Question 7.S-A.Q.1: Khan Ltd can render three different types of service (Alpha,...
Khan Ltd can render three different types of service (Alpha, Beta and Gamma) using the same staff. Various estimates for next year have been made as follows:
| \underline{ Service } | |||
| Alpha | Beta | Gamma | |
| Selling price (£/unit) | 30 | 39 | 20 |
| Variable material cost (£/unit) | 15 | 18 | 10 |
| Other variable costs (£/unit) | 6 | 10 | 5 |
| Share of fixed cost (£/unit) | 8 | 12 | 4 |
| Staff time required (hours) | 2 | 3 | 1 |
Fixed cost for next year is expected to total £40,000.
Required:
(a) If the business were to render only service Alpha next year, how many units of the service would it need to provide in order to break even? (Assume for this part of the question that there is no effective limit to market size and staffing level.)
(b) If the business has limited staff hours available next year, in which order of preference would the three services come?
(c) The maximum market for next year for the three services is as follows:
| Alpha | 3,000 units |
| Beta | 2,000 unit |
| Gamma | 5,000 units |
Khan Ltd has a maximum of 10,000 staff hours available next year.
What quantities of each service should the business provide next year and how much profit would this be expected to yield?
Khan Ltd
(a) The break-even point, if only the Alpha service were provided, would be:
\frac{Fixed costs}{Sales revenue per unit – Variable cost per unit} = \frac{£40,000}{£30 – £(15 + 6)} = 4,445 units (per year)
(Strictly it is 4,444.44 but 4,445 is the smallest number of units of the service that must be provided to avoid a loss.)
(b)
| Alpha | Beta | Gamma | |
| Selling price (£/unit) | 30 | 39 | 20 |
| Variable materials (£/unit) | (15) | (18) | (10) |
| Variable production cost (£/unit) | \underline{(6)} | \underline{(10)} | \underline{(5)} |
| Contribution (£/unit) | \underline{ 9} | \underline{ 11} | \underline{ 5} |
| Staff time (hr/unit) | 2 | 3 | 1 |
| Contribution/staff hour | £4.50 | £3.67 | £5.00 |
| Order of priority | 2nd | 3rd | 1st |
(c)
| Hours | Contribution | |
| Provide: | £ | |
| 5,000 Gamma using | 5,000 generating (that is, 5,000 × £5 = ) | 25,000 |
| 2,500 Alpha using | \underline{5,000} generating (that is, 2,500 × £9 = ) | \underline{22,500} |
| \underline{10,000} | 47,500 | |
| Fixed cost | \underline{(40,000)} | |
| Profit | \underline{7,500} |
This leaves a demand for 500 units of Alpha and 2,000 units of Beta unsatisfied.