Question

Wilson, Inc., is a wholesaler of Protoxid for industrial clients. Demand for Protoxid is stable at 350,000 units per year. Wilson orders the product from its supplier four times a year. An order is placed when the total Protoxid on hand amounts to 25,000 units. This represents a nine-day working supply plus safety stock. The company works 300 days per year. Recently, Wilson management has expressed concern over the costs of carrying inventory and is seeking to evaluate the present inventory order and safety stock policies.

As a part of the study, the following costs were identified with respect to Protoxid:

                             

Invoice price                                                    $ 32.92

Weight per unit                                               1.5 Kg

Shipping charges                                             $1.05 + $640 per truck + $0.40 per Kg

Special packaging per unit                            $3.65 ($1 is refunded on return of the shipping container)

Insurance on shipment                                  $1.76 per unit, $415 per shipment

Processing order documents                       $183

Unloading operations                                    $0.82 per unit + $1,800 per week.

Inspect for annual inventory                        $2.63 per unit

Estimated obsolescence costs                     $1.35 per unit

Inventory record maintenance                    $0.92 per unit + $2,200 per week

Inventory tax                                                   3% of invoice price

Inventory insurance                                       15% of invoice price + $4,100 per month.

The company estimates its cost of capital is 22%. In addition, it conducted a study on the costs of a stockout. The average stockout costs $5,400 due to the need to request special shipments from alternative suppliers. With various safety stock levels, the probabilities of a stockout decrease as follows:

                              Safety stock                      Probability of stockout

........................................0.............................................50%

     7,000                                             10%

   14,000                                             2%

   21,000                                             1%

To determine order quantity, assume a stockout probability per order of 2%. Order sizes are restricted to round lots of 5,000 units. The company has the capacity to store 90,000 units.

REQUIRED

a. What are the annual costs under the present order and safety stock system?

b. What is the EOQ?

c. What are the annual costs under the optimal order and safety stock system?

d. What is the reorder point under the optimal order and safety stock system?

Answer 1

a. The annual cost under the present order and safety stock system is calculated by:

annual cost = NPV * r / 1-(1+r)-n

NPV =350000

r= annual percentage rate

n= number of years

annual percentage rate = actual price * percentage of actual price

=32.92 * 3%

= 0.9876

n = 1

annual cost = 350000 * 0.9876 / 1-(1 + 0.9876) -1

   = 345660 / 1 -(1.9876)-1

= 345660 / 1 -(-1.9876)

= 345660 / 2.9876

= 115698.21

b. Inorder to find the economic order quantity or the EOQ, the formula will be:

EOQ = 2SD / H

S = ordering cost

D = annual quantity demand

H = holding cost

ordering cost = annual quantity demand / volume of order

= 350000 / 25000

=14

holding cost = total cost / number of units

= 1.05 +640 + 0.40 + 3.65+ 1.76+ 415 + 183+ 0.82+ 1800+ 2.63+ 1.35+ 0.92+ 2200

= 5250.58

EOQ = 2 * 14 * 350000 / 5250.58

= 9800000 / 5250.58

= 1866.460

= 43.202

c. higher safety stock = 21000

inorder to find the annual cost under optimal order and safety stock system,

annual cost = 2 * D * EOQ / H + safety stock

D = demand

H = holding cost

annual cost = annual cost under the present order and safety stock + safety stock / EOQ

= 115698.21 + 21000 / 43.202

= 3164.163

d. Reorder point under the optimal order and safety stock system is calculated as

reorder point = annual cost * average lead time + safety stock

= 3164.163 * 9 + 21000

= 49477.467