Page 208 - DCOM505_WORKING_CAPITAL_MANAGEMENT

Unit 12: Inventory Management

Notes
Example: Assume the following value for the inventory decision variables prior to the
discount offer
D = 1,000 S = ` 5
T = 100 C = ` 2.50

Q = 200 i = .15/365 = .00041
I = ` 10
Using these numbers yields the following values.
Total inventory loading costs = `50, C × (Q/2)
Total ordering costs = ` 25, S × (D/Q)

Cost of each purchase lot = ` 2,000, l × Q
Inventory purchase PV factor PV Holding and PV Inventory
day t × (Q × T/D) I + (1 + i(t × QT/D)) ordering Purchase
0 0 1,000 ` 2,000
1 20 .9918 `1,983
2 40 .9838 `1,967
3 60 .9759 ` 1,951
4 80 .9682 ` 1,936
100 .9606 ` 264 ` 9,817

` 264
Total present value cost = `264 + ` 9,837 = `10,101
Now assume that the supplier is willing to discount the price per unit to ` 9.50 for purchase
quantities of 500 units.
Total inventory holding costs = ` 625, C × (Q/2)
Total ordering costs = `10, S × (T/Q)
Cost of each purchase lot = `4,750 I × Q

Inventory purchase PV factor PV Holding and PV Inventory
day t × (Q × T/D) I + (1 + i(t × QT/D)) ordering Purchase
0 0 1,0000 `4,750
1 50 .9799 ` 4,654
100 .9606 ` 610 ` 9,404

` 610

Total present value cost = `609 + `9,404 = `10,014
The present value cost of the inventory can be reduced from 10,101 to `10,014 by taking advantage
of the quantity discount. In the case, the reduced cost of the inventory more than offset the
additional holding costs and the larger initial payment for the inventory lot ordered.
This approach can be used to solve for the order quantity, Q, with the least cost similar to the
approach used by the quantity discount model. A simple solution is not possible, since the

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