Bed turnover: Number of patients discharged ÷ Number of beds; Shows how intensively beds are used.
Revenue leakage: Value of services rendered − Value of services billed; Test by tracing treatment records to bills.
Cost per student: Cost per student = Total cost of the period ÷ Number of students enrolled; Use the same period for cost and students. Use average enrolment if numbers changed during the year.
Cost per student for a cost centre: Cost per student (centre) = Cost of the centre ÷ Number of students using it; Use for library, laboratory or hostel. Divide by users of that centre, not all students.
Surplus or deficit per student: Surplus (deficit) per student = Income per student − Cost per student; A negative figure means the fee and other income do not cover the cost.
Student-teacher ratio: Student-teacher ratio = Number of students ÷ Number of full-time faculty; A utilisation indicator. Compare it with the norm set by the regulator or the institution's own target.
Grant utilisation: Unspent grant = Grant received − Grant utilised for the sanctioned purpose; Check whether the unspent balance is shown as a liability or restricted fund and not as general income.
Net interest margin (bank): Net interest margin = (Interest earned − Interest expended) ÷ Average earning assets; Shows how well the bank earns on its lending and investing. Use average assets for the period.
Cost-to-income ratio: Cost-to-income ratio = Operating expenses ÷ Operating income × 100; A lower ratio signals better efficiency. Compare across branches or periods.
Claims ratio (insurer): Claims ratio = Claims incurred ÷ Net premium earned × 100; Measures underwriting quality. A rising ratio signals underpricing or weak claims control.
Expense ratio (insurer): Expense ratio = (Commission + Operating expenses of management) ÷ Net premium × 100; Shows the cost of acquiring and servicing business.
Combined ratio: Combined ratio = Claims ratio + Expense ratio; Above 100% means an underwriting loss before investment income.
Cost per transaction: Cost per transaction = Total cost of the service ÷ Number of transactions; Basic service costing unit for branches, channels or claims processing.
Absolute tonne-km (goods transport): Absolute tonne-km = Σ (Load carried in tonnes × Distance in km for each trip); Use actual load for each leg. Add all legs of the period.
Commercial tonne-km: Commercial tonne-km = Average load × Total distance travelled in the trip; Average load = Σ (Load × Distance for each leg) ÷ Total distance. When the legs are of equal length, this is the simple average: (Load on outward trip + Load on return trip) ÷ 2. In that case commercial tonne-km equals absolute tonne-km. The two differ only if leg distances or loads vary and a simple average of the leg loads is used. Commercial tonne-km is mainly used to compute cost per commercial tonne-km.
Absolute passenger-km: Absolute passenger-km = Σ (Passengers carried × Distance for each trip); Commonly used with passenger-km based on seats available when computing capacity use.
Cost per unit (transport or hotel): Cost per unit = Total cost for the period ÷ Number of cost units; Units: tonne-km, passenger-km or occupied room-days.
Occupancy percentage (hotel): Occupancy % = Room-days occupied ÷ Room-days available × 100; Room-days available = Number of rooms × Days in the period, less rooms out of order if the company's policy says so. State your basis.
Capacity utilisation (transport): Capacity utilisation % = Actual tonne-km (or passenger-km) ÷ Available tonne-km (or passenger-km) × 100; Available = Capacity × Distance run.
Average room rate: Average room rate = Room revenue ÷ Room-days occupied; Compare with the approved tariff to find leakage from discounts.
Revenue per available room: Revenue per available room = Room revenue ÷ Room-days available; Also equals Occupancy % × Average room rate.
Cost per unit of service: Cost per unit = Total cost of service ÷ Units of service delivered; Units differ by sector: billable hour, subscriber, minute, GB, kWh sold.
Capacity utilisation: Capacity utilisation % = (Actual output ÷ Available capacity) × 100; Used for network, plant and billable staff. Low utilisation means fixed cost per unit rises.
Staff utilisation: Utilisation % = (Billable hours ÷ Available hours) × 100; Key for IT firms. Bench time is not billable.
Project profit (fixed price): Profit = Contract price − (Cost incurred + Estimated cost to complete); Expected loss must be recognised in full once it is foreseen.
Percentage of completion: Completion % = (Cost incurred to date ÷ Total estimated cost) × 100; One common measure of progress. Check that the method is applied consistently.
Distribution loss: Loss % = [(Units input − Units billed) ÷ Units input] × 100; Used for power distribution. Compare with the regulator's allowed level.

Quick revision

Service output is intangible, so the cost unit is a measure of activity, not a physical item.
Common cost units: patient-day or bed-day for hospitals, student or course for education, passenger-kilometre for transport, room-night for hotels.
Capacity utilisation is a key audit check in almost every service sector.
Staff cost is usually the largest cost head in services, so test payroll and time records.
Separate fixed from variable costs before judging cost per unit.
Revenue leakage is a core risk: unbilled services, unrecorded usage, wrong rates.
Use operating statistics to cross-check cost and revenue records.
Management audit asks whether operations are economical, efficient and effective.
A good audit report states the finding, the cause, the effect and a recommendation.
Follow sector regulators' requirements where the question refers to them, and do not assume rules not given.
In a scenario, state your assumptions clearly before concluding.
Link every finding to a cost or control impact, not just an observation.

Common mistakes

Treating a service company like a manufacturer and looking for inventory valuation tests. Fix: State that inventory is minimal. Shift the focus to capacity, labour cost, usage records and revenue timing.
Choosing a vague or wrong cost unit, such as cost per hospital instead of per patient-day. Fix: Pick a unit that measures output and can be counted, and use composite units where needed.
Using available bed-days as the denominator for cost per patient day. Fix: Use occupied bed-days for cost per day. Use available bed-days only for occupancy or capacity cost.
Treating all departments as one cost centre. Fix: Always separate revenue centres from service centres and apportion the latter.
Dividing total cost by the wrong number of students, such as admitted instead of enrolled, or year-end instead of average. Fix: Use the enrolment figure for the period the cost relates to. If numbers changed, say you used the average.
Treating grants as ordinary income. Fix: Check the purpose and period of each grant. Unutilised or restricted amounts are not free income. Say so and test utilisation.
Applying manufacturing audit ideas such as stock verification and material usage to a bank or insurer. Fix: Think transactions, controls and services. Replace stock with loan files, claims files and system logs.
Treating bank audit and insurance audit as the same. Fix: For banks stress credit risk, interest margin and treasury. For insurers stress underwriting, claims, reserves, reinsurance and commission.
Using absolute tonne-km when the question asks for commercial tonne-km, or the reverse. Fix: Read the term in the question. For commercial, find the average load first. For legs of equal length, it is the simple average of the outward and return loads. Then multiply by the total distance. For equal legs the two figures match, so recheck your data if they do not.
Choosing the wrong cost unit, such as per vehicle or per room, instead of per tonne-km or per occupied room-day. Fix: Match the unit to what the customer buys and consumes. Cost per occupied room-day is the hotel norm.

Exam tips

Open any theory answer with the four service characteristics, then tie them to the sector in the question.
In case-based MCQs, look for the cost unit and capacity data first. Many options differ only by using the wrong base.
Show the formula and the numbers even for a one-line computation. This protects marks if there is an arithmetic slip.
End performance answers with a recommendation, such as raising utilisation or revising the allocation basis.
Use the sector-specific topics, such as hospitals or transport, to prepare examples you can quote.
Draw the cost-centre split first. It earns marks even if later numbers go wrong.
In MCQs, check whether the denominator is occupied or available bed-days.
For descriptive answers, structure by the patient cycle and add a test for every control.