Page 207 - DCOM505_WORKING_CAPITAL_MANAGEMENT

Working Capital Management

Notes PV day 80 cost = 1,000 × `5 + 2 × `50
= `4,990.62
Total PV cost = PV day 0 cost + PV day 40 cost + PV days 80 cost
= `90,000 + ` 89,024.39 + `4,990.62

Total PV cost = ` 1, 84,015.01
What if smallest, but more frequent, orders were placed, resulting in more payments but each of
a smaller size? The financial manager would pay less money up front for inventory and, therefore,
would have a smaller opportunity cost for those funds. In addition, the inventory carrying costs
would decline because less inventory is held. However, order costs would inverse due to the
increased number of orders placed. With the changing size and timing of the various cash flows,
the only way to assess if a change in inventory policy will enhance shareholder wealth is to
calculate the present value of the cash flows. The policy with the minimum present value cost
should be the one that results in the greatest enhancement to shareholder wealth.

We can develop a general for formulation for the present-value timeline approach to assessing
the cost of inventory management, as shown in Equation-1

¥
¥
+
(S D/Q) (C Q/ 2)
Total cost = …(1)
1 (i ¥ T)
+
Inventory Management
(p /q − ) 1 Q × 1
∑
×
= t 0 1+×i(t Q × T/D)
Where D = number of inventory units required
T = number of days in the production period
Q = inventory order quantity
I = cost of each inventory unit
S = fixed order cost per order

C = holding cost per unit of inventory
i = daily opportunity cost
To understand Equation-1, first note that the first in the equation is the present value of the
ordering costs, (S × D/Q), and the holding costs, (C × Q/2), that are assumed to be paid at the end
or the production period. The simple-interest present-value factor is 1/(1 + (i × T). The second
term is a summation of the present value of the cash flows to pay for cash inventory purchase.
The cost of inventory purchase is Q × I. The present value factor accounts for the timing of cash
purchase. The first purchase is at the beginning of the production period and C = 0. Thus, the
simple interest faction is 1/(I + 0) or 1. This second purchase, t = 1, is on day t × Q × T/D. To
understand this, first note that the daily usage rate of inventory is D/T. When Q is ordered, it
takes Q divided by the daily usage rate, or [Q/(D/T)1] days, to use it up. This can be rewritten as
Q × T/D. Inventory purchases are made on day t × (Q × T/D) for t = 0, 1, 2, 3, ….. (D/Q) – 1.
An example will illustrate this equation. Calling a treasurer’s dilemma to find the trade-off
between placing larger orders to reduce ordering costs but at increased holding and opportunity
costs of the investment, we can now assess the value of the quantity discount offered through the
use of the cash flow timeline formulation of the inventory decision.

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