Question

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RayLok Incorporated has invented a secret process to improve light intensity and, as a result, manufactures a variety of products related to this process. Each product is independent of the others and is treated as a separate profit/loss division. Product (division) managers have a great deal of freedom to manage their divisions as they think best. Failure to produce target divisional income is dealt with severely; however, rewards for exceeding one’s profit objective are, as one division manager described them, lavish.

The DimLok Division sells an add-on automotive accessory that automatically dims a vehicle’s headlights by sensing a certain intensity of light coming from a specific direction. DimLok has had a new manager in each of the 3 previous years because each manager failed to reach RayLok’s target profit level. Donna Barnes has just been promoted to manager and is studying ways to meet the current target profit for DimLok.

DimLok’s two profit targets for the coming year are $840,000 (20% return on the investment in the annual fixed costs of the division) and $30 (pre-tax) profit for each DimLok unit sold. Other constraints on the division’s operations are as follows:

Production cannot exceed sales because RayLok’s corporate advertising program stresses completely new product models each year, although the models might have only cosmetic changes.

DimLok’s selling price cannot vary above the current selling price of $210 per unit but may vary as much as 10% below $210.

A division manager can elect to expand fixed production or selling facilities; however, the target profit objective related to fixed costs is increased by 20% of the cost of any such expansion. Furthermore, a manager cannot expand fixed facilities by more than 30% of existing fixed cost levels without approval from the board of directors.

Donna is now examining data gathered by her staff to determine whether DimLok can achieve its target profits of $840,000 and $30 per unit. A summary of these reports shows the following:

Last year’s sales were 34,000 units at $210 per unit.

DimLok’s current manufacturing facility capacity is 44,000 units per year, but can be increased to 88,000 units per year with an increase of $1,040,000 in annual fixed costs.

Present variable costs amount to $100 per unit, but DimLok’s vendors are willing to offer direct materials discounts amounting to $30 per unit, beginning with unit number 64,001.

Sales can be increased up to 108,000 units per year by committing large blocks of product to institutional buyers at a discounted unit price of $180. However, this discount applies only to sales in excess of 44,000 units per year.

Donna believes that these projections are reliable and is now trying to determine what DimLok must do to meet the profit objectives assigned by RayLok’s board of directors.

Required:

1. Determine the dollar amount of DimLok’s present annual fixed costs per year.

2. Determine the number of units that DimLok must sell to achieve both profit objectives. Be sure to consider all constraints in determining your answer.

3. Without regard to your answer in requirement 2, assume that Donna decides to sell 44,000 units at $210 per unit and 42,100 units at $180 per unit.

(a) Prepare a budgeted income statement (contribution format) for DimLok showing budgeted operating income.

(b) Would this projected operating income meet the stated profit objectives?

Answer 1

Part 1)

The dollar amount of DimLok’s present annual fixed costs per year is calculated as follows:

Dollar Amount of DimLok’s Present Annual Fixed Costs = Dollar Value of Profit Target/Percentage Return on Investment in the Annual Fixed Costs = 840,000/20% = $4,200,000

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Part 2)

The relevant constraints are highlighted below:

1) Current manufacturing facility capacity is 44,000 units.

2) $1,040,000 in additional fixed charge for production up to 88,000 units.

3) A sales discount of $30 (210 - 180) per unit for sales beyond 44,000 units.

4) A variable cost decrease of $30 per unit after the production of 64,000 units

____

The number of units to achieve desired profit objectives at the current capacity is calculated as below:

Number of Units = (Fixed Costs + Desired Profit)/Contribution Margin Per Unit

Here, Fixed Costs = $4,200,000, Desired Profit = $840,000 and Contribution Margin Per Unit below 44,000 units = 210 - (100 + 30) = $80 per unit

Using these values in the above formula, we get,

Number of Units = (4,200,000 + 840,000)/80 = 63,000 units

Current capacity level will not be able to meet the profit objectives as 63,000 units exceed the plant capacity of 44,000 units.

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As current capacity is not sufficient to meet the profit objectives, DimLok will have to increase plant capacity resulting in an additional fixed charge of $1,040,000 which in turn will increase the profit target based on fixed cost to $1,048,000 [20%*(4,200,000 + 1,040,000)]. The revised contribution margin for units in the range of 44,000 to 64,000 units will be $50 per unit [180 - (100 + 30)]. Now, we can calculate the desired number of units to achieve both profit objectives as below:

Number of Units = (5,240,000 + 1,048,000)/[(80*44,000 + 50*(X - 44,000)]

Solving further, we get,

Number of Units = 6,288,000/(3,520,000 + 50X - 2,200,000)

Number of Units = 6,288,000/(1,320,000 + 50X)

Solving for X, we get,

X = (6,288,000 - 1,320,000)/50 = 99,360 units

At a level of 99,360 units, the unit constraint of 64,000 units is not met. For units exceeding 64,000 units, the variable cost is reduced by $30.

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Reduction in variable cost per unit for units in excess of 64,000 units will result in a contribution margin of $80 per unit [180 - (100 - 30 + 30)].

Now, we can calculate the desired number of units to achieve both profit objectives as below:

Number of Units = (5,240,000 + 1,048,000)/[(80*44,000 + 50*(64,000 - 44,000) + 80*(X - 64,000)]

Solving further, we get,

Number of Units = 6,288,000/(1,320,000 + 1,000,000 + 80X - 5,120,000)

Number of Units =  6,288,000/(-2,800,000 + 80X)

Solving for X, we get,

Number of Units = (6,288,000 + 2,800,000)/80 = 113,600 units (answer for Part 2)

The number of total units needed to achieve both the profit objectives is 113,600 units.

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Part 3)

(a)

The budgeted income statement is prepared as below:

DimLok Division
Proforma Income Statement
Revenue
44,000*210	9,240,000
42,100*180	7,578,000	16,818,000
Variable Costs
64,000*100	6,400,000
22,100*70	1,547,000	7,947,000
Contribution		8,871,000
Fixed Costs		5,240,000
Operating Income		$3,631,000

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(b)

Yes, the projected operating income meets the stated profit objectives shown as below:

Total Desired Profit = 20%*Fixed Cost + Profit Per Unit*Total Units Sold = 20%*5,240,000 + 30*(64,000 + 22,100) = $3,631,000 (same as calculated in Part 3a)