How to approach it
- Work backwards: required profit increase + all other incremental costs + lost contribution = revenue − maximum material cost.
- Lost contribution: reduce both sales and variable costs of the existing products.
- Labour: total hours needed; hours freed and spare normal capacity are paid at normal rate; the rest at the overtime rate.
- Material quantity: gross up output for normal loss.
- Fixed costs: include only new ones (annualise monthly salaries).
Key rules to apply
- Relevant costs are future, incremental cash flows caused by the decision.
- Opportunity cost (lost contribution) is relevant when resources or sales are displaced.
- Normal loss increases the input needed for a given output.
Common mistakes
Drawn from the examiners' comments for this sitting (summarised in our words) and from typical errors on this topic.
- Cutting the existing products' sales without cutting their costs (examiners' point).
- Ignoring hours freed by lower production of existing products, or pricing every hour at normal rate.
- Monthly supervisor salaries not converted to a year.
Similar question with worked solution
Written by us with our own numbers; it tests the same skills as Q3 without copying it.
Original practice question
Maximum material price for a new product
A company could launch a product selling 1,000,000 kg at Rs 150/kg. Each kg needs 1 kg of material input with a 4% normal loss of input, and 0.04 labour hours. Labour costs Rs 250/hour normally and 150% of that above normal capacity; variable overhead is Rs 500 per hour worked.
The launch would reduce existing contribution by Rs 6m and free 5,000 normal hours; another 10,000 normal hours are currently spare. Four supervisors would be hired at Rs 150,000 a month. Management wants profit to rise by Rs 30m.
Required: Calculate the maximum price per kg of material input.
Worked solution
| Working | Rs m |
|---|---|
| Revenue: 1,000,000 × 150 | 150.000 |
| Labour normal: 15,000 h × 250 | (3.750) |
| Labour overtime: (40,000 − 15,000) × 375 | (9.375) |
| Variable overhead: 40,000 × 500 | (20.000) |
| Supervisors: 4 × 150,000 × 12 | (7.200) |
| Lost contribution | (6.000) |
| Target profit increase | (30.000) |
| Maximum total material cost | 73.675 |
Material input = 1,000,000 ÷ 0.96 = 1,041,667 kg.
Answer: Maximum ≈ Rs 70.73 per kg (73,675,000 ÷ 1,041,667).