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Curing and preventing surplus inventories
W. B. H m S C H M A N N
AND J. R. BRAUWEILER
CURING and PREVENTING SURPLUS INVENTORIES
n line with rapid advances in the general
I management disciplines, several subspe-
cialties have been transformed from fairly routine tasks to highly sophisticated functions. In some cases, the change has occurred quietly and within the context of more spectacular developments, which may explain why the full implications of new and improved ways of doing familiar jobs are often missed. Inventory control provides an outstandMr. Hirschmann is Research Supervisor in Economics for the American Oil Comlmny, and Mr. Bmuweiler is an operations research analyst for Kraft Foods.
SPRING, 1963
ing example of this transformation. Within the memory of everyone in management except the newest business school recruit, inventory management has been a simple matter of counting stock, keeping records, and following rule-of-thumb guides on reorder and disposal. Anyone adept at attending to details could do the job and do it well. Today, however, inventory control is a specialized task requiring professional management skills. Techniques are based on a rationale derived from managerial economies, and a growing body of literature is addressed to inventory specialists. The basis for this interest in better management of inventories is not hard to find.
87
W. B, HIRSCHMANN AND J. R. BRAUWEILER
At a time when the profit squeeze is beginning to look like a long-term prospect, good management demands that costs be carefully controlled. Reduced inventories offer many firms one opportunity for significant cost savings. The usual emphasis in inventory control is on optimizing operating inventories-raw materials, goods in process, and finished goods-which is understandable since these categories comprise the bulk of inventory accounts. However, another kind of inventory that may be profitably investigated is • the maintenance inventory; although a small part of total stocks, it involves a substantial investment in some firms.
THE MAINTENANCE INVENTORY 88
Some intriguing situations are connected with the control of maintenance inventories. One of these is the fact that a skillful management can profit from past mistakes. The mistake we are dealing with is peculiar because it involves a decision that was completely justifiable at the time it was made, and one which, under the same circumstances, would be made again. At some time past, material was purchased with the expectation that it would be used for maintenance purposes. Since then, for one reason or another, the material has become surplus. While the past mistake of obtaining it may be justifiable, the present mistake of keeping it is not. Retaining this type of material is usually the result of applying a "home economics" approach in a situation where "corporate economics" should prevail. The home economics thinking is that keeping surplus material adds little to maintenance expense, and in general this is true-in household situations, On the other hand, the corporate economies approach puts the decision in its true perspective. The factor that makes the difference betwe'en the two systems is what, for practical
purposes, can be considered a partnership arrangement between a corporation and the government-an arrangement that the householder does not have. As a partner, the government takes one-half of a corporation's profits. But as a just partner, the government also shares one-half of the corporation's losses, if the corporation will but admit the losses. This arrangement offers a potential cash flow that is often ignored. Unfortunately, delay in admitting losses does not make them more palatable or reduce them; in fact, refusal to recognize that a loss has occurred tends to compound the loss. Keeping an inventory of spare parts for maintenance is justified because it costs less than lost production, the inconvenience, and the emergency measures that may result ff inventory items are not on hand when needed. Over a period of time, however, circumstances may change, so that items once considered essential are no longer required. They may be unsalable because they were designed for a particular firm's unique equipment, or because they have become obsolete. Consequently, they have no resale value; if liquidated, they would have to be sold for scrap, and there is an understandable reluctance to take the large losses entailed in scrapping. Because the costs of storage (incremental costs, in many cases) appear to be the only price of retaining such items, and because of the hope that they can somehow be worked off, the alternative of keeping them on hand seems more reasonable. Potential book losses block disposal so effectively that the accumulation of surplus may become sizable. Commonly, surplus material is sold only if there is a good market for it; "good" is usually defined as some arbitrary percentage of original cost, based on age. For example, two-year-old material may be sold only ff 60 per cent of its cost can be recovered, and three-year-old material only for 50 per cent or more of its cost. Because market salvage values tend to decrease with age, disposal requirements of this kind put surplus in the
BUSINESS HORIZONS
CURING AND PREVENTING SURPLUS INVENTORIES
position of chasing prices downhill. An inaportant consequence of focusing attention on age is that disposal policy becomes retrospective. A policy that emphasizes the future rather than the past (by estimating the expected time of need) can b e more profitable. The economics of a realistic forward look may indicate that the costs of retaining surplus are larger than they appear, and may provide an economic incentive for disposing of them. This article presents a decision-making procedure for liquidation that is future oriented. It is addressed to the economics of liquidating maintenance or other inventories that have been recognized as surplus, and are not or have not been in capital accounts; it presents simple rules for determining whether inventories have become so inactive that they may be considered surplus and therefore subject to liquidation.
THE ECONOMICS OF LIQUIDATION Two kinds of costs are associated with maintaining an inventory: that of handling and storing, and that arising from the unavailability for other uses of the money used to purchase the inventory. Because inventory earns nothing directly, and because its purchase price generally can neither be depreciated nor charged as expense against current income until it is used, inventory funds are sterile. Active inventory is not on hand long. It is usually used shortly after it is acquired. Nevertheless, the physical cost of warehousing each unit of active inventory is reported to be 4-5 per cent of its purchase price; power, light, accounting, engineering, supervision, and plans and benefits prorated add 5-6 per cent; and placing the order adds another 1-2 per cent. Such other costs as insurance, taxes, and spoilage can raise the total to about 20 per cent. The effective cost (exclusive of interest charges) of each unit of an active item in inventory is thus
SPRING, 1963
about 120 per cent of the purchase price or value carried on the books. The effective cost of inactive items is higher because most of these costs continue and accumulate.
C A S H BENEFITS OF LIQUIDATION
Even though inventory may have no net salvage value, liquidation provides after-tax cash benefits. The 100 per cent loss taken on purchase price is deductible from current income; with a corporate income tax rate of 52 per cent, a cash inflow of 52 per cent of the original purchase price results. Higher salvage values produce greater benefits: a 50 per cent salvage brings a cash benefit of 76 per cent and, of course, 100 per cent net salvage returns the original funds. Keeping material in inventory deprives a firm of the income it could earn by investing the cash benefits from liquidation. Money from the liquidation of surplus inventory is likely to be part of a firm's general funds, and available for reinvestment in its business. Individual projects may yield different rates of return, but their combined effect is to produce the firm's average rate of earnings. Liquidation money should earn at this average rate. The average rate for manufacturers, about 10 per cent per year after
80
W. B. HmSCHMANNANDJ. R. BrtAowEn.r~
90
taxes, provides a point of departure for this analysis. If the corporate income tax rate is 52 per cent, an item liquidated for a net salvage of zero provides a tax remission of 52 per cent of its original cost. If the earnings rate is at the 10 per cent level, liquidation of such an item can yield an after-tax annual income of 10 × 52 -- 5.2 per cent of the original cost. Higher salvage values, of course, yield higher annual incomes. If the firm is fortunate enough to realize 100 per cent net salvage, for example, liquidation can yield an after-tax annual income of 10 per cent of the item's original cost. Reducing inventories can be expected to reduce some of the running costs of maintenance. While the cost reduction attributable to disposing of static or slow-moving items cannot always be clearly identified, it appears reasonable to assume that disposing of such items might save charges equivalent to 5 per cent of their purchase price before taxes, or 2.4 per cent per year after taxes of 52 per cent. These warehousing savings, plus the earnings of 5.2 per cent on the realization by liquidation for a net salvage of zero, provide a benefit of 15.8 per cent before taxes, or 7.6 per cent per year after taxes. The decision to keep $1 million worth of static or unused inventory instead of liquidating for a net salvage of zero thus costs about $158,000 per year before taxes. If the inventory could be sold for 100 per cent of its original cost, the annual cost of retention would be the 10 per cent earnings possible through reinvestment in the firm, plus incremental storage charges of 2.4 per cent. These amount to 25.8 per cent before taxes, or $258,000 per year for a $1 million inventory.
COMMON APPLICATIONS KEEPn~c vS LIQUmATINC
Piece of Equipment The savings provided by liquidation can compound at a firm's average earnings rate. Eventually,
they will have grown sufficiently to permit repurchasing the liquidated inventory at no penalty. If the material is required before this point is reached, it is preferable not to liquidate, but if it is required subsequent to this point, the compounded savings from immediate liquidation will permit the firm to repurchase and still save. At high salvage values, the time within which the proceeds from liquidation will permit repurchase at no penalty is quite short. The solid line of Figure i shows the time periods for different salvage values, and for an earnings rate of 10 per cent after taxes. An inventory often has a salvage value of 10 per cent of its purchase price; with liquidation costs (handling and paper work, for example) of about 10 per cent, the net salvage is zero. The solid line of Figure I shows that a single article with a gross salvage of 10 per cent should be kept ff it will be required within five and one-half years; if it will not be required within that period, it should be liquidated. If salvage is 75 per cent, it should be kept only if it will be needed within two years.
Kind of Material If the inventory consists of a quantity of identical articles of a given kind having a 10 per cent salvage value, a five and one-half year supply should be kept, and the excess liquidated. Similarly, for 75 per cent salvage value, a two-year supply should be kept. For example, suppose a supply of standard 8" pipe worth $120,000 is on hand. Annual usage is expected to continue at the rate of $15,000 per year. Current offering price for it on the used market is $.25 on the dollar. Should such a supply be retained? The solid line of Figure 1 shows that only a four and one-half year supply, worth $67,000, should be kept; at a salvage value of 25 per cent, the $53,000 balance should be liquidated for $13,250. Assorted Inventory
For one reason or another, a firm may not be in a position to separate inventory material that will be
BUSINESS HORIZONS
CURING A N D P R E V E N T I N G
SURPLUS INVENTORIES
FmVr~ 1 CONDITIONS Cost of keeping inventory (out-ofpocket warehousing and accounting) is 5 per cent per year before taxes; income tax rate is 52 per cent; money can be reinvested at an average of 10 per cent after taxes, continuously compounded; liquidation charges for paper work, handling, and so on amount to 10 per cent of original cost; rebuying when out of stock costs 115 per cent of original cost; and there is no other penalty for out of stock. (Since surplus implies no need, there is no penalty for being out of such stock by liquidation. Surplus articles are usually used up or "worked off" in new construetion.)
Liquidation or Retention of Surplus Inventory I3C 12C IIO GROSS SALVAGE VALUE AS %
IOC 90 8O
Liquidate
7C
OF ORIGINAL 00ST
GO 50
Keep
30
\.
\\\
20
\\\\\ - . .
o..,L
,.~E.TO..
,~
. . . 0
0.
0.0
9
Years until n e e d e d ( f o r single pieces of e q u i p m e n t ) or years of supply for stock of a n i t e m ..... H a l f - l i f e ( y e a r s r e q u i r e d to use o n e - h a l f the cost of a m i s c e l laneous lot)
used within the time indicated by the chart from material that will be used later. The firm is then faced with a choice between liquidating all (and perhaps being obliged to rebuy some immediately), or keeping all (and losing the savings on items that could have been liquidated). For liquidation of all material to be justified, the firm must realize compounded savings from complete liquidation that are adequate to allow repurchase of the fractional amount needed each year at no penalty. Since the inventory is considered surplus, the firm certainly would not maintain it by replacing the articles for which it finds a use. Under these circumstances, the inventory will constantly be reduced. Furthermore, as the more usable items are removed from stock, the concentration of less usable items will progressively increase. Eventually, the firm will probably conclude that it should scrap the remainc~er, for which there are no
SPRING, 1963
foreseeable calls. As a practical matter, this process can be described as using each year a constant proportion of a declining balance. Since it may be difficult to estimate usage in terms of such a proportion, the equivalent concept of "half-life" appears more practical. Half-life is the time required to use onehalf of an inventory, in terms of its original cost. Thus, if salvage value is known, it is necessary merely to estimate half-life to determine whether or not to liquidate an entire inventory. The broken line of Figure i plots percentage salvage value of an assorted inventory against the expected half-life that is necessary to justify keeping it. For example, consider a miscellaneous lot of cast-iron fittings that originally cost $10,000. Because their fire resistance is low, their use has become limited to about $300 worth per year, or 3 per cent per year. A junk dealer offers $400 for the lot. The broken line of Figure 1 shows
91
W. B. HIBSCHMANN AND J. R. BRAUWEILER
that at a salvage value of $400/$10,000 --- 4 per cent, the half-life is about five and onehalf years. If we assume linear usage at the rate of 3 per cent per year of the present stock instead of the slower 3 per cent attrition of a declining balance, at least sixteen years will be required to use one-half the inventory. Thus, the entire lot should be liquidated for $400.
99.
Since $300 of this inventory is being used normally, it will be necessary to rebuy this amount if the entire lot is sold. The management might find it more convenient, or more comfortable, to keep a portion of the inventory rather than to dispose of all of it. The solid line of Figure 1 shows that, at 4 per cent salvage, a five and three-fourths year supply can be justifiably retained. At the rate of $300 per year, a five and three-fourths year supply is $300 × 5~ -- $1,700 or 17 per cent of the $10,000 total. Thus, because it is a miscellaneous lot, 17 per cent of each kind of article could be retained, and the 83 per cent balance liquidated for 83 per cent of $400, or $332. A heterogeneous assortment of inventory can thus be analyzed for the economic desirability of complete or partial liquidation.
retaining avoids the necessity of purchasing the material ff it should prove to be needed at some future time. The different rates of return provided by various estimated times of need are shown in the charts of Figures 2 and 3. The solid lines of Figure 2 are the break-even points for various rates of return for single articles; they correspond with the solid line of Figure 1. The broken lines of Figure 3 are the break-even points for various rates of return for the half'life of a miscellaneous lot, and correspond to the broken line of Figure 1. A management might well feel that the uncertainties of need require the rate of return promised by an investment in surplus materials to be higher than the company as a whole has averaged, since the average rate could be obtained with relative certainty simply by investing in the firm's common stock. The time within which a need must arise to provide a satisfactory rate of return can be readily determined with such charts. They are particularly meaningful for managements that are accustomed to assessing investment attractiveness by the rate-ofreturn yardstick, and have a feeling for risk from the way the promised rate of return changes with different judgments.
RETENTION AS AN OPPORTUNITY FOR PROFIT
Judging the desirability of liquidation' with the chart of Figure 1 requires weighing the relatively certain benefits of disposal against the possible benefits of retention. While such balancing is a valid way of arriving at a decision, it does not indicate the consequences of errors in judgment, or provide a feeling for the risk of loss. Such a feeling can be acquired by considering the problem in the context of an investment opportunity. The desirability of an investment is usually judged on the basis of whether the rate of return promised by the anticipated profit is adequate in the context of the firm's operations and commensurate with the attendant risk. Retaining surplus material is, in effect, an investment of net salvage currently available, tax remission, and annual storage costs;
OTHER APPLICATIONS
LIQUIDATIONOF EXCESSINVENTORY These concepts and analyses also apply to other kinds of inventories that are considered active. A portion of the spare parts inventory, for example, may contain materials for which there have been no calls for a number of years. Such materials might be considered to have become surplus in effect, and thus subject to liquidation as determined by the salvage value and usage curve (solid line) of Figure 1. If there is a penalty for being out of stock of such an article, partial liquidation may still be in order, for, if there are several identical articles of a particular kind on hand, only
BUSINESS HORIZONS
CURING AND PREVENTING SURPLUS 1NVEN~I'ORIES
Liquidation or Retention of Maintenance Inventory (percentage salvage value vs years unt~ inventory needed Sample Problems ( 1 ) Liquidating or retaining pieces of equlpment--An inventory of rotating blower assemblies worth $60,000 was specially designed for a processing unit that no longer exists, but there is a possibility of using them in future construction. They may be sold for one-third of their original cost. H o w soon must they be used to justify keeping them, if the firm requires funds so committed to promise a return of at least 15 per cent per year? Solution-The 1S per cent solid line of Figure 2 shows that, at 33 per cent salvage value, the assemblies must be used within three years. Those not needed by that time should be sold now. ( 2 ) Amount of stock to retain of a kind of article--A $120,000 supply of standard 8" pipe is on hand. Annual usage is estimated to continue at the rate of $15,000 per year. The current price for it on the used market is $.25 on the dollar. Should the firm keep such a supply on hand if it expects investments of that type to yield a return of 20 per cent per year? Solution-The 20 per cent solid line in Figure 2 shows that a two and one-half year supply, or about $37,500, should be kept, and the $82,500 balance Hquidated for 25% × $ 8 2 , 5 0 0 = $ 2 0 , 6 5 5 . ( I f the salvage is 10 per cent, a thrce-year supply, $45,000, should be kept, and the $75,000 balance sold for $7,500. ) ( 3 ) Liquidating or retaining a heterogeneous lot--A firm has a $10,000 miseellaneous lot of cast iron fittings. Because their fire resistance is low, their use has become limited to about $300 worth per year. This rate is expected to continue. A junk dealer offers $600 for the lot. If this firm desires investments of this sort to promise 10 per cent per year, should it accept the $600? Solution-(a) Annual usage is 3 per cent ( $ 3 0 0 / $ 1 0 , 0 0 0 ) . With 6 per cent salvage value, the 10 per cent solid line of Figure 2 shows that a five and three-fourths year supply. about 15 per cent, should be kept, and the 85 per cent balance sold for $510. ( b ) If the junk dealer stipulates that he will take all or none (or if the firm cannot split the stock of each item into 15 per cent and 85 per cent shares), the half-llfe chart of Figure 3 can be used. The 10 per cent broken line shows that one-half or more of the inventory will have to be used in five and one-fourth years to justify keeping all of it. The 3 per cent per year current rate of use indicates that more than 18 years will be required to use half the material. Therefore, the firm should dispose of the entire lot for the $600. ( 4 ) L i q u i d a t i n g or retaining new constrnction surplus--To avoid construction delays for a plant just completed, a small overage of miscellaneous items had been provided; about $ I 0 , 0 0 0 worth remains. The vendor will take them back for a restocking charge of 10 per cent. The firm requires such inventory to promise a minimum rate of return of 1S per cent per year. Should it return these items?
Solution-(a) For a salvage value of 90 per cent, the 15 per cent broken line of the half-life chart of Figure 3 shows that if one-half the lot is not used in nine months, it is desirable to return all for credit now. ( b ) If it is possible to sort the items, the firm should keep only those items it is sure to use within one year, as indicated by the 15 per cent solid line of Figure 2.
SPBING, 1963
or
used; use solid line chart if inventory permits) VICUnE
2
Years Until Inventory Needed (for Single Pieces) or Years of Supply 130
120 IlO 'GROSS
IO0
\
SALVAGE 90 VALUE 8o AS % 70
~
OF SO ORIGINAL ,50 COST 40
\ 10%
30 2o
LiqoidotS
O'Nis % Keep
93
10 I
0
\ i3 \
,\,
4
5
\
6
,
7
,
8
YEARS UNTIL INVENTORY IS NEEDED OR USED
FIC~ 3 Years Required to Use One.Half Original Cost of Mis. cellaneous Lot (Half-life) 130 120
lid GROSS IOC SALVAGE9C VALUE 8C AS % 7¢
OF 60 ORIGINAL SG COST
\\\\ \\ \\ \ \ \ \.,o. \
40 30 20
\, \ \,s%\ \ \ \ \,o,.\ \ \\
~"P
Io I
2
3
4
5
6
7
8
YEARS REQUIRED TO USE HALF THE COST OF A MISC LOT
w. B. HmSCHMANNANDJ. R. BRAtrwEmFaa
one or two of the articles may be sutBcient to insure against a penalty for being out of stock if an unexpected need arises. It is therefore desirable to review all working inventories to see whether the stock level has become excessively high in light of current salvage value and expected usage.
AVOIDANCE OF INACTIVE INVENTORY
94
Not only should existing inventories be weeded out, but little-used inventories should not be created. Such inventories can be created by transferring to surplus the materials left over after construction of a new unit. An excess of articles is properly provided during construction as insurance to take care of breakage, loss, defects, and so on, which might cause delays. When the plant is completed, the left-over items are essentially new, and some manufacturers will take them back for a small restocking charge. Unless some use can be foreseen in the near future, this initial high salvage value counsels immediate liquidation. Since lower salvage values justify longer retention, an initial error in keeping material with a high salvage value tends to compound itself. For example, after a major plant was built, materials worth $100,000 remained unused. The manufacturer was willing to take them back for a restocking charge of 10 per cent; their salvage value was thus 90 per cent. Liquidation charges of 10 per cent would reduce recovery to 80 per cent, but tax remission on the $20,000 of loss and expense would result in a net cash benefit of $80,000 + 52 per cent )< $20,000 -- $90,400. However, the materials were kept in the hope that they would be used in the one and one-half years noted from Figure 1. At the end of this period, salvage value had decreased to 60 per cent, at which level materials should be kept if they will be used within another two and three-fourths years. The longer they are kept, the lower the salvage value, and the greater the retention period justified.
If, unfortunately, the firm has kept these materials for five years, the storage costs and earnings on the original salvage of $90,400 will compound to $165,000 after taxes (with continuous compounding at 10 per cent per year). Thus, an original cost of $100,000 becomes an effective after-tax cost of $165,000 five years later. This effective cost will grow, of course, by compounding as time goes on and the materials remain unused. On the other hand, had the materials been liquidated immediately and had a need then arisen unexpectedly, repurchasing would have cost $115,000 before taxes (reflecting 15 per cent of the cost of purchase) or $107,200 after taxes. Thus, an after-tax penalty of $107,200 - $90,400 ~- $16,800 would have resulted. This would have been the maximum penalty, however; if the need arose sometime after liquidation, the savings in storage costs and the earnings on the $90,400 recovered would have decreased the penalty. After one and one-half years, the firm would have broken even; ff the delay had been any longer, the firm would have made a profit. Since time is required to pass information regarding such surplus through the company, to find a place for it, and to get it built into a new plant, it is easy to see how the permissible one and one-half years could be exceeded even under favorable circumstances. Immediate liquidation will generally be more profitable than straining to discover a use that might not be really satisfactory. Note that if the firm liquidates and has to rebuy after five years, its purchase cost is still $107,200. But the $90,400 recovered on liquidation has grown to $165,000; therefore, the firm is ahead $165,000 - $107,200 : $57,800 after taxes, or $120,000 before taxes. This before-tax gain is greater than the original purchase cost of $100,000. Thus the firm can not only afford to replace what proves to be needed, but can also spend an equal amount for expediting or some other
BUSINESS HORIZONS
CURING AND PREVENTING SURPLUS INVENTORIES
p e n a l t y , a n d still b r e a k e v e n w i t h t h e a l t e r n a t i v e of r e t a i n i n g t h e m a t e r i a l . l Small salvage value and low increm e n t a l s t o r a g e costs c a n b e m i s l e a d i n g in c o u n s e l i n g t h e r e t e n t i o n of l i t t l e - u s e d i n v e n tory. T h e 52 p e r c e n t t a x r e m i s s i o n p r o v i d e d b y t h e loss o n l i q u i d a t i o n raises t h e effective s a l v a g e v a l u e to m o r e t h a n o n e - h a l f t h e origin a l cost. I f t h e r a t e of r e t u r n p r o m i s e d b y r e t a i n i n g t h e m a t e r i a l s is n o t a d e q u a t e in t h e f r a m e w o r k of a firm's o p e r a t i o n s or c o m m e n s u r a t e w i t h t h e risk of loss, o r if o t h e r i n v e s t m e n t o p p o r t u n i t i e s exist w h i c h p r o m ise m o r e profits, l i q u i d a t i o n m a y b e m o r e attractive than retention.
K = annual rate of decline as a decimal, e : base of natural logs. The factor e "~r is similar to the factor for continuously discounting at interest rate R a cash flow that occurs instantaneously T years hence; this suggests that continuous discounting can conveniently handle the attrition of a heterogeneous lot. With continuous discounting, the following relations result: The dollar amount of inventory used from O to T is Vo -- V r = Vo (1 -- e-~rr), which is
Vo K e "~r d T .
o The discounted value of the amount used from O to T is
ioT
Vo K e -Kr e -RT d T : Vo K
i,l K + a
=
j
Vo K T U ( r q - n ) r where U(~r-t-n)r :
_aUTHORS' NOTE Mathematics of Analysis The financial merits of liquidating or keeping inventory can be assessed by listing the actions that result from choosing either alternative, determining the corresponding cash consequences, expresshag them in after-tax terms, and reflecting the time value of money. The latter can be done by discounting at an appropriate interest rate all cash flows to their present value. Figure 4 tabulates such a comparison for individual items of inventory. The analysis is straightforward. The resulting equation is the basis for determining the points that trace the solid lines of the charts. Figure 5 tabulates the comparison between liquidating and keeping a heterogeneous assortment of items that cannot be segregated in terms of their expected time of use. The functions for the various cash flows and the basis for determining the points that trace the broken lines of the charts are not as straightforward as those in the preceding analysis and, therefore, are developed in the following paragraphs. A heterogeneous lot whose usage is a constant dollar proportion of a continuously diminishing balance can be represented by the empirical function V r : Voe -~r
where V° = value of initial inventory in terms of original purchase price, Vr : value of inventory remaining after T years (in terms of original cost, not in terms of scrap value),
SPRING, 1963
factor for continuously discounting uniform cash flows over T years at interest rate ( K - I - R ) . The tax remission, when this amount of inventory used is charged against income, is tVo(1-e-~T), and its discounted value is tVoKTU(~-I-R)r. If an item is repurchased and the expense of repurchase is E as a fraction of purchase price, then the cost of repurchasing an item is (1-q-E), and the cost of repurchasing all items used over T years is (1-t-E)V, (1-e-~r). Their discounted value is (lq-E) Vo K T U ( K q - ~ ) r , the tax remission on use is t(lq-E) V° (1-e-Kr), and the discounted value of the tax remission is t(1-I-E)Vo KTU(~r-l-n)r. If M, as a fraction of the original purchase price, is the annual cost of maintaining the inventory, the annual cost of the stock on hand at any time is M V r : M V o e -~r, and the cost ef maintaining this declining stock from O to T is M V o e -rr d T = Me V*
o
IKJ"
The discounted value of this cost is f T M V /I J o M V o e -Kr e -nr d T = o
e-(~+~)r] :
lr + R
J
M V o TU(,:-~-n),.
The tax remission when this expense is charged against income is t MVoTU(~+n)r.
By its nature, a declining balance inventory is never all used; s o m e remains on hand "forever." Eventually, management will decide that the remaining items are of no use and they will be liquidated. The amount of this residual inventory is Voe -rr, its after-tax liquidation expense is E(1-t) Voe "rr, its tax remission for zero salvage is tVoe -xr,
95
W. B. HIRSCHIVIANNANDJ. R. B~AUWZtLZ~
FIGURE 4
D i s c o u n t e d C a s h F l o w Analysis of L i q u i d a t i n g or R e t a i n i n g Surplus I n v e n t o r y (single item or homogeneous group)
Liquidate (Buy When Needed)
Time 0
After.tax Cash Type of Consequence Cash Flow
Resulting Action
Spend L, as fraction of original purchase price, for liquidation expenses (paper work, handling, and so on). Get tax remission (Lt) by charging this expense against income at tax rate t. -L-kLt
Instantaneous
1.0
-L(I-t)
Get salvage (S) as fraction of original purchase price.
Instantaneous
1.0
-kS
Instantaneous
1.0
-kS
Get tax remission by charging loss (l-S) against income. -k(l-S)t 90
O-T T
Discount Discounted Factor Value
No inventory in stock.
None
.
.
.
.
.
-k(1-S)t .
Need for item arises. Spend E, as fraction of original purchase price, for repurchasing expense. Get tax remission (Et) by charging this expense against income. - E + Et
Instantaneous
Inr
--E(l-t) IRr
Buy replacement (1); use at once and get tax remission (t) by charging purchase price against income.
Instantaneous
Ia~
-(1-t)lRr
Uniform
URr
.MT(I-t)U~r
Instantaneous
IR~
-ktI~r
--lq-t
Retain (Maintain and Use When Needed) O
O-T
Keep inventory.
None
Maintain inventory for T years at annual cost M as fraction of purchase price.
-MT
Get tax remission (MTt) by charging this expense against income.
-kMTt
Item on hand. Use item from inventory; get tax remission (t) by charging original purchase price against income.
I ~ z = f a c t o r for continuously discounting at interest rate, R, cash flows which occur instantaneously T years hence. Ugz----factor for continuously discounting at interest rate, R, cash flows which occur uniformly over T years. When the total discounted value of liquidation equals the total discounted value of retention (that is, when the salvage value less liquidation costs plus tax remission and annual salvage savings compound to purchase price plus repurchasing expense) the alternatives are financially equivalent: -L(l-t) .6 S -6 (l-S)t - E(l-t)/Rr -- (l-t)IRr :
-MT(I-t)URr -6 tint
1
[8 -- L(l-t) -/- (1-S)t -k MTURrO-t)] × - = 1 -k E(l-t). IA¢~,
---
None -kt
If the item is "worked off" in new construction, it will probably be capitalized. In that case. the tax remission is not obtained when the item is used at time T, but over the amortization life of the equipment through depreciation charges. The total amount of the tax remission is the same as when the item is expensed (t). but its discounted value is tDna at the time of use T, and tDR,IRT at T = O, where Dn~ is the factor for discounting depreciation cash flows at interest rate ( r ) over ( a ) years. This tax remission is the same for the item used from stock as for the repurehased item; consequently, it cancels out of the equation. Thus. the equation for equivalence when the item is capitalized is the same as when it is expensed.
BUSINESS HORIZONS
CURING AND PREVENTING SURPLUS INVENTORIES
FICURE 5
Discounted Cash Flow Analysis of Liquidating or Retaining Surplus Inventory (nonseparable assortment) Liquidate (Buy W h e n N e e d e d )
Time 0
O-T
After-tax Type of Cash Consequence Cash Flow Resulting Action Spend L, as fraction of original purchase price, for liquidation expenses (paper work, handling, and so on). Get tax remission (Lt) by charging this expense against inInstantaneous come at rate t. -Lq-Lt
Discounted Value
- L ( 1-t )
Get salvage (S) as fraction of original purchase price.
-q-S
Instantaneous
+S
Get tax remission by charging loss (l-S) against income.
+(1-S)t
Instantaneous
q- (1-S) t
Buy items as needed. Spend E, as fraction of original purchase price, for repurchasing expenses. Usage declines K per cent per - ( I + E ) (l-e-K~) Continuously -(I+E)KTU(K+R)r declining year. Continuously Get tax remission by charging repurchase + t 0 + E ) (1-e-~r) declining costs against income.
+t(l~-E)KTU(t:+n)r
Retain ( M a i n t a i n and Use W h e n N e e d e d ) O
O-T
Keep inventory.
None
Maintain inventory for T years at annual cost M as fraction of original purchase price. Get tax remission by charging this expense against income.
--
I T]
Continuously declining
- M T U (~r+R)r
+ tM
Continuously declining
+tMTU (x~-R)r
Continuously declining
+tKTU (~+~)r
Instantaneous
q-tI(~-n)r*
-M
Use items from inventory as needed; get tax remission by charging original purchase price against income.
+t(1-e -~r)
Liquidate remaining inventory at no salvage; get tax remission.
~ t e 'Kr
° F o r realistic rates of usage, this term is negligible.
W h e n the total d i s c o u n t e d v a l u e of l i q u i d a t i o n equals the total d i s c o u n t e d v a l u e of retention, the alternatives are financially e q u i v a l e n t : -- L(1-t) + S + (1-S)t -- (l-t) ( I + E ) K T U ( x W R ) r = - ( 1 - t ) M T U ( K + R ) r -~ t K T U ( x + R ) r S:
(E --}-- - ) -1-t MITU(~+R)r-
1-~-t --
L
"
W h e n the values of the parameters u n d e r t h e r i g h t side of F i g u r e 5 are inserted, the resulting e q u a t i o n is t h a t used for d e t e r m i n i n g the points t h a t trace the broken lines of the charts : S : 2 0 ( 2 . 3 3 3 K-.05) U ( x - } - n ) 2 o - 0 . 9 8 3 3 .
S P R I N G , 1963
L = L i q u i d a t i o n cost as fraction of original purchase price ----- 10 per cent, or 0.10 t ~ tax rate = 52 per cent or 0.52 S = s a l v a g e v a l u e as fraction of original purchase price E : repurchase expense as fraction of original purchase price : 15 per cent or 0.15 M : a n n u a l cost of m a i n t a i n i n g i n v e n t o r y as fraction of original purchase price = S per cent or 0 . 0 5 R : a n n u a l discount or interest rate ---- 10 p e r cent or 0.10 K = rate of use as fraction of o p e n i n g i n v e n t o r y in any year T : time of l i q u i d a t i o n of inventory, i f i n v e n t o r y is kept, assumed to be 20 years U(/r+n)T ~ factor for continuously d i s c o u n t i n g u n i f o r m cash flows over T years at interest rate (K-t-R).
97
W. B. HrRSCHMANN AND J. R, BRAI.rWEILER
and the discounted value of the net proceeds of liquidation With zero salvage is [t-E(l-t)]VoI(xq-R)r, where I is the continuous discount function for instantaneous cash flows. It is necessary to make an assumption regarding this time of eventt~al liquidation. Twenty years was chosen because it is reasonably realistic and computationally convenient. For realistic rates of usage and any time period in excess of ten years, the discounted value of the tax remission obtained from liquidating the small residual stock is so small that it can be omitted without seriously affecting the analysis. The foregoing functions result in the equation for equivalence, shown with Figure 5, which can be rearranged as follows: S - (1 - t) L q- (1 - S)t q- (1 - t) MrU(xq-R)r : [1 q- ( 1 - t)E] KTU(xq-,)r. Written in this way, the equation shows that the alternatives are financially equivalent when the salvage from liquidating all the inventory (less the liquidation costs plus the tax remission from the liquidation loss and the discounted value of the storage expense that would be incurred by keeping
the inventory and using it at the rate of K per cent per year of the remaining amount over T years) is equal to the discounted value of purchasing the inventory as needed, including the expense of purchasing. Because it is difficult to assess in detail th~ attrition of a stock that declines at a constant percentage each year, the concept of half-life is employed. It also permits the attrition constant K to be determined readily, for at half-life Vr 0.5 = e -xr : e "°'70" V, Thus, half-life is attained when the product of K as a decimal and T in years equals 0.70. If the half-life, T, is 1 year, K : 0.7 or 70~. If T is two years, K : 35~. This relationship is used in solving the equation of equivalence developed in Figure 5 for plotting the points that trace the half-life, broken lines of the charts. For example, if the half-life is five years, K = 0.14, and S : 20(2.333 K-0.05) U(xq-0.1o),o- 0.9833 : 0.1001 or 10~.
98
GEORCE BEI~ABD SHAW once observed that "the universal regard for m o n e y is the one hopeful fact of our civilization." As experienced busin e s s m e n will attest, w h e n top m a n a g e m e n t ignores financial problems, believes financial m a n a g e m e n t is u n i m p o r t a n t , or in general is derelict in the h a n d l i n g of m o n e y , it does so at considerable peril.
-Francis 1. Corrigan and Howard A. W a r d F I N A N C I A L M A N A G E M E N T - - P O L I C I E S AND pRACTICES
BUSINESS HORIZONS
AND J. R. BRAUWEILER
CURING and PREVENTING SURPLUS INVENTORIES
n line with rapid advances in the general
I management disciplines, several subspe-
cialties have been transformed from fairly routine tasks to highly sophisticated functions. In some cases, the change has occurred quietly and within the context of more spectacular developments, which may explain why the full implications of new and improved ways of doing familiar jobs are often missed. Inventory control provides an outstandMr. Hirschmann is Research Supervisor in Economics for the American Oil Comlmny, and Mr. Bmuweiler is an operations research analyst for Kraft Foods.
SPRING, 1963
ing example of this transformation. Within the memory of everyone in management except the newest business school recruit, inventory management has been a simple matter of counting stock, keeping records, and following rule-of-thumb guides on reorder and disposal. Anyone adept at attending to details could do the job and do it well. Today, however, inventory control is a specialized task requiring professional management skills. Techniques are based on a rationale derived from managerial economies, and a growing body of literature is addressed to inventory specialists. The basis for this interest in better management of inventories is not hard to find.
87
W. B, HIRSCHMANN AND J. R. BRAUWEILER
At a time when the profit squeeze is beginning to look like a long-term prospect, good management demands that costs be carefully controlled. Reduced inventories offer many firms one opportunity for significant cost savings. The usual emphasis in inventory control is on optimizing operating inventories-raw materials, goods in process, and finished goods-which is understandable since these categories comprise the bulk of inventory accounts. However, another kind of inventory that may be profitably investigated is • the maintenance inventory; although a small part of total stocks, it involves a substantial investment in some firms.
THE MAINTENANCE INVENTORY 88
Some intriguing situations are connected with the control of maintenance inventories. One of these is the fact that a skillful management can profit from past mistakes. The mistake we are dealing with is peculiar because it involves a decision that was completely justifiable at the time it was made, and one which, under the same circumstances, would be made again. At some time past, material was purchased with the expectation that it would be used for maintenance purposes. Since then, for one reason or another, the material has become surplus. While the past mistake of obtaining it may be justifiable, the present mistake of keeping it is not. Retaining this type of material is usually the result of applying a "home economics" approach in a situation where "corporate economics" should prevail. The home economics thinking is that keeping surplus material adds little to maintenance expense, and in general this is true-in household situations, On the other hand, the corporate economies approach puts the decision in its true perspective. The factor that makes the difference betwe'en the two systems is what, for practical
purposes, can be considered a partnership arrangement between a corporation and the government-an arrangement that the householder does not have. As a partner, the government takes one-half of a corporation's profits. But as a just partner, the government also shares one-half of the corporation's losses, if the corporation will but admit the losses. This arrangement offers a potential cash flow that is often ignored. Unfortunately, delay in admitting losses does not make them more palatable or reduce them; in fact, refusal to recognize that a loss has occurred tends to compound the loss. Keeping an inventory of spare parts for maintenance is justified because it costs less than lost production, the inconvenience, and the emergency measures that may result ff inventory items are not on hand when needed. Over a period of time, however, circumstances may change, so that items once considered essential are no longer required. They may be unsalable because they were designed for a particular firm's unique equipment, or because they have become obsolete. Consequently, they have no resale value; if liquidated, they would have to be sold for scrap, and there is an understandable reluctance to take the large losses entailed in scrapping. Because the costs of storage (incremental costs, in many cases) appear to be the only price of retaining such items, and because of the hope that they can somehow be worked off, the alternative of keeping them on hand seems more reasonable. Potential book losses block disposal so effectively that the accumulation of surplus may become sizable. Commonly, surplus material is sold only if there is a good market for it; "good" is usually defined as some arbitrary percentage of original cost, based on age. For example, two-year-old material may be sold only ff 60 per cent of its cost can be recovered, and three-year-old material only for 50 per cent or more of its cost. Because market salvage values tend to decrease with age, disposal requirements of this kind put surplus in the
BUSINESS HORIZONS
CURING AND PREVENTING SURPLUS INVENTORIES
position of chasing prices downhill. An inaportant consequence of focusing attention on age is that disposal policy becomes retrospective. A policy that emphasizes the future rather than the past (by estimating the expected time of need) can b e more profitable. The economics of a realistic forward look may indicate that the costs of retaining surplus are larger than they appear, and may provide an economic incentive for disposing of them. This article presents a decision-making procedure for liquidation that is future oriented. It is addressed to the economics of liquidating maintenance or other inventories that have been recognized as surplus, and are not or have not been in capital accounts; it presents simple rules for determining whether inventories have become so inactive that they may be considered surplus and therefore subject to liquidation.
THE ECONOMICS OF LIQUIDATION Two kinds of costs are associated with maintaining an inventory: that of handling and storing, and that arising from the unavailability for other uses of the money used to purchase the inventory. Because inventory earns nothing directly, and because its purchase price generally can neither be depreciated nor charged as expense against current income until it is used, inventory funds are sterile. Active inventory is not on hand long. It is usually used shortly after it is acquired. Nevertheless, the physical cost of warehousing each unit of active inventory is reported to be 4-5 per cent of its purchase price; power, light, accounting, engineering, supervision, and plans and benefits prorated add 5-6 per cent; and placing the order adds another 1-2 per cent. Such other costs as insurance, taxes, and spoilage can raise the total to about 20 per cent. The effective cost (exclusive of interest charges) of each unit of an active item in inventory is thus
SPRING, 1963
about 120 per cent of the purchase price or value carried on the books. The effective cost of inactive items is higher because most of these costs continue and accumulate.
C A S H BENEFITS OF LIQUIDATION
Even though inventory may have no net salvage value, liquidation provides after-tax cash benefits. The 100 per cent loss taken on purchase price is deductible from current income; with a corporate income tax rate of 52 per cent, a cash inflow of 52 per cent of the original purchase price results. Higher salvage values produce greater benefits: a 50 per cent salvage brings a cash benefit of 76 per cent and, of course, 100 per cent net salvage returns the original funds. Keeping material in inventory deprives a firm of the income it could earn by investing the cash benefits from liquidation. Money from the liquidation of surplus inventory is likely to be part of a firm's general funds, and available for reinvestment in its business. Individual projects may yield different rates of return, but their combined effect is to produce the firm's average rate of earnings. Liquidation money should earn at this average rate. The average rate for manufacturers, about 10 per cent per year after
80
W. B. HmSCHMANNANDJ. R. BrtAowEn.r~
90
taxes, provides a point of departure for this analysis. If the corporate income tax rate is 52 per cent, an item liquidated for a net salvage of zero provides a tax remission of 52 per cent of its original cost. If the earnings rate is at the 10 per cent level, liquidation of such an item can yield an after-tax annual income of 10 × 52 -- 5.2 per cent of the original cost. Higher salvage values, of course, yield higher annual incomes. If the firm is fortunate enough to realize 100 per cent net salvage, for example, liquidation can yield an after-tax annual income of 10 per cent of the item's original cost. Reducing inventories can be expected to reduce some of the running costs of maintenance. While the cost reduction attributable to disposing of static or slow-moving items cannot always be clearly identified, it appears reasonable to assume that disposing of such items might save charges equivalent to 5 per cent of their purchase price before taxes, or 2.4 per cent per year after taxes of 52 per cent. These warehousing savings, plus the earnings of 5.2 per cent on the realization by liquidation for a net salvage of zero, provide a benefit of 15.8 per cent before taxes, or 7.6 per cent per year after taxes. The decision to keep $1 million worth of static or unused inventory instead of liquidating for a net salvage of zero thus costs about $158,000 per year before taxes. If the inventory could be sold for 100 per cent of its original cost, the annual cost of retention would be the 10 per cent earnings possible through reinvestment in the firm, plus incremental storage charges of 2.4 per cent. These amount to 25.8 per cent before taxes, or $258,000 per year for a $1 million inventory.
COMMON APPLICATIONS KEEPn~c vS LIQUmATINC
Piece of Equipment The savings provided by liquidation can compound at a firm's average earnings rate. Eventually,
they will have grown sufficiently to permit repurchasing the liquidated inventory at no penalty. If the material is required before this point is reached, it is preferable not to liquidate, but if it is required subsequent to this point, the compounded savings from immediate liquidation will permit the firm to repurchase and still save. At high salvage values, the time within which the proceeds from liquidation will permit repurchase at no penalty is quite short. The solid line of Figure i shows the time periods for different salvage values, and for an earnings rate of 10 per cent after taxes. An inventory often has a salvage value of 10 per cent of its purchase price; with liquidation costs (handling and paper work, for example) of about 10 per cent, the net salvage is zero. The solid line of Figure I shows that a single article with a gross salvage of 10 per cent should be kept ff it will be required within five and one-half years; if it will not be required within that period, it should be liquidated. If salvage is 75 per cent, it should be kept only if it will be needed within two years.
Kind of Material If the inventory consists of a quantity of identical articles of a given kind having a 10 per cent salvage value, a five and one-half year supply should be kept, and the excess liquidated. Similarly, for 75 per cent salvage value, a two-year supply should be kept. For example, suppose a supply of standard 8" pipe worth $120,000 is on hand. Annual usage is expected to continue at the rate of $15,000 per year. Current offering price for it on the used market is $.25 on the dollar. Should such a supply be retained? The solid line of Figure 1 shows that only a four and one-half year supply, worth $67,000, should be kept; at a salvage value of 25 per cent, the $53,000 balance should be liquidated for $13,250. Assorted Inventory
For one reason or another, a firm may not be in a position to separate inventory material that will be
BUSINESS HORIZONS
CURING A N D P R E V E N T I N G
SURPLUS INVENTORIES
FmVr~ 1 CONDITIONS Cost of keeping inventory (out-ofpocket warehousing and accounting) is 5 per cent per year before taxes; income tax rate is 52 per cent; money can be reinvested at an average of 10 per cent after taxes, continuously compounded; liquidation charges for paper work, handling, and so on amount to 10 per cent of original cost; rebuying when out of stock costs 115 per cent of original cost; and there is no other penalty for out of stock. (Since surplus implies no need, there is no penalty for being out of such stock by liquidation. Surplus articles are usually used up or "worked off" in new construetion.)
Liquidation or Retention of Surplus Inventory I3C 12C IIO GROSS SALVAGE VALUE AS %
IOC 90 8O
Liquidate
7C
OF ORIGINAL 00ST
GO 50
Keep
30
\.
\\\
20
\\\\\ - . .
o..,L
,.~E.TO..
,~
. . . 0
0.
0.0
9
Years until n e e d e d ( f o r single pieces of e q u i p m e n t ) or years of supply for stock of a n i t e m ..... H a l f - l i f e ( y e a r s r e q u i r e d to use o n e - h a l f the cost of a m i s c e l laneous lot)
used within the time indicated by the chart from material that will be used later. The firm is then faced with a choice between liquidating all (and perhaps being obliged to rebuy some immediately), or keeping all (and losing the savings on items that could have been liquidated). For liquidation of all material to be justified, the firm must realize compounded savings from complete liquidation that are adequate to allow repurchase of the fractional amount needed each year at no penalty. Since the inventory is considered surplus, the firm certainly would not maintain it by replacing the articles for which it finds a use. Under these circumstances, the inventory will constantly be reduced. Furthermore, as the more usable items are removed from stock, the concentration of less usable items will progressively increase. Eventually, the firm will probably conclude that it should scrap the remainc~er, for which there are no
SPRING, 1963
foreseeable calls. As a practical matter, this process can be described as using each year a constant proportion of a declining balance. Since it may be difficult to estimate usage in terms of such a proportion, the equivalent concept of "half-life" appears more practical. Half-life is the time required to use onehalf of an inventory, in terms of its original cost. Thus, if salvage value is known, it is necessary merely to estimate half-life to determine whether or not to liquidate an entire inventory. The broken line of Figure i plots percentage salvage value of an assorted inventory against the expected half-life that is necessary to justify keeping it. For example, consider a miscellaneous lot of cast-iron fittings that originally cost $10,000. Because their fire resistance is low, their use has become limited to about $300 worth per year, or 3 per cent per year. A junk dealer offers $400 for the lot. The broken line of Figure 1 shows
91
W. B. HIBSCHMANN AND J. R. BRAUWEILER
that at a salvage value of $400/$10,000 --- 4 per cent, the half-life is about five and onehalf years. If we assume linear usage at the rate of 3 per cent per year of the present stock instead of the slower 3 per cent attrition of a declining balance, at least sixteen years will be required to use one-half the inventory. Thus, the entire lot should be liquidated for $400.
99.
Since $300 of this inventory is being used normally, it will be necessary to rebuy this amount if the entire lot is sold. The management might find it more convenient, or more comfortable, to keep a portion of the inventory rather than to dispose of all of it. The solid line of Figure 1 shows that, at 4 per cent salvage, a five and three-fourths year supply can be justifiably retained. At the rate of $300 per year, a five and three-fourths year supply is $300 × 5~ -- $1,700 or 17 per cent of the $10,000 total. Thus, because it is a miscellaneous lot, 17 per cent of each kind of article could be retained, and the 83 per cent balance liquidated for 83 per cent of $400, or $332. A heterogeneous assortment of inventory can thus be analyzed for the economic desirability of complete or partial liquidation.
retaining avoids the necessity of purchasing the material ff it should prove to be needed at some future time. The different rates of return provided by various estimated times of need are shown in the charts of Figures 2 and 3. The solid lines of Figure 2 are the break-even points for various rates of return for single articles; they correspond with the solid line of Figure 1. The broken lines of Figure 3 are the break-even points for various rates of return for the half'life of a miscellaneous lot, and correspond to the broken line of Figure 1. A management might well feel that the uncertainties of need require the rate of return promised by an investment in surplus materials to be higher than the company as a whole has averaged, since the average rate could be obtained with relative certainty simply by investing in the firm's common stock. The time within which a need must arise to provide a satisfactory rate of return can be readily determined with such charts. They are particularly meaningful for managements that are accustomed to assessing investment attractiveness by the rate-ofreturn yardstick, and have a feeling for risk from the way the promised rate of return changes with different judgments.
RETENTION AS AN OPPORTUNITY FOR PROFIT
Judging the desirability of liquidation' with the chart of Figure 1 requires weighing the relatively certain benefits of disposal against the possible benefits of retention. While such balancing is a valid way of arriving at a decision, it does not indicate the consequences of errors in judgment, or provide a feeling for the risk of loss. Such a feeling can be acquired by considering the problem in the context of an investment opportunity. The desirability of an investment is usually judged on the basis of whether the rate of return promised by the anticipated profit is adequate in the context of the firm's operations and commensurate with the attendant risk. Retaining surplus material is, in effect, an investment of net salvage currently available, tax remission, and annual storage costs;
OTHER APPLICATIONS
LIQUIDATIONOF EXCESSINVENTORY These concepts and analyses also apply to other kinds of inventories that are considered active. A portion of the spare parts inventory, for example, may contain materials for which there have been no calls for a number of years. Such materials might be considered to have become surplus in effect, and thus subject to liquidation as determined by the salvage value and usage curve (solid line) of Figure 1. If there is a penalty for being out of stock of such an article, partial liquidation may still be in order, for, if there are several identical articles of a particular kind on hand, only
BUSINESS HORIZONS
CURING AND PREVENTING SURPLUS 1NVEN~I'ORIES
Liquidation or Retention of Maintenance Inventory (percentage salvage value vs years unt~ inventory needed Sample Problems ( 1 ) Liquidating or retaining pieces of equlpment--An inventory of rotating blower assemblies worth $60,000 was specially designed for a processing unit that no longer exists, but there is a possibility of using them in future construction. They may be sold for one-third of their original cost. H o w soon must they be used to justify keeping them, if the firm requires funds so committed to promise a return of at least 15 per cent per year? Solution-The 1S per cent solid line of Figure 2 shows that, at 33 per cent salvage value, the assemblies must be used within three years. Those not needed by that time should be sold now. ( 2 ) Amount of stock to retain of a kind of article--A $120,000 supply of standard 8" pipe is on hand. Annual usage is estimated to continue at the rate of $15,000 per year. The current price for it on the used market is $.25 on the dollar. Should the firm keep such a supply on hand if it expects investments of that type to yield a return of 20 per cent per year? Solution-The 20 per cent solid line in Figure 2 shows that a two and one-half year supply, or about $37,500, should be kept, and the $82,500 balance Hquidated for 25% × $ 8 2 , 5 0 0 = $ 2 0 , 6 5 5 . ( I f the salvage is 10 per cent, a thrce-year supply, $45,000, should be kept, and the $75,000 balance sold for $7,500. ) ( 3 ) Liquidating or retaining a heterogeneous lot--A firm has a $10,000 miseellaneous lot of cast iron fittings. Because their fire resistance is low, their use has become limited to about $300 worth per year. This rate is expected to continue. A junk dealer offers $600 for the lot. If this firm desires investments of this sort to promise 10 per cent per year, should it accept the $600? Solution-(a) Annual usage is 3 per cent ( $ 3 0 0 / $ 1 0 , 0 0 0 ) . With 6 per cent salvage value, the 10 per cent solid line of Figure 2 shows that a five and three-fourths year supply. about 15 per cent, should be kept, and the 85 per cent balance sold for $510. ( b ) If the junk dealer stipulates that he will take all or none (or if the firm cannot split the stock of each item into 15 per cent and 85 per cent shares), the half-llfe chart of Figure 3 can be used. The 10 per cent broken line shows that one-half or more of the inventory will have to be used in five and one-fourth years to justify keeping all of it. The 3 per cent per year current rate of use indicates that more than 18 years will be required to use half the material. Therefore, the firm should dispose of the entire lot for the $600. ( 4 ) L i q u i d a t i n g or retaining new constrnction surplus--To avoid construction delays for a plant just completed, a small overage of miscellaneous items had been provided; about $ I 0 , 0 0 0 worth remains. The vendor will take them back for a restocking charge of 10 per cent. The firm requires such inventory to promise a minimum rate of return of 1S per cent per year. Should it return these items?
Solution-(a) For a salvage value of 90 per cent, the 15 per cent broken line of the half-life chart of Figure 3 shows that if one-half the lot is not used in nine months, it is desirable to return all for credit now. ( b ) If it is possible to sort the items, the firm should keep only those items it is sure to use within one year, as indicated by the 15 per cent solid line of Figure 2.
SPBING, 1963
or
used; use solid line chart if inventory permits) VICUnE
2
Years Until Inventory Needed (for Single Pieces) or Years of Supply 130
120 IlO 'GROSS
IO0
\
SALVAGE 90 VALUE 8o AS % 70
~
OF SO ORIGINAL ,50 COST 40
\ 10%
30 2o
LiqoidotS
O'Nis % Keep
93
10 I
0
\ i3 \
,\,
4
5
\
6
,
7
,
8
YEARS UNTIL INVENTORY IS NEEDED OR USED
FIC~ 3 Years Required to Use One.Half Original Cost of Mis. cellaneous Lot (Half-life) 130 120
lid GROSS IOC SALVAGE9C VALUE 8C AS % 7¢
OF 60 ORIGINAL SG COST
\\\\ \\ \\ \ \ \ \.,o. \
40 30 20
\, \ \,s%\ \ \ \ \,o,.\ \ \\
~"P
Io I
2
3
4
5
6
7
8
YEARS REQUIRED TO USE HALF THE COST OF A MISC LOT
w. B. HmSCHMANNANDJ. R. BRAtrwEmFaa
one or two of the articles may be sutBcient to insure against a penalty for being out of stock if an unexpected need arises. It is therefore desirable to review all working inventories to see whether the stock level has become excessively high in light of current salvage value and expected usage.
AVOIDANCE OF INACTIVE INVENTORY
94
Not only should existing inventories be weeded out, but little-used inventories should not be created. Such inventories can be created by transferring to surplus the materials left over after construction of a new unit. An excess of articles is properly provided during construction as insurance to take care of breakage, loss, defects, and so on, which might cause delays. When the plant is completed, the left-over items are essentially new, and some manufacturers will take them back for a small restocking charge. Unless some use can be foreseen in the near future, this initial high salvage value counsels immediate liquidation. Since lower salvage values justify longer retention, an initial error in keeping material with a high salvage value tends to compound itself. For example, after a major plant was built, materials worth $100,000 remained unused. The manufacturer was willing to take them back for a restocking charge of 10 per cent; their salvage value was thus 90 per cent. Liquidation charges of 10 per cent would reduce recovery to 80 per cent, but tax remission on the $20,000 of loss and expense would result in a net cash benefit of $80,000 + 52 per cent )< $20,000 -- $90,400. However, the materials were kept in the hope that they would be used in the one and one-half years noted from Figure 1. At the end of this period, salvage value had decreased to 60 per cent, at which level materials should be kept if they will be used within another two and three-fourths years. The longer they are kept, the lower the salvage value, and the greater the retention period justified.
If, unfortunately, the firm has kept these materials for five years, the storage costs and earnings on the original salvage of $90,400 will compound to $165,000 after taxes (with continuous compounding at 10 per cent per year). Thus, an original cost of $100,000 becomes an effective after-tax cost of $165,000 five years later. This effective cost will grow, of course, by compounding as time goes on and the materials remain unused. On the other hand, had the materials been liquidated immediately and had a need then arisen unexpectedly, repurchasing would have cost $115,000 before taxes (reflecting 15 per cent of the cost of purchase) or $107,200 after taxes. Thus, an after-tax penalty of $107,200 - $90,400 ~- $16,800 would have resulted. This would have been the maximum penalty, however; if the need arose sometime after liquidation, the savings in storage costs and the earnings on the $90,400 recovered would have decreased the penalty. After one and one-half years, the firm would have broken even; ff the delay had been any longer, the firm would have made a profit. Since time is required to pass information regarding such surplus through the company, to find a place for it, and to get it built into a new plant, it is easy to see how the permissible one and one-half years could be exceeded even under favorable circumstances. Immediate liquidation will generally be more profitable than straining to discover a use that might not be really satisfactory. Note that if the firm liquidates and has to rebuy after five years, its purchase cost is still $107,200. But the $90,400 recovered on liquidation has grown to $165,000; therefore, the firm is ahead $165,000 - $107,200 : $57,800 after taxes, or $120,000 before taxes. This before-tax gain is greater than the original purchase cost of $100,000. Thus the firm can not only afford to replace what proves to be needed, but can also spend an equal amount for expediting or some other
BUSINESS HORIZONS
CURING AND PREVENTING SURPLUS INVENTORIES
p e n a l t y , a n d still b r e a k e v e n w i t h t h e a l t e r n a t i v e of r e t a i n i n g t h e m a t e r i a l . l Small salvage value and low increm e n t a l s t o r a g e costs c a n b e m i s l e a d i n g in c o u n s e l i n g t h e r e t e n t i o n of l i t t l e - u s e d i n v e n tory. T h e 52 p e r c e n t t a x r e m i s s i o n p r o v i d e d b y t h e loss o n l i q u i d a t i o n raises t h e effective s a l v a g e v a l u e to m o r e t h a n o n e - h a l f t h e origin a l cost. I f t h e r a t e of r e t u r n p r o m i s e d b y r e t a i n i n g t h e m a t e r i a l s is n o t a d e q u a t e in t h e f r a m e w o r k of a firm's o p e r a t i o n s or c o m m e n s u r a t e w i t h t h e risk of loss, o r if o t h e r i n v e s t m e n t o p p o r t u n i t i e s exist w h i c h p r o m ise m o r e profits, l i q u i d a t i o n m a y b e m o r e attractive than retention.
K = annual rate of decline as a decimal, e : base of natural logs. The factor e "~r is similar to the factor for continuously discounting at interest rate R a cash flow that occurs instantaneously T years hence; this suggests that continuous discounting can conveniently handle the attrition of a heterogeneous lot. With continuous discounting, the following relations result: The dollar amount of inventory used from O to T is Vo -- V r = Vo (1 -- e-~rr), which is
Vo K e "~r d T .
o The discounted value of the amount used from O to T is
ioT
Vo K e -Kr e -RT d T : Vo K
i,l K + a
=
j
Vo K T U ( r q - n ) r where U(~r-t-n)r :
_aUTHORS' NOTE Mathematics of Analysis The financial merits of liquidating or keeping inventory can be assessed by listing the actions that result from choosing either alternative, determining the corresponding cash consequences, expresshag them in after-tax terms, and reflecting the time value of money. The latter can be done by discounting at an appropriate interest rate all cash flows to their present value. Figure 4 tabulates such a comparison for individual items of inventory. The analysis is straightforward. The resulting equation is the basis for determining the points that trace the solid lines of the charts. Figure 5 tabulates the comparison between liquidating and keeping a heterogeneous assortment of items that cannot be segregated in terms of their expected time of use. The functions for the various cash flows and the basis for determining the points that trace the broken lines of the charts are not as straightforward as those in the preceding analysis and, therefore, are developed in the following paragraphs. A heterogeneous lot whose usage is a constant dollar proportion of a continuously diminishing balance can be represented by the empirical function V r : Voe -~r
where V° = value of initial inventory in terms of original purchase price, Vr : value of inventory remaining after T years (in terms of original cost, not in terms of scrap value),
SPRING, 1963
factor for continuously discounting uniform cash flows over T years at interest rate ( K - I - R ) . The tax remission, when this amount of inventory used is charged against income, is tVo(1-e-~T), and its discounted value is tVoKTU(~-I-R)r. If an item is repurchased and the expense of repurchase is E as a fraction of purchase price, then the cost of repurchasing an item is (1-q-E), and the cost of repurchasing all items used over T years is (1-t-E)V, (1-e-~r). Their discounted value is (lq-E) Vo K T U ( K q - ~ ) r , the tax remission on use is t(lq-E) V° (1-e-Kr), and the discounted value of the tax remission is t(1-I-E)Vo KTU(~r-l-n)r. If M, as a fraction of the original purchase price, is the annual cost of maintaining the inventory, the annual cost of the stock on hand at any time is M V r : M V o e -~r, and the cost ef maintaining this declining stock from O to T is M V o e -rr d T = Me V*
o
IKJ"
The discounted value of this cost is f T M V /I J o M V o e -Kr e -nr d T = o
e-(~+~)r] :
lr + R
J
M V o TU(,:-~-n),.
The tax remission when this expense is charged against income is t MVoTU(~+n)r.
By its nature, a declining balance inventory is never all used; s o m e remains on hand "forever." Eventually, management will decide that the remaining items are of no use and they will be liquidated. The amount of this residual inventory is Voe -rr, its after-tax liquidation expense is E(1-t) Voe "rr, its tax remission for zero salvage is tVoe -xr,
95
W. B. HIRSCHIVIANNANDJ. R. B~AUWZtLZ~
FIGURE 4
D i s c o u n t e d C a s h F l o w Analysis of L i q u i d a t i n g or R e t a i n i n g Surplus I n v e n t o r y (single item or homogeneous group)
Liquidate (Buy When Needed)
Time 0
After.tax Cash Type of Consequence Cash Flow
Resulting Action
Spend L, as fraction of original purchase price, for liquidation expenses (paper work, handling, and so on). Get tax remission (Lt) by charging this expense against income at tax rate t. -L-kLt
Instantaneous
1.0
-L(I-t)
Get salvage (S) as fraction of original purchase price.
Instantaneous
1.0
-kS
Instantaneous
1.0
-kS
Get tax remission by charging loss (l-S) against income. -k(l-S)t 90
O-T T
Discount Discounted Factor Value
No inventory in stock.
None
.
.
.
.
.
-k(1-S)t .
Need for item arises. Spend E, as fraction of original purchase price, for repurchasing expense. Get tax remission (Et) by charging this expense against income. - E + Et
Instantaneous
Inr
--E(l-t) IRr
Buy replacement (1); use at once and get tax remission (t) by charging purchase price against income.
Instantaneous
Ia~
-(1-t)lRr
Uniform
URr
.MT(I-t)U~r
Instantaneous
IR~
-ktI~r
--lq-t
Retain (Maintain and Use When Needed) O
O-T
Keep inventory.
None
Maintain inventory for T years at annual cost M as fraction of purchase price.
-MT
Get tax remission (MTt) by charging this expense against income.
-kMTt
Item on hand. Use item from inventory; get tax remission (t) by charging original purchase price against income.
I ~ z = f a c t o r for continuously discounting at interest rate, R, cash flows which occur instantaneously T years hence. Ugz----factor for continuously discounting at interest rate, R, cash flows which occur uniformly over T years. When the total discounted value of liquidation equals the total discounted value of retention (that is, when the salvage value less liquidation costs plus tax remission and annual salvage savings compound to purchase price plus repurchasing expense) the alternatives are financially equivalent: -L(l-t) .6 S -6 (l-S)t - E(l-t)/Rr -- (l-t)IRr :
-MT(I-t)URr -6 tint
1
[8 -- L(l-t) -/- (1-S)t -k MTURrO-t)] × - = 1 -k E(l-t). IA¢~,
---
None -kt
If the item is "worked off" in new construction, it will probably be capitalized. In that case. the tax remission is not obtained when the item is used at time T, but over the amortization life of the equipment through depreciation charges. The total amount of the tax remission is the same as when the item is expensed (t). but its discounted value is tDna at the time of use T, and tDR,IRT at T = O, where Dn~ is the factor for discounting depreciation cash flows at interest rate ( r ) over ( a ) years. This tax remission is the same for the item used from stock as for the repurehased item; consequently, it cancels out of the equation. Thus. the equation for equivalence when the item is capitalized is the same as when it is expensed.
BUSINESS HORIZONS
CURING AND PREVENTING SURPLUS INVENTORIES
FICURE 5
Discounted Cash Flow Analysis of Liquidating or Retaining Surplus Inventory (nonseparable assortment) Liquidate (Buy W h e n N e e d e d )
Time 0
O-T
After-tax Type of Cash Consequence Cash Flow Resulting Action Spend L, as fraction of original purchase price, for liquidation expenses (paper work, handling, and so on). Get tax remission (Lt) by charging this expense against inInstantaneous come at rate t. -Lq-Lt
Discounted Value
- L ( 1-t )
Get salvage (S) as fraction of original purchase price.
-q-S
Instantaneous
+S
Get tax remission by charging loss (l-S) against income.
+(1-S)t
Instantaneous
q- (1-S) t
Buy items as needed. Spend E, as fraction of original purchase price, for repurchasing expenses. Usage declines K per cent per - ( I + E ) (l-e-K~) Continuously -(I+E)KTU(K+R)r declining year. Continuously Get tax remission by charging repurchase + t 0 + E ) (1-e-~r) declining costs against income.
+t(l~-E)KTU(t:+n)r
Retain ( M a i n t a i n and Use W h e n N e e d e d ) O
O-T
Keep inventory.
None
Maintain inventory for T years at annual cost M as fraction of original purchase price. Get tax remission by charging this expense against income.
--
I T]
Continuously declining
- M T U (~r+R)r
+ tM
Continuously declining
+tMTU (x~-R)r
Continuously declining
+tKTU (~+~)r
Instantaneous
q-tI(~-n)r*
-M
Use items from inventory as needed; get tax remission by charging original purchase price against income.
+t(1-e -~r)
Liquidate remaining inventory at no salvage; get tax remission.
~ t e 'Kr
° F o r realistic rates of usage, this term is negligible.
W h e n the total d i s c o u n t e d v a l u e of l i q u i d a t i o n equals the total d i s c o u n t e d v a l u e of retention, the alternatives are financially e q u i v a l e n t : -- L(1-t) + S + (1-S)t -- (l-t) ( I + E ) K T U ( x W R ) r = - ( 1 - t ) M T U ( K + R ) r -~ t K T U ( x + R ) r S:
(E --}-- - ) -1-t MITU(~+R)r-
1-~-t --
L
"
W h e n the values of the parameters u n d e r t h e r i g h t side of F i g u r e 5 are inserted, the resulting e q u a t i o n is t h a t used for d e t e r m i n i n g the points t h a t trace the broken lines of the charts : S : 2 0 ( 2 . 3 3 3 K-.05) U ( x - } - n ) 2 o - 0 . 9 8 3 3 .
S P R I N G , 1963
L = L i q u i d a t i o n cost as fraction of original purchase price ----- 10 per cent, or 0.10 t ~ tax rate = 52 per cent or 0.52 S = s a l v a g e v a l u e as fraction of original purchase price E : repurchase expense as fraction of original purchase price : 15 per cent or 0.15 M : a n n u a l cost of m a i n t a i n i n g i n v e n t o r y as fraction of original purchase price = S per cent or 0 . 0 5 R : a n n u a l discount or interest rate ---- 10 p e r cent or 0.10 K = rate of use as fraction of o p e n i n g i n v e n t o r y in any year T : time of l i q u i d a t i o n of inventory, i f i n v e n t o r y is kept, assumed to be 20 years U(/r+n)T ~ factor for continuously d i s c o u n t i n g u n i f o r m cash flows over T years at interest rate (K-t-R).
97
W. B. HrRSCHMANN AND J. R, BRAI.rWEILER
and the discounted value of the net proceeds of liquidation With zero salvage is [t-E(l-t)]VoI(xq-R)r, where I is the continuous discount function for instantaneous cash flows. It is necessary to make an assumption regarding this time of eventt~al liquidation. Twenty years was chosen because it is reasonably realistic and computationally convenient. For realistic rates of usage and any time period in excess of ten years, the discounted value of the tax remission obtained from liquidating the small residual stock is so small that it can be omitted without seriously affecting the analysis. The foregoing functions result in the equation for equivalence, shown with Figure 5, which can be rearranged as follows: S - (1 - t) L q- (1 - S)t q- (1 - t) MrU(xq-R)r : [1 q- ( 1 - t)E] KTU(xq-,)r. Written in this way, the equation shows that the alternatives are financially equivalent when the salvage from liquidating all the inventory (less the liquidation costs plus the tax remission from the liquidation loss and the discounted value of the storage expense that would be incurred by keeping
the inventory and using it at the rate of K per cent per year of the remaining amount over T years) is equal to the discounted value of purchasing the inventory as needed, including the expense of purchasing. Because it is difficult to assess in detail th~ attrition of a stock that declines at a constant percentage each year, the concept of half-life is employed. It also permits the attrition constant K to be determined readily, for at half-life Vr 0.5 = e -xr : e "°'70" V, Thus, half-life is attained when the product of K as a decimal and T in years equals 0.70. If the half-life, T, is 1 year, K : 0.7 or 70~. If T is two years, K : 35~. This relationship is used in solving the equation of equivalence developed in Figure 5 for plotting the points that trace the half-life, broken lines of the charts. For example, if the half-life is five years, K = 0.14, and S : 20(2.333 K-0.05) U(xq-0.1o),o- 0.9833 : 0.1001 or 10~.
98
GEORCE BEI~ABD SHAW once observed that "the universal regard for m o n e y is the one hopeful fact of our civilization." As experienced busin e s s m e n will attest, w h e n top m a n a g e m e n t ignores financial problems, believes financial m a n a g e m e n t is u n i m p o r t a n t , or in general is derelict in the h a n d l i n g of m o n e y , it does so at considerable peril.
-Francis 1. Corrigan and Howard A. W a r d F I N A N C I A L M A N A G E M E N T - - P O L I C I E S AND pRACTICES
BUSINESS HORIZONS