Introduction to Corporate Finance

Ross et al.: Fundamentals

of Corporate Finance, Sixth

Edition, Alternate Edition

VII. Short−Term Financial

Planning and Management

21. Credit and Inventory
    Management

(^756) © The McGraw−Hill
Companies, 2002
places a total of 46,800/3,600 13 orders per year. If the fixed cost per order is F, the
total restocking cost for the year would be:
Total restocking cost Fixed cost per order Number of orders
F(T/Q)

[21.11]

For Eyssell, order costs might be $50 per order, so the total restocking cost for 13 orders

would be $50  13 $650 per year.

The Total Costs The total costs associated with holding inventory are the sum of the

carrying costs and the restocking costs:

Total costs Carrying costs Restocking costs

(Q/2) CC F(T/Q)

[21.12]

Our goal is to find the value of Q, the restocking quantity, that minimizes this cost. To

see how we might go about this, we can calculate total costs for some different values

of Q. For the Eyssell Corporation, we had carrying costs (CC) of $.75 per unit per year,

fixed costs (F) of $50 per order, and total unit sales (T) of 46,800 units. With these num-

bers, some possible total costs are (check some of these for practice):

Inspecting the numbers, we see that total costs start out at almost $5,000 and decline to

just under $1,900. The cost-minimizing quantity is about 2,500.

To find the cost-minimizing quantity, we can look back at Figure 21.4. What we no-

tice is that the minimum point occurs right where the two lines cross. At this point, car-

rying costs and restocking costs are the same. For the particular types of costs we have

assumed here, this will always be true, so we can find the minimum point just by setting

these costs equal to each other and solving for Q*:

Carrying costs Restocking costs

(Q*/2) CC F (T/Q*)

[21.13]

With a little algebra, we get:

Q*^2  [21.14]

To solve for Q*, we take the square root of both sides to find:

Q*  [21.15]

2 TF

CC

2 TF

CC

Restocking

Quantity Carrying Costs  Restocking Costs  Total

(Q)(Q/2 CC) (FT/Q) Costs

500 $ 187.5 $4,680.0 $4,867.5

1,000 375.0 2,340.0 2,715.0

1,500 562.5 1,560.0 2,122.5

2,000 750.0 1,170.0 1,920.0

2,500 937.5 936.0 1,873.5

3,000 1,125.0 780.0 1,905.0

3,500 1,312.5 668.6 1,981.1

CHAPTER 21 Credit and Inventory Management 729