Question

In: Finance

Luminosity Inc. produces modern light fixtures that sell for $150 per unit. The firm’s manage- ment...

Luminosity Inc. produces modern light fixtures that sell for $150 per unit. The firm’s manage- ment is considering purchasing a high-capacity manufacturing machine. If the high-capacity machine is purchased, then the firm’s annual cash fixed costs will be $60,000 per year, variable costs will be $55 per unit, and annual depreciation and amortization expenses will equal $30,000. If the machine is not purchased, annual cash fixed costs will be $25,000, variable costs will be $105 per unit, and annual depreciation and amortization expenses will equal $10,000. What is the minimum level of unit sales necessary in order for EBIT with the high-capacity machine to be higher than EBIT without that machine?

Expert Solution

EBIT refers to the earning before Interest and taxes, it can be expressed in following equation -

where,

S = sale value (Sale Price(P)*Sale quantity(Q))

VC = Variable cost

FC = Fixed cost including depreciation and amortization expenses.

We have following information provided in question -

High capacity machine-

Sale Price = $ 150

Variable cost(VC) = $ 55

Cash fixed cost = $ 60,000

Depreciation and amortization = $ 30,000

Total fixed cost (FC) = $ 90,000

Old machine -

Sale Price = $ 150

Variable cost(VC) = $ 95

Cash fixed cost = $ 25,000

Depreciation and amortization = $ 10,000

Total fixed cost (FC) = $ 35,000

Firstly, we will calculate the sale quantity (Q) at which EBIT of High capacity machine and EBIT of old machine would be equal.

EBIT of High capacity machine = EBIT of old machine

Q(Sale Price - VC) - FC = Q(Sale Price - VC) - FC

Q(150-55) - 90,000 = Q(150-105) - 35,000

95Q - 90,000 = 45Q - 35000

50Q = 55,000

Q = 55,000/50

Q = 1,100

Thus, at Sale quantity 1,100, the EBIT of both machine is same.

Therefore,

At sales quantity below 1,100 , EBIT of High capacity machine would be lower than EBIT of old machine

At sales quantity above 1,100, EBIT of High capacity machine would be higher than EBIT of old machine

Thus, Minimum level of unit sales necessary in order for EBIT with high capacity machine to be higher than EBIT without that machine is 1,101 units.

Please refer below plot of EBIT and sales units. EBIT-A is EBIT of high capacity machine and EBIT-B is EBIT of old machine.

We can see at sale unit 1,100 EBIT-A crossed over the EBIT-B . That's because the fixed cost recovery rate of high-capacity machine is higher than the old machine recovery rate of fixed cost.

jeff jeffy answered 2 years ago

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