Question

M1_IND3. A distributor of fasteners is opening a new plant and considering whether to use a mechanized process or a manual process to package the product. The manual process will have a fixed cost of $36,234 and a variable cost of $2.14 per bag. The mechanized process would have a fixed cost of $84,420 and a variable cost of $1.85 per bag. The company expects to sell each bag of fasteners for $2.75. a) What is the break-even point for the manual process (in units)? b) What is the break-even point for the mechanized process (in units)? c) A point of indifference for two processes is quantity at which each process generates the same amount of profit (review video). What is the point of indifference for the two processes? (Hint: 1) Use equations to set profit of manual process equal to mechanized process – and solve for quantity; 2) (Excel) If you have a break-even for each process – add another cell the calculates the difference for the profits between the two processes and have only one cell that represents quantity that be used to calculates costs/revenues for each process and use Goal Seek to calculate quantity that would set the difference to zero). d) Which process would you select if the quantity that is sold is greater than the quantity calculated as the point of indifference? e) Which process would you select in the quantity sold is less than the quantity calculated as the point of indifference?

Answer 1

Solution

Back-up Theory

BREAKEVEN ANALYSIS

Terminology

F = Fixed cost, v = Variable cost per unit, T = Total cost, r = Revenue per unit, R = Total revenue,

p = Profit per unit, P = Total profit, x = Number of units.

Then,

T = F + vx ……………………………………………………………………………………… (1)

R = rx …………………………………………………………………………………………… (2)

P = R – T = rx – (F + vx) = x(r - v) - F………………………………………………….………… (3)

Break-even units is that value of x at which P = 0, i.e., x(r - v) = F or x = F/(r - v) …….......……..(4)

Break-even value = xr = rF/(r - v) = F/{1- (v/r)}, where x is the break-even units ……………………………(5)

Now, to work out the solution,

Part (a)

For the manual process,F = 36,234; v = 2.14; r = 2.75.

Vide (4),

The break-even point = 36234/0.61

= 58441.94

The break-even point for the manual process (in units) = 58442 Answer 1

Part (b)

For the mechanized process, F = 84,420; v = 1.85; r = 2.75.

Vide (4),

The break-even point = 84420/0.90

= 93577.78

The break-even point for the mechanized process (in units) = 93578   Answer 2

Part (c)

For the point of indifference for two processes, we should have:

Vide (3), x(0.61) – 36234 = x(0.9) – 84420

Or, 0.29x = 48186

Or, x = 166158.62

The point of indifference for the two processes = 166159 Answer 3

Part (d)

Since for neither process, the quantity that is sold is greater than the quantity calculated as the point of indifference, neither process can be selected. Answer 4

Part (e)

Since for both processes, the quantity that is sold is less than the quantity calculated as the point of indifference, either process can be selected. Answer 5

DONE