The holding rate is four costs added up and applied to stock at cost, and on a part where safety stock dominates, three-quarters of the bill is the buffer.
Inventory carrying cost is the average value of stock at cost multiplied by a holding rate built from four parts: the cost of capital, storage, obsolescence and insurance. For part AF-7 in Supply Chain Management the rate is 7.4 + 3.1 + 2.25 + 0.65 = 13.4 per cent a year, the average stock is worth 278,534 EUR, and carrying it costs 37,324 EUR a year, 3.8324 EUR per unit held. Value the same stock at selling price, or use a 25 per cent rule of thumb, and the figure is overstated by 66 or 87 per cent.
Worked in full in Supply Chain Management by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
The holding rate is the price the company puts on a euro of stock sitting still. It sets the order quantity through the EOQ, the optimal service level through the trade-off between holding and shortage, and the value of every project that releases stock. Most planning systems carry one rate for the whole business, typed in years ago. On a part where three-quarters of the stock is safety stock, that number decides more than the forecast does.
| Input | Value |
|---|---|
| Mean weekly demand; standard deviation | 1,840; 462 units |
| Lead time; standard deviation | 6; 1.9 weeks |
| Purchase cost delivered | 28.60 EUR |
| Selling price | 47.50 EUR |
| Cost of placing one order | 385 EUR |
| Cycle service level | 98% |
| Cost of capital | 7.40% |
| Storage, variable | 3.10% |
| Obsolescence | 2.25% |
| Insurance | 0.65% |
1. Holding rate = 7.40% + 3.10% + 2.25% + 0.65% = 13.4% a year
2. Holding cost per unit = 28.60 × 13.4% = 3.8324 EUR per unit per year
3. Average stock = order quantity / 2 + safety stock = 4,384.5 / 2 + 7,546.7 = 9,739.0 units
4. Average stock at cost = 9,739.0 × 28.60 = 278,534 EUR
5. Carrying cost = 278,534 × 13.4% = 37,324 EUR a year
Excel: =(Q/2+SS)*Cost*(CoC+Storage+Obsolescence+Insurance)
The order quantity is the EOQ, 4,384.5 units, worked in how to calculate the economic order quantity; the safety stock of 7,546.7 units covers demand and a lead time that varies, and is derived in how to calculate safety stock when lead time varies.
| Component | Rate | EUR a year | Share |
|---|---|---|---|
| Cost of capital | 7.40% | 20,612 | 55.2% |
| Storage | 3.10% | 8,635 | 23.1% |
| Obsolescence | 2.25% | 6,267 | 16.8% |
| Insurance | 0.65% | 1,810 | 4.9% |
| Carrying cost | 13.4% | 37,324 | 100% |
Split by the reason the stock is there, the cycle stock costs 8,402 EUR a year and the safety stock 28,922: the buffer is 77.5 per cent of the units and of the carrying cost. At the EOQ the cycle-stock carrying cost equals the ordering cost, 21.82 orders at 385 EUR, also 8,402. Spread over the 95,680 units sold, carrying is 0.390 EUR a unit, 1.36 per cent of the purchase cost.
Only the cost that varies with the stock belongs in the rate. A warehouse lease that is paid whether the shelves are full or empty is not a carrying cost of AF-7. If a third of the 3.10 per cent storage line were fixed, the rate would be 12.37 per cent and the EOQ would rise from 4,385 to 4,564 units.
The rate moves the order quantity, which moves the stock, which moves the cost. The safety stock is held at the 98 per cent service level throughout.
| Holding rate | EOQ, units | Orders a year | Average stock | Carrying | Ordering | Total |
|---|---|---|---|---|---|---|
| 8.0% | 5,675 | 16.9 | 296,981 | 23,758 | 6,492 | 30,250 |
| 10.0% | 5,075 | 18.9 | 288,414 | 28,841 | 7,258 | 36,099 |
| 13.4% | 4,385 | 21.8 | 278,534 | 37,324 | 8,402 | 45,725 |
| 20.0% | 3,589 | 26.7 | 267,157 | 53,431 | 10,264 | 63,695 |
| 25.0% | 3,210 | 29.8 | 261,739 | 65,435 | 11,476 | 76,910 |
The stock barely moves, from 296,981 to 261,739 EUR across the whole range, because the order quantity responds only to the square root of the rate and the safety stock does not respond at all. The cost moves almost in proportion. A higher rate does not make AF-7 leaner; it makes the same pile dearer. What it should change is the service level: the book's workbook adds a shortage cost of 11,129 EUR at 98 per cent, a total of 56,854, and the rate is one side of the balance worked in how to calculate the optimal service level.
The four components and every figure above sit in blue input cells in the free workbooks for this case, with the holding rate swept from 8.0 to 25.0 per cent.
Textbooks often quote 20 to 30 per cent a year, but the right figure is your own build-up. For the illustrative part AF-7 it is 13.4 per cent: 7.4 cost of capital, 3.1 storage, 2.25 obsolescence and 0.65 insurance. Using 25 per cent instead would put its carrying cost at 69,634 EUR rather than 37,324, 86.6 per cent too high.
On cost, because the carrying cost is the return forgone on cash actually tied up, plus costs that scale with that value. AF-7's average 9,739 units are 278,534 EUR at the 28.60 purchase cost; at the 47.50 selling price they would be 462,600 and the carrying cost 61,988 EUR instead of 37,324, overstated by 66.1 per cent.
EOQ falls with the square root of the rate. For AF-7 it is 5,675 units at 8 per cent, 4,385 at 13.4 and 3,210 at 25. Average stock moves only from 296,981 to 261,739 EUR across that range, because safety stock is unchanged, while the carrying cost rises from 23,758 to 65,435 EUR a year.
This article is one calculation from Supply Chain Management. The book takes the same case from first principles to the decision, chapter by chapter, and every figure it prints is a live formula in the free companion workbooks.
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