Question

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.

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. Hand-Heid Lawn Sprinklers Estate Sprinklers Units Price per unit Variable costs Labor hours /unit Batch size 1,000,000 $9.00 2.00 2.2 hours 10,000 units 2,000,000 $8.50 4.00 1.9 hours 5,000 units 40.000 $15.00 4.50 2.1 hours 1,000 units Currently, Acme incurs total overhead of $12,776,400 per year and allocates it to individual products using labor hours as the allocation basis. Required: (Round computations and answers to two decimal places, eg $7.89, if it is a negative profit margin show the amount in parenthesis.) a. Determine product profitability under the current method for allocating overhead costs, Profit margin/unit. Hand Held per unit Lawn Sprinklers per unit Estate Sprinklers per unit b. Based on your answers to part (a), Acme's CEO wishes to expand the sales of estate sprinklers and deemphasize lawn sprinklers. However, because the firm's operating personnel seem cool to this idea, the CEO asks you to refine the product cost estimates and shore up her case. You find that $7,300,800 of the overhead is labor related, with the remainder relating to the number of batches run. How does this new information affect your estimates of product profitability? Profit margin/unit. Hand Held Lawn Sprinklers per unit per unit per unit Estate Sprinklers

Answer 1

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