CMA Intermediate · Cost Accounting

Operating Costing - Transport, Hotel and Healthcare: formula sheet

Full chapter guide

Key formulas

Cost per unit of service: Cost per unit = Total cost for the period ÷ Total units of service for the period; Use the same period for cost and units. Units may be simple or composite.
Passenger-km (absolute): Passenger-km = Number of passengers × Distance travelled; Use passengers actually carried when the question gives them; otherwise use the stated capacity × proportion.
Tonne-km (absolute): Absolute tonne-km = Σ(Load in tonnes × Distance in km); Sum trip by trip when load differs on each leg, e.g. outward and return.
Commercial (average) unit: Commercial tonne-km = Average load × Total distance travelled; Average load is the simple arithmetic mean of the loads carried, e.g. (load outward + load return) ÷ 2, not a distance-weighted mean. Do not confuse it with absolute tonne-km, which is Σ(tonnes × km).
Charge per unit with profit: Rate charged = Cost per unit + Profit per unit; If profit is a percentage on takings, rate = Cost per unit ÷ (1 − profit % of takings).
Total operating cost: Standing charges + Maintenance charges + Running charges; Prepare the cost sheet for the same period, usually a month or a year, for all heads.
Absolute tonne-km: Σ (Load in tonnes × Distance in km) for each leg or trip; Add the figures for all legs or trips. An empty return leg has zero load, so it adds nothing to absolute tonne-km.
Commercial tonne-km: Average load × Total km run; Average load = sum of the loads on all legs ÷ number of legs. For a full load out and an empty return over equal distances, the average load is half the full load, and the total km run includes the return.
Passenger-km: Seats × Occupancy % × Km run (or Σ passengers × km); Use the actual passengers if given. Otherwise use capacity at the stated occupancy.
Cost per unit: Total operating cost ÷ Total service units; Units are km, tonne-km or passenger-km, as the question asks.
Depreciation per km: (Cost of vehicle − Residual value) ÷ Estimated life in km; Treat as a running charge if it is based on km. Treat as a standing charge if it is time-based, such as per year.
Fare or rate with profit: Cost per unit + Profit per unit; If profit is a % of takings, cost is (100 − %) of takings. Then takings = cost ÷ (1 − profit rate).
Absolute tonne-km: Σ (load carried on each leg × distance of that leg); Empty legs contribute zero. Use the actual loads leg by leg.
Average load (commercial): Average load = (Sum of loads on the legs) ÷ (Number of legs); Use the simple mean of the loads, for example (load out + load back) ÷ 2. Do not weight by distance.
Commercial tonne-km: Average load × Total distance travelled (all legs); Total distance includes the empty return run. The result differs from absolute tonne-km when leg distances differ.
Passenger-km: Number of passengers × Distance travelled; For a period: passengers carried per trip × km per trip × number of trips. Use occupancy % of seating capacity if given.
Cost per unit: Total operating cost ÷ Total service units (tonne-km or passenger-km); Use the same unit basis for cost and for rate.
Rate with profit on cost: Rate per unit = Cost per unit + Profit % × Cost per unit; Profit as a percentage of cost.
Rate with profit on sales: Rate per unit = Cost per unit ÷ (1 − Profit % of sales); For example, 20% on sales means cost is 80% of the rate.
Available room-days: Available room-days = Number of rooms × Number of days open; Use the days the hotel is actually open. Check whether the year is 365 or 360 days as stated.
Occupied room-days: Occupied room-days = Available room-days × Occupancy %; Occupancy may be given for the whole year or separately for seasons. Compute each season and add.
Occupancy percentage: Occupancy % = Occupied room-days ÷ Available room-days × 100; Use this to compare performance or find break-even occupancy.
Cost per room-day: Cost per room-day = Total cost of room service ÷ Occupied room-days; Divide by occupied days, not available days.
Tariff with margin on cost: Tariff = Cost per room-day + Profit % × Cost per room-day; Use when profit is stated on cost.
Tariff with margin on tariff: Tariff = Cost per room-day ÷ (1 − Profit % on tariff); Use when profit is stated on sales. For 20% on tariff, divide by 0.80.
Break-even occupancy: Break-even room-days = Fixed cost ÷ (Tariff − Variable cost per room-day); Divide by available room-days to express as occupancy %.
Bed-days available: Bed-days available = Number of beds × Number of days in the period; Counts every bed whether occupied or empty. Check whether the question gives a 30-day month or a 365-day year.
Patient-days (occupied bed-days): Patient-days = Bed-days available × Occupancy %; Use for cost per patient-day. If beds differ by ward, calculate ward by ward.
Cost per patient-day: Cost per patient-day = Total cost of the service ÷ Total patient-days; Total cost includes fixed and variable items allocated to the service.
Cost per bed-day: Cost per bed-day = Total cost ÷ Bed-days available; Always lower than or equal to cost per patient-day, as the divisor is larger or equal.
Cost per test or per procedure: Cost per test = Cost of the diagnostic centre ÷ Number of tests; Use the same logic for X-rays, scans, operations.
Charge with profit: Charge per unit = Cost per unit + Profit per unit, or Cost per unit ÷ (1 − profit % on charge); Read whether profit is on cost or on charge.

Quick revision

Operating costing finds the cost of a service, with no stock of finished goods.
Choose the cost unit to suit the service: passenger-km, tonne-km, room-day, bed-day.
Group costs into fixed (standing), semi-variable and variable (running) heads.
Absolute units add up each trip's load times distance.
Commercial units = average load (the arithmetic mean of the loads carried on the trips) × total distance travelled.
Check whether a question gives round trips; empty return legs affect the unit calculation.
Hotel capacity is rooms times days in the period; occupancy is occupied room-days divided by available room-days.
Charge rate equals cost per unit plus the required profit per unit.
Hospital costs are divided between departments before finding cost per patient-day or bed-day.
Show a cost sheet with totals and per-unit figures for step marks.
Read the question for the profit as a percentage of cost or of sales before computing charges.

Common mistakes

Treating operating costing as job costing because each trip or patient looks like a job Fix: Remember that operating costing collects costs for a period and divides by units of service. No job-wise cost sheet is made.
Using the wrong cost unit, such as per km instead of per passenger-km Fix: Underline the unit in the question first and write it beside the final answer.
Mixing up the absolute and commercial tonne-km bases, especially for empty return legs. Fix: Absolute tonne-km counts only the loaded legs (load × distance for each leg). Under commercial tonne-km the empty legs lower the average load, so you use the total km run. The question tells you which basis to use.
Putting depreciation in the wrong head. Fix: Check the basis. If it is per km, use running charges. If it is an annual amount, use standing charges.
Treating the empty return leg as zero distance in commercial tonne-km. Fix: In commercial tonne-km, total distance includes the empty return. Only the average load reflects the empty run.
Averaging the load incorrectly, for example ignoring the empty leg. Fix: Include every leg's load, including zero, when computing the simple mean.
Dividing total cost by available room-days instead of occupied room-days. Fix: Always multiply by occupancy first. Write 'occupied room-days' as the divisor before dividing.
Treating profit on tariff as profit on cost. Fix: If profit is on tariff, divide cost by (1 − profit %). If on cost, multiply by (1 + profit %).
Using bed-days available instead of patient-days (or the reverse). Fix: Underline the unit in the question. Bed-day uses all beds; patient-day uses occupied beds only. State the unit in your answer line.
Ignoring occupancy when beds and days are given. Fix: Always check for an occupancy % or number of patients. Patient-days = beds × days × occupancy.

Exam tips

Theory questions often ask for features and applicability. Give four or five points, each with a one-line service example.
For the difference between operating and job costing, write a short two-column comparison on basis, output, period and cost unit.
In MCQs, check whether the question asks for absolute or commercial units before multiplying.
In numericals, show the cost sheet layout and the unit calculation separately so you earn step marks even if one figure is wrong.
Write the unit with every final answer, such as ₹ per passenger-km.
Always start with the service units. Many students lose the whole answer from a wrong tonne-km or passenger-km.
Draw the cost sheet with three clear heads and subtotals, even when the MCQ-style hint only asks for the rate.
In MCQs, check the period and the unit of the answer. Options are often built on the common errors: the wrong tonne-km basis, or annual costs not divided by 12.