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
Chapter 4 - Page 62
Try Q = 10,000 gallons. 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 (This solution was arrived at by trial and error.) 4.
Holding Costs $2,500
Purchase Costs $2,800,000
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: Try Q (actually, EOQ) = 2,581.99 units.
Chapter 4 - Page 63
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) 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 Opportunity Cost 15% 20,000+ $35.50
Results of random trial solutions: Q PV Cost
Chapter 4 - Page 64
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 =
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.
t 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Quantity 10,000 10,000 10,000 10,000 10,000 10,000 10,000 10,000 0 0 0 0 0 0 0 0
Cost Per 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
Purchase 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
$370,000.00
PV of PV Factor Holding & PV of (simpleOrdering Inventory interest) Costs Purchase 1.0000 0 370,000 0.9816 0 363,190 0.9639 0 356,627 0.9467 0 350,296 0.9302 0 344,186 0.9143 0 338,286 0.8989 0 332,584 0.8840 0 327,072 0.0000 0 0 0.0000 0 0 0.0000 0 0 0.0000 0 0 0.0000 0 0 0.0000 0 0 0.0000 0 0 0.0000 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)
Chapter 4 - Page 66
ASSUMPTIONS Order costs(F) Holding costs per unit (H) Total period quantity (T) Planning Period Delivery Time (days) Opportunity Cost
$50.00 $3.00 200,000 250 2 20%
Discount options Quantity Cost Per (Q) Unit (C') 0-1,999 $5.00 2K - 3,999 $4.99 4K - 5,999 $4.98 6K - 7,999 $4.97 8K - 9,999 $4.96 10M + $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 = 250 days / 50 orders =
t 0 1 2 3 4 5 6 7 8 9 10 11
$19,920 50 5
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
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
Inventory Purchase Day 0 5 10 15 20 25 30 35 40 45 50 55
every 10 days Day 0 (annuity due) orders / planning period 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
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
Chapter 4 - Page 67
12 13 14 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 4,000 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 4.98 4.98 4.98
60 65 70 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
0.9682 0.9656 0.9631 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 0 0 0
19,286 19,235 19,184 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
$7,475.90
$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
Chapter 4 - Page 68
---|-------------|-----------------|--------------|---------------------|---------------|-----------> $19,920 $19,920 $19,920 etc. $19,920 | | purchasing $19,865.57 | | costs $19,811.44 | | etc. | etc. (discounting at 20% / yr. simple interest) | $17,562.32 | $934,634.82 $7,475.90
= PV of sum of purchases = PV of holding and order costs
$942,110.72
= total value of inventory cost
$8,500 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 = 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.
a.) b.)
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 supplier’s quantity discount schedule “max’s 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 EOQ = SQRT(2 * T * F / H) EOQ = 7,071 Results of random trial solutions when k = 0%:
Chapter 4 - Page 69
Q 4000 5000 6000 7300 for error,
8000 9000 10000
c.)
PV Cost $488,875 $488,625 $488,725 $488,573 = Lowest level of present value of inventory cost $488,725 optimum order quantity, found by trial and $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
Q 3,000
C' * T $487,500.00
F $1,250.00
H $225.00
TC $488,975.00
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
Quantity 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
Inventory Purchases Per Day 0 22 44 66 88 110 131 153 175 197
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
PV of Inventory Purchase 29,250 28,818 28,398 27,990 27,594 27,209 26,835 26,471 26,116 25,771
Chapter 4 - Page 70
10 11 12 13 14 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 3,000 3,000 3,000 3,000 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 9.75 9.75 9.75 9.75 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
219 241 263 285 307 329 350 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
0.8696 0.8584 0.8475 0.8368 0.8264 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 0 0 0 0 0
25,435 25,107 24,788 24,477 24,174 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
Chapter 4 - Page 71
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.) User determined from part c.)
=
3,000
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. 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
Chapter 4 - Page 72
February March April May June
160 237 200 105 76
31
15 47
#N/A 62
23 39 62
19 23 42
11 17 28
Balance Fraction Matrix Month of Ending inventory fractions for purchases made in previous months Purchase Purchases Feb Mar Apr May June February 160 19% 9% March 237 20% 10% April 200 20% 10% May 105 22% 10% June 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. 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 COGS
1000
Feb
Mar
Apr
May
June
1500
2100
2700
3500
4800
Chapter 4 - Page 73
End. Inv.
300
450
630
810
1050
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
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 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
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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
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
