The Acme Corporation manufactures a number of different kinds of sprinklers in three broad product lines. The following table provides relevant information about the product lines.
Homework Answers
Answer a)
Calculation of Profit per unit under Current Plan
|
Particulars |
Hand-Held |
Lawn Sprinklers |
Estate Sprinklers |
|
Selling Price per unit |
$ 9.00 |
$ 8.50 |
$ 15.00 |
|
Less: Variable Costs per unit |
$ 2.00 |
$ 4.00 |
$ 4.50 |
|
Contribution Margin per unit |
$ 7.00 |
$ 4.50 |
$ 10.50 |
|
Less: Overhead Costs per unit |
$ 4.62 |
$ 3.99 |
$ 4.41 |
|
Profit per unit |
$ 2.38 |
$ 0.51 |
$ 6.09 |
Note: If overheads are allocated on the basis of direct labour hours, profit per unit is highest in Estate Sprinklers (i.e. $ 6.09 per unit), followed by Hand-hand sprinklers (i.e. $ 2.38 per unit) and least in the case of Lawn Sprinklers (i.e. $ 0.51 per unit).
Working Notes:
|
Product |
Number of Units |
Labour hours per unit |
Total Labour Hours |
Allocated Overheads based on Labour hours |
Overhead per unit |
|
Hand-Held |
1,000,000 |
2.20 |
2,200,000 |
$ 4,620,000 |
$ 4.62 |
|
Lawn Sprinklers |
2,000,000 |
1.90 |
3,800,000 |
$ 7,980,000 |
$ 3.99 |
|
Estate Sprinklers |
40,000 |
2.10 |
84,000 |
$ 176,400 |
$ 4.41 |
|
Total |
6,084,000 |
$ 12,776,400 |
|||
Total Labour hours
Total Labour hours = Number of units produced X Labour hours per unit
Hand-Held:
Total Labour hours = 1,000,000 units X 2.20 Labour hours per unit
= 2,200,000 labour hours
Lawn Sprinklers:
Total Labour hours = 2,000,000 units X 1.90 Labour hours per unit
= 3,800,000 labour hours
Estate Sprinklers:
Total Labour hours = 40,000 units X 2.10 Labour hours per unit
= 84,000 labour hours
Overhead Rate per direct Labour hour
Overhead Rate per direct Labour hour = Total Estimated overheads/ Total estimated direct labour hours
= $ 12,776,400/ 6,084,000 direct labour hours
= $ 2.10 per direct labour hour
Therefore overhead rate is $ 2.10 per direct labour hour.
Allocation of overheads based on direct labour hours
Allocated overheads = Number of direct labour hours X overhead rate per direct labour hour
Hand-Held:
Allocated overheads = 2,200,000 labour hours X $ 2.10 per direct labour hour
= $ 4,620,000
Lawn Sprinklers:
Allocated overheads = 3,800,000 labour hours X $ 2.10 per direct labour hour
= $ 7,980,000
Estate Sprinklers:
Allocated overheads = 84,000 labour hours X $ 2.10 per direct labour hour
= $ 176,400
Overhead rate per unit
Overhead rate per unit= Total allocated overheads/ Total units produced
Hand-Held:
Overhead rate per unit = $ 4,620,000/ 1,000,000 units
= $ 4.62 per unit
Lawn Sprinklers:
Overhead rate per unit = $ 7,980,000/ 2,000,000 units
= $ 3.99 per unit
Estate Sprinklers:
Overhead rate per unit = $ 176,400/ 40,000 units
= $ 4.41 per unit
Answer b)
Calculation of Profit per unit based on proposed allocation overheads
|
Particulars |
Hand-Held |
Lawn Sprinklers |
Estate Sprinklers |
|
Selling Price per unit |
$ 9.00 |
$ 8.50 |
$ 15.00 |
|
Less: Variable Costs per unit |
$ 2.00 |
$ 4.00 |
$ 4.50 |
|
Contribution Margin per unit |
$ 7.00 |
$ 4.5 |
$ 10.50 |
|
Less: Overhead Costs |
|||
|
Labour Related |
$ 2.64 |
$ 2.28 |
$ 2.52 |
|
Batch Wise |
$ 1.014 |
$ 2.028 |
$ 10.14 |
|
Profit per unit |
$ 3.346 |
$ 0.192 |
-$ 2.16 |
Conclusion: The contention of the company’s CEO to expand the production of Estate sprinklers and to deemphasize lawn sprinklers is incorrect. It is because, if overhead costs are allocated on each product based on the number of direct labour hours and number of batches separately, each lawn sprinkler is providing a profit of $ 0.192 as against loss per unit of $ 2.16 in case of Estate Sprinklers.
Thus it can said that since Lawn sprinklers are more profitable than estate sprinklers, the proposed decision to expand the production of Estate sprinklers and to deemphasize lawn sprinklers should not be implemented.
Working Notes:
Overhead Allocation based on Direct Labour hours: $ 7,300,800.
|
Product |
Number of Units |
Labour hours per unit |
Total Labour Hours |
Allocated Overheads based on Labour hours |
Overhead per unit |
|
Hand-Held |
1,000,000 |
2.20 |
2,200,000 |
$ 2,640,000 |
$ 2.64 |
|
Lawn Sprinklers |
2,000,000 |
1.90 |
3,800,000 |
$ 4,560,000 |
$ 2.28 |
|
Estate Sprinklers |
40,000 |
2.10 |
84,000 |
$ 100,800 |
$ 2.52 |
|
Total |
6,084,000 |
$ 7,300,800 |
|||
Total Labour hours: Total labour hours for each product calculated in part (a) are used.
Overhead Rate per direct Labour hour
Overhead Rate per direct Labour hour = Total Estimated overheads/ Total estimated direct labour hours
= $ 7,300,800/ 6,084,000 direct labour hours
= $ 1.20 per direct labour hour
Therefore overhead rate is $ 1.20 per direct labour hour.
Allocation of overheads based on direct labour hours
Allocated overheads = Number of direct labour hours X overhead rate per direct labour hour
Hand-Held:
Allocated overheads = 2,200,000 labour hours X $ 1.20 per direct labour hour
= $ 2,640,000
Lawn Sprinklers:
Allocated overheads = 3,800,000 labour hours X $ 1.20 per direct labour hour
= $ 4,560,000
Estate Sprinklers:
Allocated overheads = 84,000 labour hours X $ 1.20 per direct labour hour
= $ 100,800
Overhead rate per unit
Overhead rate per unit= Total allocated overheads/ Total units produced
Hand-Held:
Overhead rate per unit = $ 2,640,000/ 1,000,000 units
= $ 2.64 per unit
Lawn Sprinklers:
Overhead rate per unit = $ 4,560,000/ 2,000,000 units
= $ 2.28 per unit
Estate Sprinklers:
Overhead rate per unit = $ 100,800/ 40,000 units
= $ 2.52 per unit
Overhead Allocation based on Number of batches:
|
Product |
Number of Units |
Number of units per batch |
Number of batches for each product |
Allocated Overheads based on number of batches |
Overhead per unit |
|
Hand-Held |
1,000,000 |
10,000 batches |
100 |
$ 1,014,000 |
$ 1.014 |
|
Lawn Sprinklers |
2,000,000 |
5,000 batches |
400 |
$ 4,056,000 |
$ 2.028 |
|
Estate Sprinklers |
40,000 |
1,000 batches |
40 |
$ 405,600 |
$ 10.14 |
|
Total |
540 |
$ 5,475,600 |
|||
Overhead Allocation based on Number of batches = Total overhead costs – overheads allocated based on direct labour hours
= $ 12,776,400 - $ 7,300,800
= $ 5,475,600
Calculation of number of batches
Number of batches = Total number of units produced/number of units per batch
Hand-Held:
Total number of batches= 1,000,000 units/ 10,000 units per batch
= 100 units per batch
Lawn Sprinklers:
Total number of batches= 2,000,000 units/ 5,000 units per batch
= 400 units per batch
Estate Sprinklers:
Total number of batches= 40,000 units/ 1,000 units per batch
= 40 units per batch
Overhead Rate per batch
Overhead Rate per direct Labour hour = Total Estimated overheads/ Total number of batches
= $ 5,475,600/ 540 batches
= $ 10,140 per batch
Therefore overhead rate is $ 10,140 per batch.
Allocation of overheads based on number of batches
Allocated overheads = Number of batches X overhead rate per batch
Hand-Held:
Allocated overheads = 100 batches X $ 10,140 per batch
= $ 1,014,000
Lawn Sprinklers:
Allocated overheads = 400 batches X $ 10,140 per batch
= $ 4,056,000
Estate Sprinklers:
Allocated overheads = 40 batches X $ 10,140 per batch
= $ 405,600
Overhead rate per unit
Overhead rate per unit= Total allocated overheads/ Total units produced
Hand-Held:
Overhead rate per unit = $ 1,014,000/ 1,000,000 units
= $ 1.014 per unit
Lawn Sprinklers:
Overhead rate per unit = $ 4,056,000/ 2,000,000 units
= $ 2.028 per unit
Estate Sprinklers:
Overhead rate per unit = $ 405,600/ 40,000 units
= $ 10.14 per unit
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