The optimal decision on downsizing.

ABSTRACT

Conventional economic reasoning assumes that a firm that is initially at an optimal level of operations at which no change in any parameter would yield a higher profit-per-share, may need to downsize its operations to another optimum level if it experiences a "market shock." Such a shock may take the form of lower selling prices due to decreasing demand for the firm's products, a sudden increase in the cost of goods and services used by the firm, a major technological change leading to a less labor-intensive production, etc. However, the literature disregards human capital factors that may alter the optimal decision. These factors impose an additional cost burden, which is mitigated by the sale of assets that are longer needed.

This paper offers a model aimed at establishing a rule for deciding whether or not a firm should optimally downsize its activity, with the extreme case being a complete shutdown. Furthermore, it helps to determine the extent of downsizing that should be implemented in view of the various factors, including human capital, if the optimal decision is to downsize activities.

We conclude that the higher the impact of negative morale factors and the burden of increased social benefit liabilities as a result of downsizing, the more severe the downsizing measures that are required to achieve an optimal level.

1. INTRODUCTION

Company downsizing and restructuring has become a common business strategy for improving a company's financial standing. McKinley, Zhao, and Rust (2000) report that more than forty seven million jobs have been eliminated in the U.S. since 1997 as a result of downsizing. According to the U.S. Department of Labor's current Population Study, conducted in January 2002, four million employees lost long-tenured jobs between 1999 and 2001. Moore, Gruenberg, and Gruenberg (2004) contend that about 6593 firms in the U.S. have engaged in a process of repeated downsizing leading to a situation in which about 5.5 million employees have been laid off more than once. Whereas downsizing and restructuring were undertaken in the past by companies facing difficult economic situations, nowadays a series of mass downsizing actions has become a prevalent strategy aimed at maintaining constant competitiveness in a world of rapidly changing economic conditions. Consequently, a considerable number of employees suffer the negative effects of mass layoffs, such as lower physical health, depression, anxiety, and feelings of job insecurity (Winefield, 1995). Several longitudinal studies have shown that these adverse effects persist over time (Moyle, 1998). When company downsizing and restructuring carry such high costs for the individuals involved, as well as for society at large, this process should be undertaken (if at all) only after it is demonstrated that the benefits accruing convincingly exceed the costs incurred.

1.1 The Cost of Downsizing

While job cuts are likely to produce savings in the short term, few studies have attempted to evaluate the medium and long-term effects of this action, and little longitudinal research has been conducted on the effects on employees of downsizing episodes (Moore, Gruenberg, and Gruenberg, 2004). It should be noted that job elimination not only incurs extraordinary large initial direct outlays, such as severance pay, remuneration for early retirement programs, outplacement services, and so on, but also other direct and indirect costs. These may include losses resulting from the negative effects of the downsizing program on remaining employees. In their meta-analysis, Mckee-Ryan, Song, Wanberg, and Kinicki (2005) demonstrate that physical and psychological well-being deteriorate significantly during unemployment, and we suspect that this adverse effect starts building up when employees begin to suspect they might lose their jobs in the near future. It has been suggested that survivors of downsizing and corporate restructuring view their jobs as continually vulnerable and display negative health outcomes (Kalimo, Taris, & Schaufeli, 2003). Work force reduction may produce feelings of insecurity, stress due to the added workload of taking on the tasks of dismissed colleagues, and other psycho-social outcomes. Employees may begin to feel that they are less valued or respected and may thus start to nurture feelings of mistrust toward their employers, with the possible unfortunate result of a decline in morale (e.g., Dickey, 1997; Downs, 1995; Van Horn-Christopher, 1996). In such a climate, remaining employees may also display a tendency for rigid behaviors in the workplace. Loyalty to the employer may suffer as job protection becomes the employees' first priority. If, as a result, organizational commitment plummets, then staff turnover is also likely to increase even among the firm's most valued employees. (For morale decline see, for example, Evans, Lunz, & Jalland, 1996; Franks & Mayer, 1996; the 1997 AMA Survey.)

Clearly, some of these behaviors may adversely affect productivity or level of services. They may thus jeopardize the success of the downsizing project undertaken to improve the organization's competitive posture, the major objective of the intervention in the first place. Because of these errant behaviors and the potential production gaps left by the dismissed workers, remaining employees may be forced to undergo a battery of training procedures to enable them to perform new tasks. Management may also have to adopt the necessary measures to assist some employees to cope with the anxiety and insecurity resulting from these changes. These and other disquieting and disappointing consequences of downsizing are eminently reviewed by Cameron (1988) in the introduction to his seminal paper.

Furthermore, until the obstacles generated by the downsizing process are overcome, the company may have to rely in part on outsiders, or may even be compelled to rehire some of the dismissed workers. It stands to reason that all these "compensatory" procedures may entail large additional expenditures during the transition period.

1.2 Toward a Cost-Benefit Analysis

The existence of these heavy financial burdens may help account for the ambivalence in the literature regarding the net-real, post-tax benefits of downsizing. The downsizing option must always be evaluated by comparing the expected financial benefits and costs and analyzing the financial advisability of the project. In other words, planners need to ask if the long-term goals of the corporation will be advanced once the estimated financial and social costs engendered by the layoffs have been carefully assessed and compared with the potential real savings to be gained by the plan.

The goal of any profit-oriented business is ultimately to maximize the wealth of its owners. Wealth is measured mainly by the market value of the company's shares, which is affected by numerous variables, including

profitability, the financial stability of the entity, and expected growth in earnings. The decision to lay off workers must therefore include an in-depth analysis of the effects of downsizing on these variables. Two examples may serve to illustrate this point.

1. Profitability. The 1997 AMA survey indicates that for firms that were engaged in job cutting in the 1990s, the ratio of those that had reduced operating expenses a year after the downsizing operation to those that had experienced cost increase was approximately 5:2. Although it is unclear to what extent this reduction can be attributed exclusively to downsizing, it may be assumed that this organizational intervention contributed in most cases to the lowering of operational costs.

2. Share value. Job elimination often has an immediate and positive effect on the market value of the firm's shares (e.g., Hasting 1996). According to the 1997 AMA Survey, 37% of the firms sampled that had cut jobs at least once during the 1990s reported an appreciation of their stock values after one year.

While cost saving is the primary motivation behind the decision to reduce the work force - and in over a third of the cases the results supported this move-the question remains as to the lasting effect of downsizing on the market share value of the company.

Palliam and Shalhoub (2002) contend that empirical evidence indicates that share values do not rise in the long run. Moreover, Cascio, Young and Morris (1997) found that companies which combined employee downsizing with asset restructuring generated higher profitability (i.e., returns) on assets and increased share value (i.e., stock returns) than other firms in the same economic sector. Thus, since downsizing alone has not been shown to have a significant impact on profitability, a new conceptual approach is needed to predict its probable outcomes.

2. FORMULATING THE OPTIMAL DECISION ON DOWNSIZING

Consider a firm, which produces a certain product and sells Q units for a given price of P per unit. The product is sold in a highly competitive market, so that the quantity sold by the firm has no effect on the price. Taking into account the overall costs incurred by the firm, C, its net profits, H after taxes, F are:

[PI] = (PQ - C)(1 - [tau]) (1)

For the sake of simplicity without a loss of generality of the conclusions, we assume a single period model, where a decision has to be made at time [t.sub.0] and the final and only outcome occurs at time [t.sub.1]. (The results are extended into a multi-period model in Appendix 1 .) The firm is held by shareholders who own N shares, and at [t.sub.0] expect an end-of-period profit-per-share of [PI]/N 1/1+k where k is the shareholder cost of capital rate. (8) The firm's management, whose interests are assumed to be aligned with those of the shareholders, therefore wishes to maximize (9) [PI]/N 1-/1+k].

The analysis commences at a point where the firm is initially at an optimal level at which, by economic reasoning, no change in any parameter would yield a higher profit-per-share. At timer [t.sub.0], however, the firm experiences a "market shock," such as a lower selling price due to decreasing demand for its product, or a sudden increase in the cost of raw materials. Thus, at time [t.sub.0], like any normal company experiencing a "decreasing return to scale," our firm finds itself in a non-optimal position requiring it to downsize or restructure.

The following model aims to establish a rule for deciding whether the firm should optimally downsize its activity. (10) Furthermore, and perhaps more importantly, it seeks to determine, in light of the factors discussed in the previous section, the extent of downsizing that should be implemented if the optimal decision is to downsize activities.

The firm's production function is dependent on two basic inputs: labor measured in terms of the dollar cost of labor, W, and other inputs, M, such as equipment, materials, and real estate. Additionally, several human capital factors affect labor productivity. These include:

(a) Disability claims (D)

Relying on a survey of 300 firms, Peak (1997) argues that job elimination contributes to an increase in disability claims. The 1997 AMA Survey reveals that 13% of the companies surveyed reported a rise in disability claims immediately following dismissals (versus 5% reporting a decline). After one year or more, however, the survey found an increase in 8% of the cases, as compared to a decline in 7%. This expected cost factor must be deducted from the projected cash inflows The costs of D are estimated per dollar cost of labor, i.e., D.W.

(b) The cost of withdrawal behavior (WD)

According to the 1997 AMA Survey, 23% of the responding firms indicated an increase in employee turnover one year or more after job cuts, while 11% experienced a decline in turnover. Turnover is merely one manifestation of withdrawal behavior at work, which also comprises withholding efforts at work, lateness, and absenteeism (Tziner, 2002). Such behavior typically incurs extra cost to the employer (e.g., Evans, Lunz, & Jalland, 1996; Sagie, Birati, & Tziner, 2002; Tziner & Birati, 1996). The costs of WD are estimated as a function of the dollar cost of labor, i.e., WD.W.

(c) Changes in morale (ML)

The 1997 AMA Survey also found a sharp decline in morale (74%) during the first year after downsizing, compared to an increase in morale of only 32% After one year or more, the rates were 29.5% and 19.9, respectively. Indeed, several empirical studies have found the morale of remaining workers to be adversely affected by downsizing (e.g., Balutis, 1996). The morale factor affects productivity both directly and indirectly through a change in withdrawal behavior, WD. ML is estimated per dollar cost of labor, i.e., ML.W.

(d) Level of employees' knowledge and expertise (K)

The knowledge and expertise accumulated by the work force through experience at work is also adversely affected by the departure of thhose employees who are dismissed (Cameron, 1998; Fisher & White, 2000). This factor is similarly estimated per dollar cost of labor, i.e., K.W.

The production function, Q, is therefore affected by several variables, and can be represented by:

Q = q(W, M, ML(WD, D)W, KW). (2)

The cost function, comprised of the costs of labor and other inputs such as raw materials, equipment, and real estate, can be represented by:

C=c(W,M). (3)

Assuming for the sake of simplicity that other inputs are a fixed proportion, [alpha], of labor costs, then [d[PI] =

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (4)

where P[[partial derivative]Q/[partial derivative]W + [alpha] [partial derivative]Q/[partial derivative]W]dW represents the classical economic impact of changes in inputs on the level of production, taking into consideration "economy of scale," (11) [[partial derivative]C/[partial derivative]W + [alpha] [partial derivative]C/[partial derivative]W]dW represents changes in costs due to changes in inputs.

The novel aspect of this production function is the human capital variables, represented by

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

i.e., the impact of morale, withdrawal behavior, disability claims, etc. on employees' productivity and consequently on the level of production.

A normal firm experiencing "decreasing returns to scale" will thus find an optimum level (12) if

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (13)

2.1 A Market Shock Requiring a Downsizing Decision

Assume that at a certain point in time the firm experiences a "market shock" resulting from one of the following circumstances:

(a) Lower prices for its products due to decreasing demand, increased power of competing products, such as imports, etc.

(b) Higher cost of goods, services or labor due to changes in commodity prices, regulatory changes, etc.

(c) Changes in technology rendering its product obsolete. This factor has recently become the major cause of market shocks.

In response to the sudden market shock, the firm contemplates downsizing measures. Equation (5) demonstrates the rule that should be followed in making this decision. In addition to the above analysis, the firm should also take into account the immediate costs and revenues that will be incurred only once at time [t.sub.0]. These include: a) Social benefits to employees, such as severance pay to laid off employees, extra payments for early retirement plans, and all other expenses related to the layoffs, e.g., outplacement services, extended health coverage, retraining, etc.

The total present value (14) of these costs is assumed to be a proportion, p of the cost of labor for the employees who were laid off, i.e.:

[[beta]dW. (6)

(b) Extended liability or penalties for termination of leasing or purchase contracts that are related to other inputs and are terminated due to the layoffs. These costs are obviously not a linear function of the size of the layoffs. They can be represented by:

[gamma](M)dM=[gamma](M)[alpha]dW, (7)

where [gamma] is the proportion of cuts in other inputs, dM, which are governed by an open contract that is terminated.

(c) Property, equipment, and materials owned by the firm that may be sold simultaneously with labor layoffs:

(dM-[gamma]dM)=[alpha](1-[gamma]))dW. (8)

Based on equations (7) and (8), the net immediate outlay due to a downsizing action is therefore:

[[beta]dW + [gamma]l(M)[alpha]dW) + [alpha](1-[gamma]))dW=[[beta] + [gamma][alpha]I(M) - [alpha](1-g)]dW. (9)

If this outlay is positive, i.e., the expense of social benefits is higher than revenues in lieu of the sale of assets, then the firm can borrow the necessary funds at rate r. Alternatively, if revenues are higher than expenses, it is hard to imagine that the firm undergoing downsizing can find an investment opportunity with a better rate of return than k (initial return to shareholders). Thus, we assume that whether the outlay is positive or negative, the applicable return/cost will be r.

In this case the new optimal level for the firm is obtained at:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Graphically, we can see two possible patterns of optimal decision, one that leads the firm to an optimal downsizing and one that calls for a complete shutdown (Graph 1).

[GRAPHIC OMITTED]

The firm starts at point A. As long as D[PI]is positive, the firm will continue to downsize until the graph hits the horizontal axis. Total net gain is the area under the graph. (If, however, downsizing behaves like the dotted line, a complete shutdown is called for).

It is clear that the human capital factors have a major unambiguous effect on the optimal downsizing decision. Ironically, the stronger the human capital factors, the more severe the optimal downsizing of labor, which in turn intensifies the human capital effects. From equation (10) we may infer the following propositions:

A. The stronger the expected impact of downsizing on the remaining employees' morale, disability claims, and other effects on productivity, the more severe downsizing of the labor force that is required. In the extreme case, no downsizing action will be sufficient, implying the need for a complete shutdown.

B. The larger the immediate burden of the firm's liabilities to the laid off employees (such as severance pay, early retirement expenses, etc.) the more severe downsizing of the labor force that is required.

3. A NUMERICAL EXAMPLE

Equations (1) and (2) are given in implicit form. Assuming any reasonable functional form for the production and cost functions will yield the conclusions above. For the sake of simplicity, we assume basic explicit production and cost functions, which comply with economic reasoning (increasing marginal costs) without detracting from the generalizability of the conclusions.

Assume a fixed proportion simple linear production function comprised of classical inputs, such as labor and other physical inputs, and human capital factors:

Q = a1.W + a2.M + (a3.ML + a4.K)W

ML = a5.WD + a6.D

For our purposes here, the coefficients will be set arbitrarily. However, in real cases the actual value of these coefficients must be estimated empirically using the research methods of business psychology. The cost function is assumed to be dependent only on classical economic inputs: C = a7.[W.sup.2] + a6.[M.sup.2].

Let us first consider the optimal solution in terms of the size of the labor force before and after a market shock without taking into account any human capital factors.

We start with an optimum of 700 costs of employees and a profit-per-share of 944.349 (Table 1). The market shock is represented by a reduction in the price of the company's products from 500 to 480.

The result is that the new optimal profit is 870.312 per share, which entails a downsizing of 38 costs of labor (Table 2), or laying off 4% of the labor force.

We will now add the human capital factors. We start with an optimum of 682.43 profit-per-share and a labor force of 700 as in the previous case (Table 3).

As a result of a similar market shock (the price of the company's products is reduced from 500 to 480), the firm is faced with increased withdrawal behavior of 20.5 instead of 20, along with other human capital expenses, which leads to a new optimal profit-per-share of 518.17 and a downsizing of the labor force from 700 to 610 or 6.8%, as opposed to only 4% in the previous case. This is in line with propositions A and B (Table 4).

4. CONCLUSIONS

The highly competitive environment in both domestic and global markets is forcing firms to take steps, often painful ones, to improve their position in the market place. One of the policies that has been widely adopted in recent years is the reduction of the work force.

The present article posits that before taking any action involving major changes in the structure of the most important resource in the company--human capital--the organization should undertake a very careful financial-economic analysis to evaluate the long-term consequences of such a step. It must be remembered that any major operational change should promote the primary objective of a profit-seeking company, namely, to increase the wealth of the existing shareholders (Bruton, Keels, & Skook, 1996).

Our model enables careful consideration of all variables affected by the reduction of the work force, making it possible to arrive at an improved notion of the desirability of the program. These variables can be subsumed under the headings of Financial Benefits to the Firm (payroll and related cost savings) and Extra Costs (direct and indirect) likely to be incurred as a result of downsizing. The additional cost items include severance pay, supplements to early retirement plans, losses due to increased staff turnover, disability claims, and reduced productivity resulting from a possible decline in staff morale.

Applying this model, we conclude that the stronger the expected impact of job reduction on the productivity effects of the remaining employees, the more severe the downsizing of the labor force that is required. Moreover, the larger the immediate burden of the firm's liabilities to the laid off employees, the more severe downsizing needed to achieve an optimal level.

APPENDIX 1--A MULTI-PERIOD EXTENSION

The above analysis assumes a "going concern," that is, the firm will continue to operate in the same manner once the downsizing adjustment has been made, until it encounters another market shock that may require additional adjustment. Thus, it is also assumed that the effects of human capital factors due to downsizing are permanent.

If, instead, we add a time dimension (a multi-period scenario) and assume that the effects of human capital factors are short term, e.g., employees' morale deteriorates after a downsizing action but returns to the original level after a certain period of time, the results in Propositions A and B will be mitigated. Given that the multi-period goal is to maximize the value-per-share, then the overall gain per share as a result of downsizing is expected to be:

1/N [integral][partial derivative][PI]/[partial derivative]t [e.sup.-kt] dt [integral] [partial derivative][PI]/ [partial derivative]W dW,

where [integral] [partial derivative][PI]/[partial derivative]t [e.sup.-kt] dt is the present value factor over t, t = [t.sub.0], [infinity], and [integral] [partial derivative][PI]/ [partial derivative]dW over W, W = [W.sub.0], [W.sup.*] (15),

has to be divided into permanent effects and short term effects on human capital factors. The permanent factors are represented by:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (11)

and the short term human capital factors by:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

Thus equation (10) becomes:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (12)

where t1 is the date at which the effects of the human capital factors return to the original level.

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Assa Birati, Netanaya Academic College, ISRAEL

Eli Kraizberg, Netanya University College, Netanya, ISRAEL

Aharon Tziner, Netanya University College, Netanyahu, ISRAEL

Mitchell Kellman, City University of New York, New York, USA

Dr. Assa Birati earned his Ph.D at the University of Cincinnati. Currently he is a professor at Netanaya Academic College, Israel.

Dr. Eli Kraizberg earned his PH.D at New York University, Stern Business School. Currently he is lecturing at Netanya University College, Netanya, Israel.

Dr. Aharon Tziner, earned his Ph.D at Tel Aviv University 1981. Currently he is a Full Professor and Dean at Netanya University College, Netanya, Israel.

Dr. Mitchell Kellman, is a full time professor at City University of New York, USA.

(8) Similarly, in a multi-period scenario, it can easily be demonstrated that the shareholders wish to maximize the value per-share or [PI]/Nk instead of profit-per-share per period.

(9) In a single period scenario. See Appendix 1.

(10) A particular case, albeit an extreme one, would be a complete shutdown.

(11) Increasing or decreasing returns to scale, i.e., increased or decreased efficiency to size, respectively.

(12) First order condition of optimization.

(13) Note that a constant tax rate, z, plays no role in this optimization since the tax rate does not affect the optimal point.

(14) The value at the time that the downsizing decision has to be made.

(15) [W.sup.*] is the new optimal point after downsizing action has been taken.

TABLE 1
Table 1 represents the case in which the firm optimizes its production
in the absence of human capital factors (a4,a5,a6 are all zero). The
optimal point is where the firm employs 700 of labor force and the
profit-per-share is 944.349.

       Assumptions        W    Revenue   Cost      Profit
                                                   per
                                                   share

 p     500   a1     4     50   1350000   48247.50  130.175
 w     700   a2     5     100  2700000    192990   250.701
 m    7000   a3     3     500  13500000  4824750   867.525
alfa   10    a4     0     600  16200000  6947640   925.236
 wd     0    a5     0     698  18846000  9402550   944.345
 D      0    a6     0     699  18873000  9429511   944.349
 K      0    a7     1     700  18900000  9456510   944.349  optimum
 N    10000  a8  0.18299  701  18927000  9483548   944.345

TABLE 2

Table 2 represents the case in which the firm optimizes its production
in the absence of human capital factors, but a market shock in the
form of a reduction in the price of the firm's product (from 500 to
480) has occurred. The optimal downsizing is where the firm employs
672 of labor force instead of 700 and the profit-per-share is 870.312.

       Assumptions        W    Revenue   Costs      Profits
                                                    per
                                                    share

P       480  a1        4  50   1296000   48247.50   124.775
W       672  a2        5  200  5184000    771960    441.204
M      6720  a3        3  500  12960000   4824750   813.525
a        10  a4        0  670  17366400   8663321   870.308
WD        0  a5        0  671  17392320   8689201   870.312
D         0  a6        0  672  17418240   8715120   870.312  optimum
K         0  a7        1  673  17444160   8741077   870.308
N     10000  a8  0.18299  674  17470080   8767073   870.301

TABLE 3
Table 3 represents the case in which the firm optimizes its production
taking into account human capital factors. The optimal point is where
the firm employs 700 of labor force and the profit-per-share is 682.43.

       Assumptions        W    Revenue   Costs      Profits
                                                    per
                                                    share

p       500  a1        4  50    975000     34825    94.018
w       700  a2        5  300  5850000    1253700   459.630
m      7000  a3        3  697  13591500  6767319.4  682.418
alfa     10  a4        4  698  13611000  6786751.7  682.425
wd       20  a5       -2  699  13630500  6806211.9  682.429
D         5  a6       -1  700  13650000   6825700   682.430  optimum
K        30  a7        1  701  13669500  6845215.9  682.428
N     10000  a8   0.1293  702  13689000  6864759.7  682.424

TABLE 4
Table 4 represents the case in which the firm optimizes its production
taking into account human capital factors, but a market shock in the
form of a reduction in the price of the firm's product (from 500 to
480) has occurred. The optimal downsizing is where the firm employs
610 of labor force instead of 700 (as compared to optimization in the
absence of human capital factors, which required a downsizing to only
672).

       Assumptions         W   Revenue     Cost     Profits
                                                    per
                                                    share

 p     480   a1     4     50    849600     34825    81.478
 w     609   a2     5     300  5097600    1253700   384.390
 m    6090   a3     3     607  10314144  5132494.6  518.165
alfa   10    a4     4     608  10331136  5149419.5  518.172
 wd   20.5   a5    -2     609  10348128  5166372.3  518.176
 D     5.2   a6    -1     610  10365120   5183353   518.177  optimum
 K     30    a7     1     611  10382112  5200361.5  518.175
 N    10000  a8  0.1293   612  10399104  5217397.9  518.171