Chapter 4

Inventory Management

Contents
The Concept of Inventory
Basics of Managing the Average Inventory Balance
Inventory Management and the Cash Flow Timeline
Monitoring the Inventory Balance
Reducing the Size of the Inventory Investment

Page 58

Chapter 4 - Page 59

Answers to Questions:
1.

Making sure that the company does not run out of inventory to satisfy production
or customer needs but doing so at a reasonable cost.

2.

Inventory is a difficult item to manage because it crosses so many different lines

of authority. Marketing is concerned about inventory because sales will be hurt if
stock outs occur. Production will be hurt if stockouts of raw materials and work
in process occur. The financial manager is concerned about the level of
investment in inventory and the costs associated with that investment.

3.

It serves the role of shock absorber. If inefficiencies were eliminated in the

production flow then less inventory would be needed.

4.

Raw materials: shock absorber between the firm and the supplier. Work-inprocess: shock absorber for inefficiencies in the production system. Finished
goods: shock absorber between the firm and its customers.

5.

The financial manager is concerned with the amount of and cost of capital tied up
in the inventory investment.

6.

EOQ stands for the economic order quantity, that order quantity that minimizes
the inventory management total cost function.

7.

By adding a safety stock.

8.

Variability in demand, the production process, and delivery time will tend to
increase the optimal size of the safety stock. High inventory carrying costs tend
to reduce the optimal level of safety stock holding stock out costs constant.

9.

The present value timeline solution allows for the cost of capital directly whereas
the EOQ solution does not.

10.

Inventory levels can be reduced by reducing the inefficiencies in the firm's

production systems, by increasing the reliance of supplier deliveries, and by
increasing the accuracy of forecasts of sales.

11.

It is influenced by sales trends.

12.

A balance fraction approach is not influenced by sales trends. Thus shifts in

balance fractions is a direct result of changes in inventory holding patterns.

Chapter 4 - Page 60

Solutions to Problems: Chapter 4

1.

Ardmore Farm and Seed - EOQ, average inventory balance, and reorder
point.
ASSUMPTIONS
Order costs (F)
$25.00
Holding costs per gal. (H)
$0.25
Total annual quantity (T)
80,000
Order Quantity (Q)
10,000
Planning Period
365
Delivery Time (days)
7

a.)

Calculating annual inventory costs.

Total cost = (F * T/Q) + (H * Q / 2) = (25 * 80,000 / 10,000) + (0.25 * 10,000 /

2)
Total Cost = $1,450
b.)

Calculating the EOQ.

EOQ =
SQRT(2 * F * T / H) = (2 * 25 * 80,000 / 0.25)0.5
EOQ =
4,000 Gallons

c.)

Calculating the number of orders and the average inventory balance.

Optimal Number of Orders = T / EOQ = 80,000 / 4000
Optimal Number of Orders = 20
Average Inventory Balance =
EOQ / 2 = 4000 / 2
Average Inventory Balance = 2000 Gallons

d.)

Calculating the reorder point.

Daily Usage Rate = T / # of Days in Planning Period = 80,000 / 365
Daily Usage Rate = 219.18 Gallons per day
Reorder Point = Daily Usage Rate * Delivery Time = 219.18 * 7
Reorder Point = 1,534.25 Gallons

2.

Lott Manufacturing, Inc. - EOQ, average inventory balance, and reorder

point
ASSUMPTIONS
Order costs (F)
$50.00
Holding costs per unit (H)
$3.00
Total period quantity (T)
200,000
Order Quantity (Q)
10,000
Planning Period
250
Delivery Time (days)
2

Chapter 4 - Page 61

a.)

Calculating the EOQ.

EOQ =
SQRT(2 * F * T / H) = (2 * 50 * 200,000 / 3.00)0.5
EOQ =
2,581.99 Units

b.)

Calculating the EOQ savings.

Total cost = (F * T/Q) + (H * Q / 2) = (50 * 200,000 / 10,000) + (3.00 *
10,000/2)
Total Cost @10,000 units =
$16,000
Total Cost EOQ = (F * T / Q) + (H * Q / 2) where Q = 2,581.99 units
= (50 * 200,000 / 2,581.99) + (3.00 * 2,581.99 / 2) = $7,746
Savings with EOQ = $8,254
c.)

= $16,000 - $7,746 per planning period

Calculating the optimal number of orders and average inventory balance.

Optimal Number of Orders = T / EOQ = 200,000 / 2,581.99 =
Optimal Number of Orders = 77
Average Inventory Balance =
EOQ / 2 = 2,581.99 / 2
Average Inventory Balance = 1,290.99 Units

d.)

Calculating the reorder point.

Daily Usage Rate = T / # of Days in Planning Period = 200,000 / 250
Daily Usage Rate = 800 Units per day
Reorder Point = Daily Usage Rate * Delivery Time = 800 * 2
Reorder Point = 1,600 Units

3.

Ardmore farm and Seed - considering quantity discounts (see problem 1).
ASSUMPTIONS
Order costs(F)
$25.00
Discount options
Cost Per
Holding costs per gal. (H)
$0.25
Quantity ( Q )
Unit ( C' )
Total annual quantity (T)
80,000
0-4,999
$40.00
Planning Period
365
5,000-9,999
$39.00
Delivery Time (days)
7
10,000-19,999
$37.00
20,000+
$35.00
Total Cost = (F * (T / Q) + (H * (Q / 2) ) ) + (C' * T)
(The solution is arrived at by trial and error, partially shown below.)
It might be useful in class to plug in four quantities (Q), and show what happens,
as below:
Try EOQ = 4,000 gallons
Then total cost = order costs + holding costs + purchase costs
= (25)(80,000) / 4,000 + (0.25)(4,000) / 2 + (40)(80000)
= $500.00 + $500.00 + $3,200,000 = $3,201,000
Try Q = 10,000 gallons.

Chapter 4 - Page 62

Then total cost = (25)(80,000) / 10,000 + (0.25)(10,000) / 2 + (37.00)

(80,000)
= $200 + $1,250 + $2,960,000 = $2,961,450
Try Q = 20,000 gallons.
Then total costs = (25)(80,000) / 20,000 + (0.25)(20,000) / 2 + (35.00)(80,000)
= $100 + $2,500 + $2,800,000 = $2,802,600
(This is the lowest cost solution with order costs = $100, holding costs =
$2,500, and purchase costs = $2,800,000 for a total of $2,802,600.
Finally, try Q = 30,000 gallons.
Then total costs = (25)(80,000) / 30,000 + (0.25)(30,000) / 2 + (35.00)(80,000)
= $66.67 + $3,750 + $ 2,800,000 = $2,803,816.67
Notice how the order costs and the purchase costs fall (and then remain constant),
but see how the holding costs rise and eventually offset the decline in the other
two costs. This can also be shown by using the disk program below and
"selecting" various order quantities to see the effect upon the holding, ordering,
and purchase costs.
Select Order Quantity = 20,000
Total cost = (F * (T/Q) + (H * (Q/2) ) ) + (C' * T)
Total
Order
Price
Quantity
Cost
Costs
$35.00
20,000
$2,802,600 $100
$2,800,000
(This solution was arrived at by trial and error.)
4.

Holding
Costs
$2,500

Purchase
Costs

Lott Manufacturing, Inc. - considering quantity discounts (see problem 2).

ASSUMPTIONS
Discount options
Order costs(F)
$50.00
Quantity
Cost Per
Holding costs per unit (H) $3.00
(Q)
Unit (C ' )
Total period quantity (T)
200,000
0-1,999
$5.00
Planning Period
250
2K - 3,999
$4.99
Delivery Time (days)
2
4K - 5,999
$4.98
6K - 7,999
$4.97
8K - 9,999
$4.96
10,000 +
$4.95
Total Cost = (F * (T / Q) + (H * (Q / 2) ) ) + (C' * T)
(The solution is arrived at by trial and error, partially shown below.)
It might be useful in class to plug in four quantities (Q), and show what happens,
as below:

Chapter 4 - Page 63

Try Q (actually, EOQ) = 2,581.99 units.

Then total cost = order costs + holding costs + purchase costs
= (50)(200,000) / 2,581.99 + (3.00)(2,581.99) / 2 + (4.99)(200,000)
= $3,872.985 + $3,872.985 + $998,000 = $1,005,745.97
Try Q = 4,000 gallons.
Then total cost = (50)(200,000) / 4,000 + (3.00)(4,000) / 2 + (4.98)(200,000)
= $2,500 + $6,000 + $996,000 = $1,004,500
(This is the lowest cost solution with order costs = $2,500, holding costs =
$6,000,
and purchase costs = $996,000 for a total of $1,004,500.
Try Q = 6,000 gallons.
Then total costs = (50)(200,000) / 6,000 + (3.00)(6,000) / 2 + (4.97)(200,000)
= $1,666.67 + $9,000 + $994,000 = $1,004,666.67
Finally, try Q = 8,000 gallons.
Then total costs = (50)(200,000) / 8,000 + (3.00)(8,000) / 2 + (4.96)
(200,000)
= $1,250 + $12,000 + $992,000 = $1,005,250
Notice how the order costs and the purchase costs fall, but see how the holding
costs rise to eventually offset the decline in the other two costs.
This can also be shown by using the disk program below and "selecting"
various order quantities to see the effect upon the holding, ordering, and
purchase costs.
Select Order Quantity = 4,000
(This solution was arrived at by trial and error.)
Total cost = (F * (T/Q) + (H * (Q/2) ) ) + (C' * T)
Price
$4.98
5.

Quantity
4,000

Total
Cost
$1,004,500

Order
Costs
$2,500

Holding
Costs
$6,000

Purchase
Costs
$996,000

Ardmore Farm and Seed - considering cost of capital (refer to Problems 1

and 3)
ASSUMPTIONS
Order costs (F)
$25.00
Discount options
Holding costs per gal. (H)
$0.25
Quantity (Q)
Cost Per Unit

( C' )
Total annual quantity (T)
Planning Period
Delivery Time (days)
Opportunity Cost
Results of random trial solutions:

80,000
365
7
15%

0-4,999
5,000-9,999
10,000-19,999
20,000+

$40.00
$39.00
$37.00
$35.50

Chapter 4 - Page 64

Q
PV Cost
4,000
$2,992,916.84
6,000
$2,923,096.43
8,000
$2,928,578.28
10,000
$2,783,501.27
= Lowest level of present value of
inventory
12,000
$2,787,725,.32
cost for optimum order quantity,
found by
14,000
$2,792,599.50 trial and error
16,000
$2,798,786.37
(Note: this is one-half of the 20,000 EOQ found in problem 3. )
Inventory purchase = 10,000 * $37.00 =

$370,000.00 every 45.625 days,

beginning Day 0
(annuity due)
Number of orders = 80,000 / 10,000 =
8
orders per year
365 days / 8 orders =
45.63
days between orders,
beginning Day 0
Holding cost = (0.25)(10,000) / 2
$1,250.00
occurs at end of
planning period
Ordering cost = (50)(80,000)/10,000
$400.00
occurs at end of
planning period
Total inventory cost =
$2,783,501.27 occurs at end of
planning period
Note: Do not be misled by all of the zeros in the spreadsheet printout below.
Because it is an interactive spreadsheet, when the order quantity changes, many
of the zero cells change to positive numbers to reflect a different order sequence.

Inventory
t
Quantity
0
10,000
1
10,000
2
10,000
3
10,000
4
10,000
5
10,000
6
10,000
7
10,000
8
0
9
0
10
0
11
0
12
0
13
0
14
0
15
0

Cost Per

Purchase

PV Factor
(simple

Unit
37.0
37.0
37.0
37.0
37.0
37.0
37.0
37.0
0
0
0
0
0
0
0
0

Day
0.000
45.625
91.250
136.875
182.500
228.125
273.750
319.375
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0

interest)
1.0000
0.9816
0.9639
0.9467
0.9302
0.9143
0.8989
0.8840
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000

PV of
Holding &
Ordering
Costs
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0

PV of
Purchase
370,000
363,190
356,627
350,296
344,186
338,286
332,584
327,072
0
0
0
0
0
0
0
0

Chapter 4 - Page 65

16
17
18
19
20
21
22
23
24
25
26
27
28
29

0
0
0.0
0
0
0.0
0
0
0.0
0
0
0.0
0
0
0.0
0
0
0.0
0
0
0.0
0
0
0.0
0
0
0.0
0
0
0.0
0
0
0.0
0
0
0.0
0
0
0.0
0
0
0.0
80,000 = total annual quantity ( T )

0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000

0
0
0
0
0
0
0
0
0
0
0
0
0
0
$1,261

0
0
0
0
0
0
0
0
0
0
0
0
0
0
$2,782,240

Total Present Value Cost = PV of holding & order costs + PV of inventory purchase
costs = $1,261 + $2,780,979 = $2,782,240
TIMELINE ILLUSTRATION OF CASH FLOWS:
Day 0 Day 45.6
Day 91.3 Day 136.9 etc. Day 319.4
Day 365
---|------------|------------------|--------------|---------------------|---------------|----------->
$370K

$370K
$370K
$370K
etc.
$370K
|
|
purchasing
$363,190
|
|
costs
$356,627
|
|
etc.
|
etc. (discounting at 15% / year simple interest)
|
$327,072
|
$2,780,979
$1,261

= PV of sum of purchases
= PV of holding and order costs

$2,782,240

= total present value of inventory cost

$1650
holding
and
order
costs
|
|
|
|
|

Note: This is similar to pricing a bond, only the PMTS are in the form of an
annuity due, so the formula (using compound interest) would be:
PV = (PMT)(PVIFA k, n )(1 + k) + FV (PVIF k, n )
PV = ($370,000)(PVIFA 15% / 8 , 8 )[1 + (15% / 8)] + ($1,650)(PVIF 15% / 8, 8 )
PV = $2,776,184.74 + $1,422.14 = $2,777,606.88 which is slightly less
than the $2,782,240 found when using simple interest.
6.

Lott Manufacturing, Inc. - considering cost of capital (refer to problems 2

and 4)
ASSUMPTIONS
Discount options
Order costs(F)
$50.00
Quantity
Cost Per

Chapter 4 - Page 66

Holding costs per unit (H)

Total period quantity (T)
Planning Period
Delivery Time (days)
Opportunity Cost

$3.00
200,000
250
2
20%

(Q)
0-1,999
2K - 3,999
4K - 5,999
6K - 7,999
8K - 9,999
10M +

Unit (C')
$5.00
$4.99
$4.98
$4.97
$4.96
$4.95

Results of random trial solutions:

Q
PV Cost
2,000
$492,155.00
4,000
$942,110.72 = Lowest level of present value of inventory cost
for
5,000
6,000

$943,290.82
$942,793.62

optimum order quantity, found by trial and error

Inventory purchase = 4,000 * $4.98 =

beginning
Orders / year = 200,000 / 4,000 =

$19,920
50

every 10 days
Day 0 (annuity due)
orders / planning

period
250 days / 50 orders =

t
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14

Holding cost = $3.00 * 4,000 / 2 =

$6,000

Ordering cost = $50 * 200,000 / 4,000 =

$2,500

Total inventory cost at end of planning

period =

$8,500

Quantity
4,000
4,000
4,000
4,000
4,000
4,000
4,000
4,000
4,000
4,000
4,000
4,000
4,000
4,000
4,000

Cost
Per Unit
of Inventory
4.98
4.98
4.98
4.98
4.98
4.98
4.98
4.98
4.98
4.98
4.98
4.98
4.98
4.98
4.98

Inventory
Purchase
Day
0
5
10
15
20
25
30
35
40
45
50
55
60
65
70

days between orders,

beginning Day 0
occurs at end of
planning period
occurs at end of
planning period

PV Holding
& Ordering
PV Factor Cost
1.0000
0
0.9973
0
0.9946
0
0.9918
0
0.9892
0
0.9865
0
0.9838
0
0.9812
0
0.9786
0
0.9759
0
0.9733
0
0.9707
0
0.9682
0
0.9656
0
0.9631
0

PV of Inv.
Inventory
Purchase
19,920
19,866
19,811
19,758
19,704
19,651
19,598
19,545
19,493
19,441
19,389
19,337
19,286
19,235
19,184

Chapter 4 - Page 67

15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49

4,000
4,000
4,000
4,000
4,000
4,000
4,000
4,000
4,000
4,000
4,000
4,000
4,000
4,000
4,000
4,000
4,000
4,000
4,000
4,000
4,000
4,000
4,000
4,000
4,000
4,000
4,000
4,000
4,000
4,000
4,000
4,000
4,000
4,000
4,000

4.98
4.98
4.98
4.98
4.98
4.98
4.98
4.98
4.98
4.98
4.98
4.98
4.98
4.98
4.98
4.98
4.98
4.98
4.98
4.98
4.98
4.98
4.98
4.98
4.98
4.98
4.98
4.98
4.98
4.98
4.98
4.98
4.98
4.98
4.98

75
80
85
90
95
100
105
110
115
120
125
130
135
140
145
150
155
160
165
170
175
180
185
190
195
200
205
210
215
220
225
230
235
240
245

0.9605
0.9580
0.9555
0.9530
0.9505
0.9481
0.9456
0.9432
0.9407
0.9383
0.9359
0.9335
0.9311
0.9288
0.9264
0.9241
0.9217
0.9194
0.9171
0.9148
0.9125
0.9102
0.9080
0.9057
0.9035
0.9012
0.8990
0.8968
0.8946
0.8924
0.8902
0.8881
0.8859
0.8838
0.8816

200,000

= total annual quantity ( T )

0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
$7,475.90

19,134
19,083
19,034
18,984
18,934
18,885
18,836
18,788
18,739
18,691
18,643
18,595
18,548
18,501
18,454
18,407
18,361
18,314
18,268
18,223
18,177
18,132
18,087
18,042
17,997
17,953
17,908
17,864
17,821
17,777
17,734
17,691
17,648
17,605
17,562
$934,634.82

Total Present Value Cost = PV of holding & order costs + PV of inventory

purchase costs = $7,475.90 + $934,634.82 = $942,110.72
TIMELINE ILLUSTRATION OF CASH FLOWS:
Day 0
Day 5
Day 10
Day 15 etc.
Day 245
Day 250
---|-------------|-----------------|--------------|---------------------|---------------|----------->
$19,920 $19,920
|

$19,920 etc.
|

$19,920
purchasing

$8,500
holding and

Chapter 4 - Page 68

$19,865.57 |
|
$19,811.44
|
etc.
etc.
(discounting at 20% / yr. simple interest)
$17,562.32
$934,634.82 = PV of sum of purchases
$7,475.90
= PV of holding and order costs

costs
|
|
|
|

order costs
|
|
|
|
|
|
|

$942,110.72 = total value of inventory cost

Note: This is similar to pricing a bond, only the PMTS are in the form of an
annuity due, so the formula (using compound interest = 20% / 73 5-day
periods in a year) would be:
PV = (PMT)(PVIFA k, n )(1 + k) + FV (PVIF k, n )
PV = ($19,920)(PVIFA

20% / 73 , 50

)[1 + (20% / 50)] + ($8,500)(PVIF 20% / 73, 50 )

PV = $932,151.23 + $7,413.24 = $939,564.47 which is slightly less than the

$942,110.72 found when using simple interest.
7.

ERRATA NOTE: This problem as written in the text contains a flaw that
poses a problem for astute students. The problem puts no limit on discounts,
such that if one orders sufficient quantity eventually the price falls to zero.
Advise students prior to assigning the problem that the suppliers quantity
discount schedule maxs out at 2,500 per order = $9.75/oz.
Beverly Cosmetics - EOQ, optimal order quantity and the cost of capital.
ASSUMPTIONS
Discount options
Order costs ( F )
$75.00
Quantity
Cost Per
Holding costs per unit ( H )
$0.15
(Q)
Unit (C' )
Total annual quantity ( T )
50,000
1-499
$10.00
Planning Period (in days)
365
500-999
$9.95
Opportunity Cost (per year)
25%
1000-1499
$9.90
1500-1999
$9.85
2,000-2,499 $9.80
2500+
$9.75

a.)

EOQ = SQRT(2 * T * F / H)
EOQ =
7,071

b.)

Results of random trial solutions when k = 0%:

Q
PV Cost
4000
$488,875
5000
$488,625
6000
$488,725

Chapter 4 - Page 69

7300
for
8000
and error,
9000
10000
c.)

$488,573
= Lowest level of present value of inventory cost
$488,725
optimum order quantity, found by trial
$488,625
$488,625

when k = 0%

Results of random trial solutions when k = 25%:

Q
PV Cost
1000
$445,876
2000
$440,947
3,000
$439,317
= Lowest level of present value of inventory cost

for
4000
5000
6000

$440,091
$440,941
$441,886

optimum order quantity, found by trial and error,

when k = 25%

Total Cost = (C' * T) + (F * (T / Q) + (H * (Q / 2) ) )

C'
$9.75
$488,975.00

Q
3,000

C' * T
$487,500.00

F
$1,250.00

H
$225.00

TC

Select Order Quantity

= 3,000
Total PV of inventory cost = $439,317
Note: Do not be misled by all of the zeros in the spreadsheet printout below.
Because it is an interactive spreadsheet, when the order quantity changes, many
of the zero cells change to positive numbers to reflect a different order sequence.
.

t
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14

Quantity
3,000
3,000
3,000
3,000
3,000
3,000
3,000
3,000
3,000
3,000
3,000
3,000
3,000
3,000
3,000

Cost Per
Unit of
Inventory
9.75
9.75
9.75
9.75
9.75
9.75
9.75
9.75
9.75
9.75
9.75
9.75
9.75
9.75
9.75

Inventory
Purchases
Per Day
0
22
44
66
88
110
131
153
175
197
219
241
263
285
307

PV Holding
& Ordering
PV Factor
Costs
1.0000
0
0.9852
0
0.9709
0
0.9569
0
0.9434
0
0.9302
0
0.9174
0
0.9050
0
0.8929
0
0.8811
0
0.8696
0
0.8584
0
0.8475
0
0.8368
0
0.8264
0

PV of
Inventory
Purchase
29,250
28,818
28,398
27,990
27,594
27,209
26,835
26,471
26,116
25,771
25,435
25,107
24,788
24,477
24,174

Chapter 4 - Page 70

15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50

3,000
2,000
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0

9.75
9.8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0

329
350
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0

0.8163
0.8065
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000

0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0

23,878
15,806
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0

50,000 = Total annual quantity ( T )

$1,200.00
$438,117
Total Present Value Cost = PV of holding & order costs + PV of inventory
purchase costs = $391.30 + $455,820 = $439,317.07
d.)

Economic Order Quantity

EOQ solution from part a.)

7,071

Optimal Order Quantity(w/o Cost of Cap.)

User determined from part b.)

7,300

Optimal Order Quantity(with Cost of Cap.)

3,000

Chapter 4 - Page 71

User determined from part c.)

Compare the three answers and discuss whether the answers make sense to
you.
It seems logical that considering a quantity discount would generally justify a
larger optimal order quantity. However, once the cost of capital iis considered,
this would work against having a larger investment in inventory, reducing the
optimal order quantity.

Chapter 4 - Page 72

8.

EBCO, Inc. - COGS, inventory invested, and balance matrices.

a.)

Calculating average daily COGS.

Average Daily COGS (quarterly) = (COGS mo. 1 + COGS mo. 2
+ COGS mo. 3) / 90 days
Average Daily COGS in Inventory = Ending Inventory / Average Daily COGS
ASSUMPTIONS
January

February

COGS
100
150
Ending
40
50
Inventory
Average Daily COGS (Quarterly)
Average Days COGS in Inventory
Purchases = EI - BI + COGS

March

April

May

June

225
62

200
62

125
42

90
28

5.28
11.75
237

6.39
9.70
200

6.11
6.87
105

4.61
6.07
76

Example: March quarterly COGS = (100 + 150 + 225) / 90 = 5.278

Example: March average daily COGS in inventory = 62 / 5.278 = 11.75
Example: March purchases = 62 - 50 + 225 = 237
b.)

Interpretation:
It appears as though inventory is being held for a shorter time period with each
successive month from 11.75 days in March to only 6.87 days in May.

c.)

Calculating a balance fraction matrix.

ASSUMPTIONS
Balance Amount Matrix
Month of
Ending inventory balances for purchases made in previous months
Purchase
Purchases
Feb
Mar
Apr
May
June
February
160
31
15
March
237
47
23
April
200
39
19
May
105
23
11
June
76
17
#N/A 62
62
42
28
Balance Fraction Matrix
Month of
Purchase
February
March
April
May
June

Ending inventory fractions for purchases made in previous months

Purchases
160
237
200
105
76

Feb

Mar

19%

9%
20%

Apr
10%
20%

May

10%
22%

June

10%
22%

Chapter 4 - Page 73

Example: February balance fraction for February purchases = 31 / 160 = 19.4%

Example: March balance fraction for February purchases = 15 / 160 = 9.4%
Example: March balance fraction for March purchases = 47 / 237 = 19.8%
A larger portion of each month's purchase remains as an inventory balance with
each successive month through March. Balance fractions for the month of
purchase increase from 19% in February to 22% in May. Thus, inventory
turnover is actually slowing down slightly.
d.)

Explaining the difference in answers b and c.

The balance fraction approach relates the level of inventory at a particular point
in time to the level of purchases that originally generated that inventory. This
provides a more accurate reflection of inventory usage compared to days COGS
held in inventory. Days COGS held in inventory is influenced by trends in the
activity level of the firm since it uses the average daily COGS in its calculation.
Since these two measures approach the monitoring of inventory differently, there
is no reason to think that they would give identical results.

9.

Wynn Manufacturing, Inc. - COGS, inventory investment, and balance

matrices.

a.)

Calculating average daily COGS.

Average Daily COGS (Quarterly) = (COGS mo. 1 + COGS mo. 2 +
+ COGS mo. 3) / 90 days
Average Daily COGS in Inventory = Ending Inventory / Average Daily COGS
ASSUMPTIONS
Jan

Feb

Mar

Apr

May

June

1500
450

2100
630

2700
810

3500
1050

4800
1440

Avg. Daily COGS (quarterly)

51.11
Days COGS Held in Inv.
12.33
Purchases = EI - BI + COGS 1650 2280

70.00
11.57
2880

92.22
11.39
3740

122.22
11.78
5190

COGS
End. Inv.

1000
300

Example: March quarterly COGS = (1000 + 1500 + 2100) / 90 = 51.11

Example: March average daily COGS in inventory = 630 / 51.11 = 12.32
Example: March purchases = 630 - 450 + 2100 = 2280
b.)

Inventory is being held for a shorter time period with each succeeding month with
average days COGS dropping from 12.33 days in March to 11.39 days in May.

Chapter 4 - Page 74

c.)

Calculating a balance fraction matrix.

ASSUMPTIONS
Balance Amount Matrix
Month of
Ending inventory balances for purchases made in previous months
Purchase
Purchases
Feb
Mar
Apr
May
June
February
1650
330
174
March
2280
456
234
April
2880
576
302
May
3740
748
402
June
5190
1038
#N/A
630
810 1050
1440
`
Month of
Purchase
February
March
April
May
June

Balance Fraction Matrix

Ending inventory fractions for purchases made in previous months

Purchases
1650
2280
2880
3740
5190

Feb
20%

Mar
11%
20%

Apr
10%
20%

May
10%
20%

June

11%
20%

Example: February balance fraction for February purchases =330 /

1650=20.00%
Example: March balance fraction for February purchases = 174 / 360 = 10.54%
Example: March balance fraction for March purchases = 456 / 2280 = 20.00%
Discussion: There is a generally a constant balance of inventory after each
succeeding month of purchase. This differs from the result using days
COGS
held in inventory.
d.)

Explaining the disparity between parts b and c.

The balance fraction approach relates the level of inventory at a particular point
in time to the level of purchases that originally generated that inventory. This
provides a more accurate reflection of inventory usage compared to days COGS
held in inventory. Days COGS held in inventory is influenced by trends in the
activity level of the firm since it uses the average daily COGS in its calculation.
Since, these two measures approach the monitoring of inventory differently, there
is no reason to think that they would give identical results.

10.

Float-Rite - calculating days COGS held in inventory.

Month
June
July
Sales
$50,000
$35,000
Cost of goods sold
$25,000
$17,500
Ending inventory
$7,000
$5,000

August
$20,000
$10,000
$3,000

Chapter 4 - Page 75

30-day averaging period, days COGS held in inventory

= $3,000 / ($10,000 / 30))

9.00

60-day averaging period, days COGS held in inventory

= $3,000 / ($17,500 + $10,000) / 60

6.55

90-day averaging period, days COGS held in inventory

= $3,000 / ($25,000 + $17,500 + $10,000) / 90)

5.14