ADVANCED MANAGEMENT ACCOUNTING

ACC60804
TUTORIAL 4 (SOLUTIONS)

QUESTION 1
1. a. Use the EOQ model to determine the optimal number of pairs of shoes per order.

2 𝑥𝑥 120,000 𝑥𝑥 250
EOQ = �
2.40

EOQ = 5,000 pairs of shoes per order.

1. b. Assume each month consists of approximately 4 weeks. If it takes 1 week to receive an order, at what point
should warehouse OR2 reorder shoes?

Reorder point = lead time x daily/weekly usage

Option Reorder point = 1-week x (120,000 ÷ 12 months ÷ 4 weeks)
Reorder point = 2,500 pairs of shoes
The company will make a new order when the inventory falls to 2,500 pairs.

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1. c. Although OR2's average weekly demand is 2,500 pairs of shoes (120,000 ÷ 12 months ÷ 4 weeks),
demand each week may vary with the following probability distribution:
1 2 3=2-1 4 5=3xSC 7 6
8=5x6x7 9=3xHC 10=9+8
No. of Expected Holding Total
Safety Stockout Stockout orders Stockout Cost Expected
Average Demand Stock units cost ($2) Probability cost ($2.40) Costs ($)

2500 3000 500 0 0 0.04 24* 0 1,200 1,200

2500 2750 250 250** 500 0.04 24 480 600 1,080

2500 2500 0 500# 1000 0.04 24 960
250## 500 0.20 24 2400
3360 0 3,360
*24 = 120,000 ÷ 5,000 (EOQ) = 24 orders per year
**Stockout units  3,000 – 2,750 = 250 pairs
# Stockout units  3,000 – 2,500 = 500 pairs
## Stockout units  2,750 – 2,500 = 250 pairs

The exhibit shows that annual relevant total stockout and carrying costs are the lowest ($1,080) when a safety
stock of 250 pairs of shoes is maintained. Therefore, Warehouse OR2 should hold a safety stock of 250 pairs. As
a result, Reorder point with safety stock = 2,500 pairs + 250 pairs = 2,750 pairs. Reorder quantity is unaffected by
the holding of safety stock and remains the same as calculated in requirement 1. Reorder quantity = 5,000 pairs
Warehouse OR2 should order 5,000 pairs of shoes each time its inventory of shoes falls to 2,750 pairs.

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QUESTION 2
2. a. What is the optimal number of motors that Phillips's managers should order according to the EOQ model?

2 𝑥𝑥 52,000𝑥𝑥 360
EOQ = �
6.50

EOQ = 2,400 units

2. b. At what point should managers reorder the motors, assuming that both demand and purchase-order lead time are
known with certainty?

Reorder point = lead time x daily/weekly usage

Option Reorder point = 2 weeks x 1,000
Reorder point = 2,000 units

2. c. How much safety stock should the assembly plant hold? How will this affect the reorder point and reorder quantity?

1 2 3=2-1 4 5=3xSC 6 7 8=5x6x7 9=3xHC 10=9+8

No. of Expected Holding
Safety Stockout Stockout orders Stockout Cost Total Expected
Average Demand Stock units cost ($5) Probability cost ($6.50) Costs ($)
2000 2400 400 0 0 0.05 22 0 2,600 2,600
2000 2200 200 200** 1000 0.05 22 1100 1,300 2,400
2000 2000 0 400# 2000 0.05 22 2200
200## 1000 0.20 22 4400
6600 0 6,600
*52,000 ÷ 2,400 = 21.66 @ 22 orders per year
** stockout units If the demand 2,400 = 2,400 – 2,200 = 200 units
# stockout units if the demand 2,400 = 2,400 – 2,000 = 400 units
## stockout units if the demand 2,200 = 2,200 – 2,000 = 200 units

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The exhibit shows that annual relevant total stockout and carrying costs are the lowest ($2,400) when a safety stock of 200 units of
the motor is maintained. Therefore, the company should hold a safety stock of 200 motors. As a result, Reorder point with safety
stock = 2,000 units + 200 units = 2,200 units. Reorder quantity is unaffected by the holding of safety stock and remains the same as
calculated in requirement 1. Reorder quantity = 2,400 motors. The company should order 2,400 units each time its inventory falls to
2,200 units.

QUESTION 3

3. a. Calculate the economic order quantity as originally determined by the company’s managing director.

Note: Holding cost [45 + 10% x $50

b. Calculate the optimum economic order quantity, applying the managing director’s assumptions and allowing for the
purchasing manager’s bonus and for supplier quantity discounts.
Key information from question 6:
 Cost per unit = $50
 Selling price per unit $60
 Demand (D) = 10,000 units
 Delivery cost = ordering cost = $25 per order
 Holding cost = $45 + $5 (ROI = 10% x $50)
 Purchasing manager’s bonus = 10% x (10,000 – total relevant costs)
 Quantity discount = 200 units  $49.90

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 To calculate whether it is worthwhile to purchase inventory at a purchase discount, the comparison between annual costs
under the EOQ policy and under the purchase discount policy must be calculated.

Total cost with reorder quantity (EOQ) at 100 units $

Total holding cost (100/2) x $50 2,500
Total ordering cost (10,000/100) x $25 2,500
Annual relevant costs 5,000
purchasing manager's bonus (10% x (10,000 – 5,000) 500
Annual Purchase cost ($50 x 10,000) 500,000
Total annual costs 505,500

Total cost with quantity discount at 200 units $

Total holding cost (200/2) x $49.99(W1) 4,999
Total ordering cost (10,000/200) x $25 1,250
Annual relevant costs 6,249
purchasing manager’s bonus (10% x (10,000-6,249) 375.10
Annual Purchase cost ($49.90* x 10,000) 499,000
Total annual costs 505,624.10

W1: Holding Cost – 200 units.

HC = $45 + ROI
ROI = 10% x PC/unit = 10% x 49.90* = $4.99
HC = $45 + $4.99 = $49.99

*$49.90 is the purchase cost per unit for purchasing 200 units and above.

The annual cost difference in favour of 100 units is $124.10 (505,624.10 - 505,500). It is not worthwhile purchasing at a quantity
discount.

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c. Adopting the financial director’s assumptions and an expected value approach, and assuming that it is a condition of the
supplier’s contract that the order quantity is to be constant for all orders in the year, determine the expected level of safety
(i.e. buffer) stock the company should maintain. For this purpose, use the figures for the economic order quantity you have
derived in answering (b). Show all workings and state any assumptions you make.

 The order quantity is to be constant for all orders in the year. For this purpose, use the figures for the economic order quantity you
have derived in answering (b). Thus, the average usage when demand is certain is 100 units.
 First, determine the probability of distribution.

The expected value approach, also known as expected value theory or

expected utility theory, is a concept used in decision theory and probability
theory to assess the potential outcomes of a decision or situation with
uncertain outcomes. It involves calculating the expected value of an action
to make rational decisions in situations involving risk or uncertainty.

EV = Σ [Outcome Value * Probability]

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 Next, determine the optimum safety stock by preparing the following table. Remember to exclude the purchasing manager’s bonus.

1 2 3=2-1 4
5=3xSC 6 7
8=5x6x7 9=3xHC 10=9+8
Stockout Expected Holding Total
Safety Stockout No. of
Average Demand cost Probability Stockout Cost Expected
Stock units orders
($10) cost ($45) Costs ($)
100 106 6 0 0 0.04 100 0 270 270
100 104 4 2 20 0.04 100 80 180 260
100 102 2 4 40 0.04 100 160
2 20 0.1 100 200
360 90 450
100 100 0 6 60 0.04 100 240
4 40 0.1 100 400
2 20 0.16 100 320
960 0 960
• Stockout cost is the $10 lost contribution (Selling price - cost per unit)
Note: Stockout cost is the cost associated with not having enough inventory to meet customer demand.
It represents the loss of potential profit due to missed sales opportunities or other adverse effects when a business runs out
of stock.

• No of orders= 10,000/100 = 100

• HC per unit = $50 - Purchasing manager's bonus = $50 - 10% of holding cost inventory = 50 - (50x10%)

In conclusion, the optimum safety stock is 4 units. The reorder point when demand is uncertain is 104 units. Costs are minimized if
a safety stock of 4 units is maintained.

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d. As an outside consultant, write a report to the managing director on the company’s stock ordering and stock holding
policies, referring where necessary to your answers to (a)–(c). The report should inter alia refer to other factors he should
consider when taking his final decisions on stock ordering and stock holding policies.
The following items should be included in the report:
(i) The disadvantages of ordering from only one supplier (e.g. vulnerability of disruption of supplies due to strikes/production difficulties
or bankruptcy);
(ii) Failure to seek out cheap or alternative sources of supply.
(iii) It is assumed no large price increases are anticipated that will justify holding additional stocks or that the stocks are not subject
to deterioration or obsolescence.
(iv) It is assumed that lead time will remain unchanged. However, investigations should be made as to whether this or other suppliers,
can guarantee a shorter lead time.
(v) The need to ascertain the impact on customer goodwill if a stockout occurs. The answer to (c) assumes that the company will
merely lose the contribution on the sales and long-term sales will not be affected if a stockout occurs.