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MENG 445 Production and Inventory Control Breakeven Analysis. Dr. Lotfi Gaafar The American University in Cairo. Introduction to Breakeven Analysis. Breakeven Analysis in the context of Production planning addresses the decision of whether to make or buy a product.

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MENG 445 Production and Inventory ControlBreakeven Analysis

Dr. Lotfi GaafarThe American University in Cairo

Gaafar 2005

introduction to breakeven analysis
Introduction to Breakeven Analysis
  • Breakeven Analysis in the context of Production planning addresses the decision of whether to make or buy a product.
  • Making the product involves two cost elements:
    • Fixed costs such as machine renting cost and operation expenses
    • Variable costs such as raw material cost
  • Buying the product involves only one cost element, the selling price. However, the price may either be constant or variable based on the quantity.

Gaafar 2005

linear breakeven analysis
Linear Breakeven Analysis

Assumptions: (1) Price is constant (p); (2) We have fixed costs; (3) We have constant variable cost.

Buy Cost (BC) = pQ

Making is better

Cost

Make Cost (MC) = FC + vQ

Buying is better

Variable cost: vQ

Fixed Cost: FC

Savings : S = BC – MC = pQ – FC – vQ

Breakeven: S = 0, pQ = FC + vQ

Quantity (Q)

Q’

Gaafar 2005

linear breakeven analysis4
Linear Breakeven Analysis

A particular product sells for a price of $70. If the fixed cost are $800/month and the variable cost per unit is $30/unit, determine the breakeven quantity. [20]

Gaafar 2005

nonlinear breakeven analysis
Nonlinear Breakeven Analysis

Assumptions: (1) Price varies with demand; (2) We have fixed costs; (3) We have constant variable cost.

$

Make Cost (MC) = FC + vQ

Buy Cost (BC) = pQ

Break-even

output

maximum

savings

Break-even

output

Fixed Cost: FC

p = (a – bQ)

  • Savings (S) = pQ – FC – vQ = (a – bQ)Q – FC – vQ
  • S = aQ – bQ2 – (FC+vQ)
  • S = (a-v)Q – bQ2 –FC ………….. (1)
  • Set (1) equal to zero to determine breakeven.
  • Differentiate (1) with respect to Q and set the result equal to zero to find Q that maximizes the savings.

Gaafar 2005

nonlinear breakeven analysis6
Nonlinear Breakeven Analysis

A particular product has a unit price that starts at $78 with a $0.1 discount for each unit purchased. If the fixed cost are $800/month and the variable cost per unit is $30/unit, determine the demand quantity that maximizes the savings of making and the breakeven quantities. [240, 17.28, 462.72]

Gaafar 2005

time value of money
Time Value of Money

Suppose a firm is considering manufacturing a new product and the following data have been provided:

Sales price $12.50/unit

Equipment cost $200,000

Overhead cost $50,000/year

Operating and maintenance cost $25/operating hour

Production time/1000 units 100 hours

Planning horizon 5 years

Minimum attractive rate of return 15%

Determine the sales volume that would make manufacturing this product profitable.

[10,966]

Gaafar 2005

time value of money8
Time Value of Money

Consider a contractor who experiences a seasonal pattern of activity for compressors. The manager currently owns eight compressors and suspects that this number will not be adequate to meet the demand. The contractor realizes that there will arise situations when more than eight compressors will be required, and is considering purchasing an additional compressor for use during heavy demand periods. Local equipment rental firm will rent compressors at a cost of $50/day.

Compressors can be purchased for $6000. The difference in operating and maintenance costs between owned and rented compressors is estimated to be $3000/year.

Letting X denote the number of days a year that more than eight compressors are required, perform a breakeven analysis. Assume a planning horizon of 5 years, zero salvage values, and 20% minimum attractive rate of return. [100.128]

Gaafar 2005

basic definitions
Basic Definitions
  • Fixed/Variable Costs - If costs change appreciably with fluctuations in business activity, they are “variable.” Otherwise, they are “fixed.” A widely used cost model is: Total Costs = Fixed Costs + Variable Costs
  • Price is the amount of money, goods or services that must be given up to acquire ownership or use of a product.
  • Recurring/Nonrecurring Costs are repetitive and occur when an organization produces goods or services on a continuing basis, they are “recurring.” Otherwise they are “nonrecurring.” Variable costs are recurring since they repeat with each unit of output.
  • Direct/Indirect Costs - If costs can be reasonably measured and allocated to a specific output, they are “direct.” Otherwise they are “indirect.”

Gaafar 2005

basic definitions10
Basic Definitions
  • Overhead Costs - All costs of providing goods or services other than direct labor and direct material. Indirect costs are a subset of overhead costs. Fixed overhead relates more to plant capacity than production volume (variable overhead). Allocation of overhead to specific outputs may be in proportion to:

1. Direct labor hours

2. Direct material costs

3. Machine hours

  • Opportunity Costs - The cost of forgoing the chance to earn interest (or profit) on investment funds.

Gaafar 2005