CA Intermediate · Cost and Management Accounting

Service Costing: formula sheet

Full chapter guide

Key formulas

Cost per unit of service: Cost per service unit = Total cost of the service ÷ Number of service units; Use the total cost for the same period and the same service as the units.
Composite cost unit: Composite unit = Measure 1 × Measure 2 (e.g. passenger-km = passengers × km); Used where one measure alone is not fair, such as transport and hospitals (patient-days).
Absolute (weighted) units: Absolute passenger-km = Σ (passengers carried × distance for each trip); Use when passengers or loads differ across trips. Commercial units use average load times distance.
Classification of service costs: Total cost = Fixed (standing) charges + Semi-variable (maintenance) charges + Variable (running) charges; Helps to control cost and to see which costs change with activity.
Cost-unit examples: Transport: passenger-km, tonne-km | Hospital: patient-day, bed-day | Hotel: room-day | Power: kWh | Canteen: meal; Pick the unit that fits the service and that ICAI usually names in the question.
Cost per unit (service): Cost per unit = Total cost for the period ÷ Total service units for the period; Use the same period for cost and units. Total cost means fixed + variable + semi-fixed parts.
Passenger-km: Passenger-km = Number of passengers × Distance travelled in km; Where passengers vary by trip, sum each trip. Ensure you count only the days or trips actually run.
Absolute tonne-km: Absolute tonne-km = Σ (load carried on each leg in tonnes × distance of that leg in km); Use the actual load on each leg. An empty return leg adds zero.
Commercial tonne-km: Commercial tonne-km = Average load in tonnes × Total distance travelled in km; Average load includes legs with zero load. Average load = (sum of loads on all legs ÷ number of legs) when legs are of equal distance. Where legs differ, use the average the question gives or says to compute. Example: 10 tonnes out and empty back gives average load 5 tonnes.
Bed-day: Bed-days = Number of beds × Days available (or occupied, as the question asks); Check whether the question wants available bed-days or occupied bed-days.
Room-day: Room-days = Number of rooms × Days available (or occupied); Occupancy % = Occupied room-days ÷ Available room-days × 100
Semi-fixed cost split: Fixed part + (variable rate × activity) = Total semi-fixed cost; If a question gives two activity levels, variable rate = Change in cost ÷ Change in activity.
Total operating cost: Total cost = Standing charges + Maintenance charges + Running charges; Prepare the sheet for the period given, then convert all items to that same period.
Cost per km: Cost per km = Total operating cost ÷ Total km run; Use km actually run by the vehicle, including empty running.
Passenger-km (absolute): Absolute passenger-km = Σ (Passengers carried on each trip × Distance of that trip); Sum this trip by trip when loads vary. Use it when actual passengers are given.
Passenger-km (occupancy basis): Passenger-km on occupancy basis = Seating capacity × Occupancy % × Total km run, or Seating capacity × Km per day × Days × Occupancy %; Use when occupancy is given as a percentage of capacity. Do not multiply by days again if total km is already given. This is not the same as commercial passenger-km, which is the average of passengers at each stage × total distance. Follow the basis the question names.
Tonne-km (absolute): Absolute tonne-km = Σ (Tonnes carried × Distance of each leg); Empty return legs add zero tonne-km but their km still add cost.
Tonne-km (commercial): Commercial tonne-km = Average load × Total distance travelled. Average load = (Σ tonnes carried at each stage) ÷ number of stages, with stages of equal distance. For loaded-out, empty-back: average load = (Load + 0) ÷ 2; Absolute uses each leg's own load × its own distance. Commercial averages the loads first, then multiplies by total distance. Example with equal stages: stage 1 is 10 tonnes over 100 km and stage 2 is 30 tonnes over 100 km. Absolute = 10 × 100 + 30 × 100 = 4,000. Commercial = (10 + 30) ÷ 2 × 200 = 20 × 200 = 4,000. For a simple loaded-out, empty-back trip both also agree: 10 tonnes, 200 km each way gives 10 × 200 = 2,000 (absolute) and (10 ÷ 2) × 400 = 2,000 (commercial). When stage distances are unequal, the two figures can differ, because commercial is a convention that averages the loads without weighting them by distance. Use the commercial basis only when the question names it, and follow the basis the question names.
Cost per passenger-km or tonne-km: Cost per unit = Total operating cost ÷ Total passenger-km (or tonne-km); Fare = Cost per unit + profit per unit, where profit per unit is computed on the stated base (on takings: fare = cost per unit ÷ (1 − x%)).
Fare with profit on takings: If profit is x% of takings: Takings = Cost ÷ (1 − x%); If profit is x% of cost: Takings = Cost × (1 + x%).
Total units (days-based): Units = Number of rooms or beds × Days in period × Occupancy %; Rooms or beds × days alone gives available units. Multiplying by occupancy gives occupied units (units sold). Use the days stated in the question.
Cost per unit: Cost per unit = Total cost of the period ÷ Total units of service; Total cost includes both fixed and variable costs for the period.
Rate with profit on cost: Charge per unit = Cost per unit × (1 + Profit % on cost); Use when profit is stated as a percentage of cost.
Rate with profit on revenue: Charge per unit = Cost per unit ÷ (1 − Profit % on revenue); Use when profit is stated as a percentage of sales or charge.
Cost per unit with fixed and variable costs: Cost per unit = Variable cost per unit + Fixed cost ÷ Units; When occupancy changes, the variable cost per unit stays the same, but the fixed cost is spread over the new number of units. Use this to find the new cost per unit.
Power cost per kWh: Cost per kWh = Total cost ÷ Units sold (kWh); Units sold = units generated − units lost or used internally.

Quick revision

Service costing finds cost per unit of service, usually a composite unit.
Services are intangible, perishable, inseparable and variable, and cannot be stored as stock.
Absolute passenger-km = passenger capacity of the vehicle × distance. Commercial passenger-km = average (actual) passengers carried × distance.
Absolute tonne-km = load capacity of the vehicle × distance. Commercial tonne-km = average (actual) load carried × distance.
Use whichever basis the question asks for: capacity for absolute units, actual load for commercial units.
Bed-day and room-day depend on the number of days the facility was available or occupied, so read the question carefully.
Occupancy affects the units: use occupied days when cost is per occupied unit.
Classify costs as fixed, semi-variable or variable before you total them.
Cost per unit = total cost for the period ÷ total service units for the period.
Profit added on cost is a percentage of cost; profit on fare is a percentage of fare. Read which one is asked.
Show working notes for units and for cost totals, since they earn step marks.
State the final rate with its unit, such as ₹ per passenger-km.

Common mistakes

Showing closing stock or WIP of a service in the answer. Fix: Remember that services are consumed as they are produced. Show no stock adjustment.
Using only km or only passengers as the cost unit for transport. Fix: Use a composite unit such as passenger-km. Compute it as passengers × distance.
Mixing absolute and commercial tonne-km Fix: Read the question for the word absolute or commercial. For absolute, sum load × distance leg by leg. For commercial, use average load × total distance.
Counting an empty return leg as loaded Fix: Take the load actually carried on each leg. An empty return leg has zero load, so add zero for it in absolute tonne-km.
Using seating capacity instead of passengers actually carried. Fix: Multiply capacity by occupancy % when occupancy is given. Use actual passengers if actual loads are given.
Ignoring empty return km in cost per km, or counting them in tonne-km. Fix: Empty km add to km run and to cost. They add nothing to tonne-km. Keep the two counts separate.
Ignoring occupancy when counting units Fix: Always multiply capacity by days by occupancy %. Write the units line first in your working.
Mixing annual and monthly figures Fix: Convert every cost to the period of the statement before totalling.

Exam tips

Learn the standard cost unit for each service. MCQs often ask you to match service to unit.
Define it as service costing. You may add that it is also known as operating costing in some textbooks, but do not confuse it with operation costing.
In a difference question, give four to five points with one-line contrasts. Avoid long paragraphs.
In numericals, show the unit calculation as a separate line. Marks are often given for it.
There is no negative marking, so attempt every MCQ. Eliminate any option that mentions stock of services.
Draw the trip legs with load and distance before any calculation. It gives a clean working note and secures step marks.
Check whether the question wants available or occupied units. Hospital and hotel MCQs often turn on this single word.
When a cost is semi-fixed, show the split in a line of working. Even if the final figure is wrong, you earn marks for the method.