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$$s two profit targets for the coming year are $$1,140,000(25\%$ 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$$s selling price cannot vary above the current selling price of $$270$ per unit but may vary as much as $10\%$ below $$270.$

A division manager can elect to expand fixed production or selling facilities; however, the target profit objective related to fixed costs is increased by $25\%$ of the cost of any such expansion. Furthermore, a manager cannot expand fixed facilities by more than $35\%$ 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 $$1,140,000$ and $$20$ per unit. A summary of these reports shows the following:

Last year$$s sales were $45,000$ units at $$270$ per unit.

DimLok$$s current manufacturing facility capacity is $55,000$ units per year, but can be increased to $110,000$ units per year with an increase of $$1,150,000$ in annual fixed costs.

Present variable costs amount to $$150$ per unit, but DimLok$$s vendors are willing to offer direct materials discounts amounting to $$50$ per unit, beginning with unit number $75,001.$

Sales can be increased up to $130,000$ units per year by committing large blocks of product to institutional buyers at a discounted unit price of $$220.$ However, this discount applies only to sales in excess of $55,000$ 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 $55,000$ units at $$270$ per unit and $26,375$ units at $$220$ 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?

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