Question

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 $1,150,000 (20% return on the investment in the annual fixed costs of the division) and $20 (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 $250 per unit but may vary as much as 10% below $250. 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 $1,150,000 and $20 per unit. A summary of these reports shows the following: Last year’s sales were 44,000 units at $250 per unit. DimLok’s current manufacturing facility capacity is 54,000 units per year, but can be increased to 108,000 units per year with an increase of $1,140,000 in annual fixed costs. Present variable costs amount to $130 per unit, but DimLok’s vendors are willing to offer direct materials discounts amounting to $20 per unit, beginning with unit number 74,001. Sales can be increased up to 128,000 units per year by committing large blocks of product to institutional buyers at a discounted unit price of $230. However, this discount applies only to sales in excess of 54,000 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 54,000 units at $250 per unit and 32,680 units at $230 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

1. Determine the dollar amount of DimLok’s present annual fixed costs per year.
Profit target based on 20% of annual fixed costs	$   1,150,000.00
Fixed Costs = 1,150,000/20%	$   5,750,000.00
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.
First Constraint
Current Capacity	54000	Units
Additional fixed charge for production up to 108,000 units.	$1,140,000
a sales discount of $20 per unit for sales beyond 54,000 units.
a variable cost decrease of $20 per unit after the production of 74,001units
Second Constraint
Contribution per unit below the 54000 unit level = $250 selling price - ($130 variable cost per unit + $20 profit per unit)	$             100.00	per unit
Number of units to achieve the desired profit objectives = (Fixed charges + Desired profit) / Contribution per unit
Number of units to achieve the desired profit objectives = (5750000 + 1150000)/100	69,000.00	Units
69,000 units exceeds capacity by 15,000 units(69000 - 54000)units
Therefore ,the calculation with the current facility at the capacity level of 54,000 units will not meet the profit objectives.
Third Constraint
In order to achieve the profit targets, DimLok must increase plant capacity, thus incurring an additional $1,140,000 in fixed costs. This in turn will increase the profit target based on fixed costs to $1,378,000 {.20 x ($5,750,000 + $1,140,000)}	$1,378,000.00
Contribution per unit below the 54000 unit level = $230 selling price - ($130 variable cost per unit + $20 profit per unit)	$               80.00	per unit
Number of units to achieve the desired profit = (Fixed charges + Desired profit) = Contribution
Number of units to achieve the desired profit = (5750000+1140000+1378000) = ($100 per unit x 54,000 units) + $80(X - 54,000 Units)	89,850.00	Units
89850 units exceeds the 74001 unit constraint; variable costs are reduced by $20 per unit for production in excess of 740001 units
Fourth Constraint
The contribution margin for production in the 74,000 to 108000 units range, with the variable cost per unit reduced to $60 per unit is determined as follows
Contribution per unit below the 54000 unit level = $230 selling price - ($110 variable cost per unit + $20 profit per unit)	$             100.00	per unit
Number of units to achieve the desired profit = (5750000+1140000+1378000) = ($100 per unit x 54,000 units) + ($80 per unit x 20,000 units) $100(X - 74,000 Units)	86,680.00	Units
DimLok must sell 86,680 units in order to achieve both profit objectives of 20 percent return on fixed costs and $20 per unit sold.
c)
DimLok Division
Pro Forma Income Statement
Revenue
54,000 units x $250	$ 13,500,000.00
(86,680 - 54000) units x $230	$   7,516,400.00	$        21,016,400.00
Variable cost
74,000 units x $130	$   9,620,000.00
(86,680 - 74000) units x $110	1,394,800.00	$        11,014,800.00
Contribution		$        10,001,600.00
Fixed Cost		$          6,890,000.00
Operating Profit		$          3,111,600.00
The profit objectives {(20 percent of the annual fixed costs) + ($20 per unit produced)} are met as shown below.
20% x 6890000 + 20 x 86680	$   3,111,600.00