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 $800,000 (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 $200 per unit but may vary as much as 10% below $200.

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 $800,000 and $20 per unit. A summary of these reports shows the following:

Last year’s sales were 30,000 units at $200 per unit.

DimLok’s current manufacturing facility capacity is 40,000 units per year, but can be increased to 80,000 units per year with an increase of $1,000,000 in annual fixed costs.

Present variable costs amount to $80 per unit, but DimLok’s vendors are willing to offer direct materials discounts amounting to $20 per unit, beginning with unit number 60,001.

Sales can be increased up to 100,000 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 40,000 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.

Total Fixed Costs:

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.

Required Sales Volume (units):

3. Without regard to your answer in requirement 2, assume that Donna decides to sell 40,000 units at $200 per unit and 24,000 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

1	The dollar value of DimLoks present annual fixed costs is calculated as follows:
	Profit target based on 20% of annual fixed costs	800000
	Total Fixed Costs	$800000/.20
		$4,000,000
2	DimLok must sell 64000 units in order to achieve both profit objectives of 20 percent return on fixed costs
	and $20 per unit sold
	The solution must consider the following constraints
a	40000 unit capacity for the current facility
b	$1000000 additional fixed charge for production up to 80000 units
c	a sales discount of $20 per unit for sales beyond 40000 units
d	a variable cost decrease of $20 per unit after the production of 60000 units
	The calculation with current facility at capacity level of 40000 units will not meet the profit objectives.
	Contribution per unit below the 40001 unit level.
	$200 S.P -($80 variable cost per unit +$20 profit per unit)
	$100 contribution per unit to 40000
	Calculation of the number of units to achieve the desired profit objectives.
	Fixed Charges +Desired Profit /Contribution per unit
	$4000000+$800000/$100 per unit
	48000 units
	48000 units exceeds capacity by 8000 units.
	In order to achieve the profit targets Dimlok must increase plant capacity thus incurring an additional $1000000 in fixed costs.
	This is turn will increase the profit target based on fixed costs to $1000000{.2($4000000+$1000000)}
	The contribution for production in the 40001 to 60000 units range with the selling price reduced to $180 per units as below:
	$180 S.P -($80 variable cost per unit +$20 profit per unit)
	$80 contribution per unit
	Calculation of number of units to achieve overall profit objectives.
	Fixed Charges +Desired Profit
	($5000000+$1000000
	$100 per unit *40000 units +$80 (X-40000 units)
	65000 units.
	65000 units exceeds the 60000 unit constraint variable cost are reduced by $20 per unit for production in excess of 60000 units.
	The contribution margin for production in the 60000 to 80000 units range with the variable cost per unit reduced to $60 per unit
	is determined as below:
	$180 S.P -($60 variable cost per unit +$20 profit per unit )
	$100 contribution per unit
	Calculation of number of units to achieve overall profit objectives
	Fixed Charges +desired profit
	($5000000+$1000000)
	$100 per unit *40000 units + ($80 *20000 units )+ $100(X-60000 units)
	64000 units
3	Dimlok Division
a	Proforma Income Statement
	Revenue
	40000 units * $200	$8,000,000
	24000 units *$180	$4,320,000	$12,320,000
	Variable costs
	60000 units * $80	$4,800,000
	4000 units * $60	$240,000	$5,040,000
	Contribution		$7,280,000
	Fixed Costs		$5,000,000
	Operating Income		$2,280,000
b	The profit objective {(20 percent of annual fixed costs)+($20 per unit produced )} are met as
	below
	(.20 *$5000000)+($20 *64000 units produced)
	$1000000+$1280000
	$2,280,000