Solutions to Problems: Chapter 4
1.
Ardmore Farm and Seed - EOQ, average inventory balance, and reorder point.
ASSUMPTIONS
Order costs (F)
Holding costs per gal. (H)
Total annual quantity (T)
Order Quantity (Q)
Planning Period
Delivery Time (days)
$25.00
$0.25
80,000
10,000
365
7
a.) Calculating annual inventory costs.
Total cost = (F * T / Q) + (H * Q / 2)
Total Cost =
$1,450
b.) Calculating the EOQ.
EOQ =
SQRT(2 * F * T / H)
EOQ =
4,000
c.)
4000.00
4000.00
Gallons
Calculating the number of orders and the average inventory balance.
Optimal Number of Orders =
T / EOQ
Optimal Number of Orders =
20
Average Inventory Balance =
Average Inventory Balance =
EOQ / 2
2000
d.) Calculating the reorder point.
Daily Usage Rate = T / # of Days in Planning Period
Daily Usage Rate =
219.18
Gallons per day
Reorder Point = Daily Usage Rate * Delivery Time
Reorder Point =
1,534.2
Gallons
2.
3.
EOQ =
Order costs (F)
Holding costs per gal. (H)
EOQ = (2 * F * T / H)^.5
T=
4,500
$40.00
$50.00
12,656,250
Lott Manufacturing, Inc. - EOQ, average inventory balance, and reorder point
ASSUMPTIONS
Order costs (F)
Holding costs per unit (H)
$50.00
$3.00
Total period quantity (T)
Order Quantity (Q)
Planning Period
Delivery Time (days)
200,000
10,000
250
2
a.) Calculating the EOQ.
EOQ =
SQRT(2 * F * T / H)
EOQ =
2,581.99
b.) Calculating the EOQ savings.
Total cost = (F * T / Q) + (H * Q / 2)
Total Cost @10,000 units =
$16,000
Units
Total Cost EOQ = (F * T / Q) + (H * Q / 2) where Q =
Total Cost @
2581.99 units =
$7,746
Savings with EOQ =
c.)
$8,254
Calculating the optimal number of orders and average inventory balance.
Optimal Number of Orders =
T / EOQ
Optimal Number of Orders =
77
Average Inventory Balance =
Average Inventory Balance =
EOQ / 2
1,291
d.) Calculating the reorder point.
Daily Usage Rate = T / # of Days in Planning Period
Daily Usage Rate =
800
Units per day
Reorder Point = Daily Usage Rate * Delivery Time
Reorder Point=
1,600
Units
4.
5.
2,581.99 Units
Order costs (F)
EOQ
Total period quantity (T)
EOQ =
SQRT(2 * F * T / H)
Holding costs per unit (H) =
$55.00
24,000
100,000
$0.0191
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
COGS
End. Inv.
100
40
February
March
April
May
June
150
50
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
Average Daily COGS (Quarterly)
Average Days COGS in Inventory
Purchases = EI - BI + COGS
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
Month of
Purchase
February
March
April
May
June
Month of
Purchase
February
March
April
May
June
Balance Amount Matrix
Ending inventory balances for purchases made in previous months
Purchases February
March
April
May
June
160
31
15
237
47
23
200
39
19
105
23
11
76
17
NA
62
62
42
28
Balance Fraction Matrix
Ending inventory fractions for purchases made in previous months
Purchases February
March
April
May
June
160
19%
9%
237
20%
10%
200
20%
10%
105
22%
10%
76
22%
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.
6. 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
January
COGS
1000
End. Inv.
300
February
1500
450
Avg. Daily COGS (quarterly)
Days COGS Held in Inv.
Purchases = EI - BI +
1650
COGS
March
2100
630
April
2700
810
May
3500
1050
June
4800
1440
51.11
12.33
70.00
11.57
92.22
11.39
122.22
11.78
2280
2880
3740
5190
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.
c.)
Calculating a balance fraction matrix.
ASSUMPTIONS
Month of
Purchase
February
March
April
May
June
Balance Amount Matrix
Ending inventory balances for purchases made in previous months
Purchases February
March
April
May
June
1650
330
174
2280
456
234
2880
576
302
3740
748
402
5190
1038
NA
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 February
March
April
May
June
1650
20%
11%
2280
20%
10%
2880
20%
10%
3740
20%
11%
5190
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.