Topic 10: Other Topics in Working Capital Management
Outlines:
I. Setting the Target Cash Balance
II. Setting the Optimal Inventory Order
I. Setting the Target Cash Balance
Cash is necessary (1) to pay for daily transactions, (2) to establish a precaution level
against unforeseen fluctuations in cash flows, and (3) to take advantage of trade
discounts. Cash is costly because it is a non-earning asset.
Thus, there is a tradeoff between benefits and costs for holding cash.
William Baumol noticed that cash balances are similar to inventories. The Baumol
model minimizes the total costs of holding cash.
Assumption: the firm uses cash at a steady, predictable rate, say $100,000 per week.
In this model, there are two cost components: (1) holding (or opportunity) costs, and (2)
transactions costs.
Opportunity cost rate of holding cash, r, is the cost of borrowing to hold cash (or the rate
of return foregone on marketable securities if the firm sells marketable securities to
obtain cash). r is usually annualized.
Total opportunity (holding) costs increase linearly in the $ amount of cash balance. This
leads to the straight line in Figure 22-2 (p. 272).
When you go to a bank to borrow (or sell marketable securities to raise cash), there is a
fixed charge per transaction, F. The more often you borrow (or sell), i.e., the higher the
total transaction costs. If you hold a larger amount of cash balance, there are three
effects: (1) it takes longer to deplete the cash balance, (2) it takes longer to borrow again,
and (3) fewer transactions and lower total transactions costs. This leads to the bottom
convex line in Figure 22-2. The aggregation of the straight line and the bottom convex
line is the top convex line, total costs of holding cash.
Total amount of net new cash needed for transactions during the entire year, T, = 52
weeks  $100,000 per week = $5,200,000. Suppose that r = 15%, F = $150. Then the
optimal cash transfer, C*, is given as follows:
C* =
2 FT
=
r
2($150)($5,200,000)
= $101,980
0.15
That is, the firm should go to the bank to borrow (or sell marketable securities) in the
amount of $101,980 when its cash balance approaches zero. This policy will minimize
the total costs of holding cash.
The total costs of holding cash (per year) are:
Total Costs = Holding Costs + Transactions Costs
= (Average Cash Balance)(Opportunity Cost Rate) + (Number of Transactions)(Cost per
Transaction)
= (C*/2)(r) + (T/ C*)(F)
= ($101,980/2)(0.15) + ($5,200,000/$101,980)($150)
= $15,297.06
Note that the Baumol model does not take all the potential benefits into consideration.
Recall that cash is necessary (1) to pay for daily transactions, (2) to establish a precaution
level against unforeseen fluctuations in cash flows, and (3) to take advantage of trade
discounts. (2) and (3) are neglected.
In practice, many firms use Monte Carlo simulations to set their target cash balances
based on some “safety stock” of cash that holds the risk of running our of money to some
acceptably low level. This quantitative method is complement with managerial
experiences. Cash managers usually adjust the target balances obtained by simulations
on a judgmental basis.
II. Setting the Optimal Inventory Order
Inventories are similar to cash balances. They are obviously necessary but also costly.
The economic ordering quantity (EOQ) model is similar to the Baumol model in that the
EOQ model is to minimize total inventory costs.
Total inventory costs have two components: (1) total carrying costs, and (2) total ordering
costs.
Annual total carrying costs (financing costs, storage costs, inventory insurance costs,
depreciation and obsolescence, etc.), TCC, generally rise in direct proportion to the size
of inventory. This is represented by the straight line in Figure 22-3, p. 281.
Total ordering costs are lower when the firm orders inventories less frequently (large-size
orders). This leads to the bottom convex line in Figure 22-3. The aggregation of the
straight line and the bottom convex line is the top convex line, total inventory costs.
The optimal solution for minimizing total inventory costs is:
Q* = EOQ =
2 FS
CP
where C is the percentage cost of carrying, P is inventory cost (purchase cost or
production cost) per unit (thus, CP is carrying cost per unit), F is fixed costs per order,
and S is the annual total order size.
Example: A retail firm sells 120,000 units in a year. The fixed charge per order is $100.
The firm purchases its inventory at a price $2 per unit.
Suppose that the average inventory value is $30,000. The financing charges, storage
costs, inventory insurance costs, mark down costs (depreciation and obsolescence) to
carry the inventory for the entire year are $3,000, $2,000, $500, and $1,000, respectively.
Then the percentage cost of carrying is ($3,000+$2,000+$500+$1,000)/$30,000 = 21.7%.
Q* = EOQ =
2 FS
=
CP
2($100)(120,000)
=7,436.37 units
(0.217)($ 2)
That is, the firm should place an order in the amount of 7436.37 units when its inventory
approaches zero. That is, the firm will place 120,000/7436.37 = 16.14 orders per year.
Total Inventory Costs = Total Carrying Cost + Total Ordering Cost
= (C)(P)(A) + (N)(F)
where A is the average inventory = Q*/2, N is the number of orders per year.
Total Inventory Costs = (C)(P)(A) + (N)(F)
= (0.217)($2)(7,436.37/2) + (16.14)($100)
= $3,227.69
Limitation #1: The previous calculation assumes the average inventory value is $30,000.
Because inventory cost per unit is $2, we essentially assume that the average inventory is
15,000 units. The size of average inventory is a function of optimal order size, Q*. So
before we solve for the solution, we have already made an assumption about the size of
the solution. To deal with this problem, we usually need to write an algorithm such that
this calculation is repeated until the assumed average inventory value is close enough to
the one implied by the solution.
Limitation #2: The previous calculation assumes that you will receive the inventory
immediately after you place the order. But this is rarely true. In addition, to deal with
the costs of running short (stock-out costs), firms usually add additional safety stocks. If
the firm decides the optimal safety stock to be 500 units, the maximum inventory will be
7,436.37 + 500 = 7,936.37 units. The firm should place an order in the amount of
7436.37 units when its inventory approaches 500 units. This makes the average
inventory to be (7,436.37/2) + 500 = 4218.19 units.
-----------------------------------------------------------------------------------------------------------Homework:
End-of-chapter problem (22-2), p. 291: the Barenbaum Industries problem. Due in one
week.
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