Thursday, September 26, 2013

Break-Even Analysis

The objective of most business enterprises is to make as much profit as possible.  The purpose of break-even analysis is to determine the number of units of a product (the volume) to produce that will equate total revenue with total cost.  At this point, referred to as the break-even point, profit is zero.  The break-even point gives the manager a point of reference in determining how many units will be needed to ensure a profit.

The three components of break-even analysis are volume, cost and profit.

Volume is the level of production by a company.  Volume can be expressed as the number of units (quantity) produced and sold, as the dollar volume of sales or a percentage of total capacity available,

Costs
Two types of costs are typically incurred in the production of a product: fixed costs and variable costs.  Fixed costs are generally independent of the volume of units produced,  That is, fixed costs remain constant regardless of how many units of product are produced within a given range.  The costs of items such as the following, taken together, result in total fixed costs: Rent on plant and equipment, taxes, insurance, management and staff salaries, advertising, interest on investment, depreciation on plant and equipment, heat and light, janitorial services.

Variable costs are determined on a per-unit basis.  Thus, total variable costs depend on the number of units produced.  The costs of the following items are variable costs: raw materials and resources, direct labor, packaging, material and product handling, maintenance, freight

Total variable costs are function of the volume and the variable cost per unit.  This relationship can be expressed mathematically as :
 total variable cost = VCv
where: Cv = variable cost per unit; v = volume (number of units)

The total cost of an operation is computed by summing total fixed cost and total variable cost, as follows:
total cost = total fixed cost + total variable cost or TC = Cf +VCv where Cf = fixed cost

Profit
The third component in our break-even model is profit.  Profit is the difference between total revenue and total cost.  Total revenue is the volume multiplied by the price per unit.

Total revenue = vp where p (price per unit)

Total profit = total revenue - total cost

break - even volume = Cf/p - Cv

break-even sales volume = pv

break-even volume as percentage of capacity = v/k

1.  The Texas Electronics Company produces calculators.  The annual fixed cost of producing calculators is $280,000.  The variable cost of producing a calculator is $8.  The company sells the calculators for $26.  Given an annual volume of 60,000 calculators, determine the total cost, total revenue, profit, break-even volume, and break-even sales volume.  If production capacity is 80,000 calculators, determine the break-even volume as a percentage of capacity.

2. The Willow Furniture produces tables.  The fixed monthly cost of production is $8,000, and the variable cost per table is $65.  The tables sell for $180 apiece.  For a monthly volume of 300 tables, determine the total cost, total revenue, and profit, determine the monthly break-even volume for the Willow Furniture Company operation. Determine the break-even sales volume.

3.  The Retread Tire Company recaps tires.  The fixed annual cost of the recapping operation is $60,000.  The variable cost of the recapping a tire is $9.  The company charges $25 to recap a tire.  For an annual volume of 12,000 tires, determine the total cost, total revenue, and profit.  Determine the annual break-even volume.  Determine the break-even sales volume.  If the maximum operating capacity of the Retread Tire Company is 8,000 tires annually, determine the break-even volume as a percentage of capacity.

4.  The Rolling Creek Textile Mill produces cotton denim.  The fixed monthly cost is $21,000, and the variable cost per yard of denim is $0.45.  The mill sells a yard of denim for $1.30.  For a monthly volume of 18,000 yards of denim, determine the total cost, total revenue, and profit.  Determine the monthly break-even volume. If the maximum operating capacity of the Rolling Creek Textile Mill  is 25,000 yards of denim per month, determine the break-even volume as a percentage of capacity.


Tuesday, September 17, 2013

Inventory Model

An inventory is a stock or store of goods,  It may be thought of as a resource or a list of some category of materials, machines, people, money or information for some organizational unit at some time.  Proper inventory management is an essential function of all business operations. Most of the problems in inventory fall into one of the following categories A. The proper quantity of inventory to order at any given time (How much to order? B. the proper time to order the quantity (When to order?).  Four basic costs are associated with inventories: purchase cost; holding or carrying cost; ordering costs and shortage cost.  Annual cost of inventory is the sum of the annual ordering cost and annual carrying cost.

1. Holding or carrying cost relates to physically holding items in storage.  This cost is proportional to the amount of inventory and the time over which it is held.  They include interest, insurance, taxes, depreciation, obsolescence, deterioration, spoilage, pilferage, breakage, and warehousing cost (heat, light, rent, security).

2.  Ordering or set up costs are costs associated with ordering and receiving inventory.  This cost is incurred whenever an inventory is replenished.  These costs include determining how much is needed, typing up invoices, inspecting goods upon arrival for quality and quantity, moving the goods to temporary storage.

3.  Purchase or Direct Production cost is for vendor supply environments or direct production cost in case of items produced by user.  In either situation the unit cost may be constant for all replenishment quantities, or it may vary with the quantity purchased or produced.

4.  Shortage costs result when demands excess the supply of inventory on hand.  The cost can include the opportunity cost of not making a sale, loss of customer goodwill, lateness charges, and similar costs. Furthermore, if the shortage occurs in an item carried for internal use, the cost of lost production or downtime is considered a shortage cost.

Exercises

1.  Suppose that MYCOLA company has a beverage product that has a constant annual demand rate of 7200 cases.  A case of soft drink costs P288.  Ordering cost is P200 per order and inventory carrying cost is charged at 25% of the cost per unit.  Identify the following aspects of the inventory policy: a) economic order quantity; b) annual carrying cost; c) total annual cost

2.  Electronic village stocks and sells a particular brand of personal computer.  It costs the store P450 each time it places an order with the manufacturer for the personal computers.  The annual cost of carrying the PCs in inventory is P170.  The store manager estimates that annual demand for the PCs will be 1200 units.  Determine the optimal order quantity and the total minimum inventory cost.

3. The Docs Company purchases a component used in the manufacture of automobile generators directly from the supplier.  Docs's generator production operation which is operated at a constant rate, will require 10,000 components per month throughout the year (120,000 units annually).  Assume ordering cost at P2500 per order, unit cost is P40,000 per component, and annual inventory holding costs are charged at 20%.  Answer the following: a) WHat is the EOQ for this componet?; b) What are the total annual inventory holding and ordering costs associated with the recommended EOQ?

4.  Mimi Corporation has an annual sales of 9000 CD's.  Each inventory item has a value of P200.  Ordering cost is P400 per order.  Carrying cost is 25% of average inventory value.  Find the following: a) optimal number of order per year; b) prior order quantity; c) annual carrying and ordering costs; d) total annual cost.

5.  The annual inventory requirement at the Q and A Enterprises is 14400 units.  Price is P60 per unit.  Ordering cost is P800 per order.  Carrying cost is 25% of average inventory.  Find the following a) economic order quantity; b) annual carrying cost; c) annual ordering cost; d) total annual cost.

6.  The K and V Company is panning to stock its product which is classified as an inventory item.  The company has developed the following information: annual usage is 16,200 units, cost of the inventory per unit is P730; ordering cost is P220 per order; carruing cost is 28% of inventory value per year.  Determine the optimum number of units per order.

7.  The Atlantic Paper company produces paper from wood pulp, which it purchases from the Adirondack Lumber Products Company.  Atlantic needs 450,000 pounds of wood pulp per year (365 days) to meet its customers' demand for paper.  Each order of pulp costs Atlantic P700, and it costs 0.30 per pound per year to carry a pound of pulp in inventory.  It takes 8 days for Atlantic to receive an order from the Adirondack Company.  Determine the following: a) economic order quantity; b) minimum total annual inventory cost.



Monday, September 9, 2013

FORECASTING

Forecasting is the art and science of predicting future events.  It may involve taking historical data and projecting them into the future with some sort of mathematical model.

The three categories of Forecasting Time Horizons are:
1. Short-range forecast this has a time span of up to one year but is generally less than three months.
2.  Medium-range forecast that generally spans from three months up to three years.
3.  Long-range forecast three years or more is its time span.

Types of Forecasts
1. Economic forecasts  model of this type are valuable in helping business prepare medium-to-long range forecasts.
2.  Technological forecasts are concerned with the rates of technological progress.Such forecasts can be critical in such high technology industries such as nuclear power, aerospace, oil and computing.
3.  Demand forecast is a projection of a company's sales for each time period in the planning horizon.

Quantitative Forecasting Techniques
1. Moving Averages  are useful if we can assume that market demands will stay fairly steady over time.
2.  Weighted Moving Averages when there is a trend or pattern, weights can be used to place more emphasis on recent values.
3.  Exponential Smoothing is a forecasting method that is easy to use and efficiently handled by computers, although it is a type of moving average technique, it involves very little record keeping of past data.
4.  Regression Analysis it is the most common quantitative causal forecasting model.


Practice Exercises
1. The sales at Ed's Catering are shown in the middle column of the following table.  A three-month moving average appears on the right.
______________________________________________________________________________
Month                             Actual Sales    Three-month moving average Three-month weighted moving average
January                                             15
February                                           18
March                                               21
April                                                 19
May                                                 24
June                                                 23
July                                                  21
August                                             26
September                                       29
October                                           31
November                                       30
December                                       29
________________________________________________________________________________

2. Period                Actual Demand               Forecast (0.10)                   Forecast (0.40)
1                                      42
2                                      40
3                                      43
4                                      40
5                                      41
6                                      39
7                                      46
8                                      44
9                                      45
10                                    38
11                                    40
12
_________________________________________________________________________________

3. Year                                      Local Payroll                           Sales
1992                                                 2                                        1
1993                                                 3                                        3
1994                                                 2.5                                     4
1995                                                 2                                        2
1996                                                 2                                        1
1997                                                 3.5                                     7

4. Hours of study                      Exam score
           25                                      93
           12                                      57
           18                                      55
           26                                      90
           19                                      82
            20                                     95
            23                                     95
            15                                     80
            22                                     58
            8                                       61

5.  Sales              Profit
          7                0.15
          2                 0.10
         6                  0.13
         4                  0.15
        14                 0.25
        15                 0.27
        16                 0.24
        12                 0.20
        14                 0.27
        20                  0.44
        15                 0.34
          7                 0.17

6.  Month                  Delivered Orders per month     three-month moving      three-month weighted
January                                     120
February                                   90
March                                       100
April                                          75
May                                           110
June                                            50
July                                             75
August                                        130
September                                  110
October                                       90

7.  Attendance and Promotional Expenditure Data
Year                     Promotional Expenditures                             Home Attendance
1975                                     5.7                                                        7
1976                                     5.5                                                       10
1977                                     6.5                                                         9
1978                                     9.0                                                        12
1979                                    6.9                                                          8
1980                                     8.1                                                         14
1981                                     9.5                                                         15
1982                                    10.2                                                        17
1983                                     8.2                                                         16
1984                                     10.6                                                       18

8.