5 Chapter Calculation
Page 194 Example
Product
(1)
A department works one 8-hour shift, 250 days per year, and
has these figures for usage of a machine that is currently being
considered:
Di Annual
Demand (2)
Pi Standard
processing time per
unit .(Hr) (3)
Processing time
needed (Hr) (2)*(3)
Di * Pi
1
400
5.0
400*5 =2000
2
300
8.0
300*8 = 2400
3
700
2.0
700*2 =1400
Working one 8-hour shift 250
days a year provides an
annual capacity= 8 *250 =
2000 hours per year=T
Required volume = 5800
hours/(2000hours/machine
=2.90 machines
5800
k
NR =
pD
i
i =1
T
i
= 5800/2000
where
N R = number of required machines
pi = standard processing time for product i
Di = demand for product i during the planning horizon
T = processing time available during the planning horizon
Page 202 Cost-Volume Analysis
Cost-volume analysis
Focuses on the relationship between cost,
revenue, and volume of output
Fixed Costs (FC)
tend to remain constant regardless of output volume
Variable Costs (VC)
vary directly with volume of output
VC = Quantity (Q) x variable cost per unit (v)
Total Cost
TC = Q x v
Total Revenue (TR)
TR = revenue per unit (R) x Q
Break-Even Point (BEP)
BEP
The volume of output at which total cost and
total revenue are equal
Profit (P) = TR TC = R x Q (FC +v x Q)
= Q(R v) FC
QBEP
FC
=
R v
P + FC
Q=
Rv
TR = Q *r
TP = TR TC
TC =FC + Q * v
Page 204 Example 3
The owner of Old-Fashioned Berry Pies, S. Simon, is contemplating adding
a new line of pies, which will require leasing new equipment for a month
payment of $6,000. Variable cost would be $2 per pie, and pies would
retail for $7 each.
FC =$6,000, v = $2/pie, R =$ 7/pie
BEP , TP=0 = TR=TC
a. How many pies must be sold in order to break even?
QBEP
FC
=
R v
=$6,000/($7-$2) = 1,200 pies per month
b.
What would be the
profit (loss) be if
1,000 pies are
made and sold in a
month?
= 1000 (7-2) 6000
Profit (P) = TR TC = R x Q (FC +v x Q) = Q(R v)
= - $1,000
c. FC many pies must be sold to realize a profit of $4,000?
How
P + FC
Profit (P) = TR TC = R x Q (FC +v x Q) = Q(R v)
Q=
FC
Rv
Q = ($4000 + $6000)/($7-$2) = 2000 pies
d. If 2,000 can be sold, a profit target is $5,000, What price should be charged per pie?
Profit = Q(R- v) FC $5000 = 2000(R - $2) -$6000 = 2000R -$4000 -$6000 = 2000R
-$10000
R =$15000/2000 = $7.5/pie
No 2/211 In a job shop, effective capacity is only 50 percent of design capacity,
and annual output is 80 percent of effective output. What design would
be capacity needed to achieve an actual output of eight jobs per week.
Actual output
Efficiency =
= 80%
Effective capacity
Actual output = .8 (Effective capacity)
Effective capacity = .5 (Design capacity)
Actual output = (.5)(.8)(Effective capacity)
Actual output = (.4)(Design capacity)
Utilization
Actual output = 8 jobs
Utilization = .4
Actual output
=
Design capacity
Actual output
8
Design Capacity =
= = 20 jobs
Effective capacity .4
No. 3/211 A producer of pottery is considering the addition of a new plant
to absorb the backlog of demand that now exists. The primary location
being consider will have fixed costs of $9200 per month and variable costs
of 70 cents per unit produced. Each item is sold to retailers at a price that
averages 90 cents.
FC =
VC =
Rev =
Q BEP
$9,200/month
$ .70/unit
$ .90/unit
a. What volume per month is
required in order to breakeven?
FC
$9,200
=
=
= 46,000 units
Rev VC $.90 $.70
QBEP
FC
=
R v
b. What profit would be realized on a month volume of 61,000 units 87,000
units?
b.
Profit = Rev x Q (FC + VC x Q)
1. P61,000 = $.90(61,000) [$9,200 + $.70(61,000)] = $3,000
2. P87,000 = $.90(87,000) [$9,200 + $.70(87,000)] = $8,200
No. 3/211 c. What volume is needed to obtain a profit of $16,000 per month?
Specified profit + FC $16,000 + 9,200 / month
Q=
=
= 126,000 units.
Rev VC
$.90 / unit $.70 / unit
d. What volume is needed to provide a revenue of $23,000 per month?
d.
Total Revenue = Rev x Q, so Q =
Total Revenue
$23,000
=
= 25,556 units
R
$.90 / unit
$100,000
e. Plot the total
costs & total
revenue lines?
TR =$90,000 @ Q = 100,000 units
TR =$90,000 @ Q =100,000 units
TC = $79,200 @ Q = 100,000 units
TR
TC
Cost
$50,000
TC =$79200 @ Q = 100,000 units
$9,200
0
Volume (units)
100,000
Chapter 5 Overview
Strategic Capacity Planning for Products and Services
Goal;185 Key Questions;186
Capacity decisions;187
Effective Capacity;189
Measuring System Effectiveness :
Efficiency,Utilization;188
Economies of Scale,
Diseconomies of Scale, The
Capacity Strategies; 191
optimal operating level is at
Leading, Following,Tracking
the minimum average unit
cost ;200
k
NR =
Cost-Volume Analysis; 202;
204 Example 3, BEP,
pD
i
i =1
i
Calculating Processing Requirements; 193
T
where
N R = number of required machines
pi = standard processing time for product i
Di = demand for product i during the planning horizon
T = processing time available during the planning horizon
Capacity cushion = 100% - Utilization ; 192