# Exchange Curve

Exchange curve (EC) is also called optimal policy curve which is useful for planning aggregate inventory level in an organization. The total number of orders (TO) per year is plotted against the total investment in inventories (TI) per year. When TI is given, rational inventory policy tries to minimize TO. The exchange of TI and TO is such that TI.TO = K = Constant.

K’s value is 1/ 2 [ Σ √ Di Vi ]2

Where Di = Annual Requirement of ith item, 12 x 6 / 24

Vi = Unit Price for ith item, i = 1… N.

Exchange Curve as seen from the diagram is a rectangular hyperbola. The exchange curve in the diagram is for a situation where the ordering cost is not explicitly known. At any point on the EC, there is an optimal, trade off between TI and TO.

Application of EC:

It is a tool to plan aggregate inventory. It assesses quickly the rationality of prevailing inventory policies. EC is plotted first by computing the value of K for selected group of items. TO and TI are determined under prevailing situation. If point C in EC is our prevailing situation, it is irrational. To rationalize it, there are two alternatives – AC or BC such that we reduce inventory to B for the same ordering effort or reduce the number of orders to A for the same inventory. It is a mechanism useful at the macro level.

Inventory Turnover:

It is the figure that indicates the number of times the inventory is rotated in a year, e.g. inventory equal to one month’s consumption means a turnover of 12 times and inventory equal to six month’s consumption means an inventory turnover of 2 times. The turnover ratio indicates how best the capital tied up in inventory is utilised. Consider the following illustration:

Opening inventory 7 lakhs

Closing inventory 5 lakhs

Average inventory 6 lakhs

Consumption during the year 24 lakhs

Average inventory as the number
of month’s consumption 3 months

Inventory turnover rate 4 times a year

Inventory turnover greatly affects the profitability of the company. Consider the following example.

Company X Company Y Company Z

Cost of sales (Rs) 50 lakhs 50 lakhs 50 lakhs

Gross Profit 15% 7.5 lakhs 7.5 lakhs 7.5lakhs

Material consumed 25 lakhs 25 lakhs 25 lakhs

Inventory held as month’s
Consumption 1 month 6 months 12 months
Turnover rate 12 2 1
Value of Inventory held 2.1 lakhs 12.5 lakhs 25 lakhs

Inventory carrying
cost @ 25% 52,500 3.13 lakhs 6.25 lakhs

Net profit (Rs) 6.98 lakhs 4.37 lakhs 1.25lakhs

In XYZ company, there was a sales turnover of 2 crore in 1996. It earned a profit of Rs 20 lakhs. The capital employed was Rs 100 lakhs.

1) Percentage of profit on sales = 20 lakhs x 100 / 200 = 10%
2) Turnover of Investment = 200 lakhs / 100 = 2
3) Percentage of Return on Investment = 10 x 2 = 20%

In 1997, the company reduced its inventories by 20 lacs. The other things i.e. sales turnover and profits, remained the same.

1) Capital employed= 80 lakhs
2) Turnover of Investment= 200 lakhs / 80 lakhs = 2.5

A large part of capital is tied up to inventories, and hence reduction in inventory money improves the returns on assets, though profits on sales remain the same. Consider the following example.

Our earnings are sales revenue minus costs of materials, labor, sales costs, administrative costs etc.

Our capital employed is worth our inventories, cash, fixed assets, plant and equipment etc.

Percentage of profits on sale = Earnings x 10 / Sales Revenue —A

Turnover of investment = Sales Revenue / capital employed –B

A x B = Percentage Return on Investment

Percentage of Profit on sales x Turnover of Investment

Percentage Return on Investment 10 x 2.5 = 25%

It is obvious that a reduction in inventory increases the returns.