Analysis of a sales force incentive plan for accurate sales forecasting and performance

189

Analysis of a sales force incentive plan for accurate sales forecasting and performance

Murali K. Mantrala and Kalyan Raman College of Business Administration, University of Florida, Gainesville, FL 32611, U.S.A.

Firms require accurate sales forecasts to set plans that reflect growth opportunities as well as avoid costs such as those due to stock-outs and excess inventories. Sales forecast accuracy may be improved by using information from salespeople who possess better knowledge than central planners about their territories’ sales prospects. However, salespeople may understate sales estimates when their compensation depends on fulfillment of quotas based on their sales forecasts. This paper analyzes an incentive plan introduced by Gonik (1978) that aims to reward a salesperson for self-selecting a demanding forecast as well as its actual fulfillment. We derive the salesperson’s response to this plan in a stochastic environment and show how management may adjust the plan parameters to elicit desired sales estimates. The paper concludes with directions for implementation and an assessment of the benefits and limitations of the Gonik scheme.

1. Introduction

A firm’s profitability is affected by the accuracy of sales forecasts that guide its decisions about production capacity, inventory and distribution of a product in an accounting period. When actual sales are much less than the forecast, overhead costs of production may not be covered and/or the firm has to hold costly inventories. Similarly, the n’irm incurs costs when actual sales greatly exceed the forecast and thereby strain production capacity or result in stock-outs.

Many industrial firms attempt to improve sales forecast accuracy by using salespeople’s estimates of their own sales in bottom-up

Intern. J. of Research in Marketing 7 (1990) 189-202 North-Holland

development of the forecasts (White, 1984; Wotruba and Thurlow, 1976). The management of these firms acknowledge that experi- enced salespeople are likely to have more precise information about sales prospects in their own territories than central planners who are not close to the market. In addition to the informational advantages, there may also be motivational advantages in sales force participation in forecasting. In particular, sales forecasts are frequently used to set sales quotas for salespeople (White, 1984). Indeed a sales representative’s sales quota is usually set equal to or slightly above the sales forecast (Churchill, Ford and Walker, 1990, p. 242). The sales representative may feel more motivated and committed to fulfilling a sales quota that is based on his own estimates rather than one set by a less informed manager. However, it is precisely in these circumstances that managers frequently ex- press serious concerns about sales force participation in forecasting (White, 1984).

One concern is that if a salesperson is paid a bonus for quota fulfillment then he may understate his sales expectations in order to get a lower target that is easily fulfilled. Al- though the forecast turns out to be “accurate”, the firm has missed an opportunity for additional sales that could have been planned and actually realized. On the other hand, when the sales force compensation is inde- pendent of actual performance relative to the quota, salespeople may not give adequate attention to preparing their sales forecasts and/or be indifferent to any discrepancy between the forecast and their actual sales output. Such behavior is again counterproductive from the viewpoint of the firm.

The problems and opportunities presented

0167~8116/90/$03.50 8 1990 - Elsevier Science Publishers B.V. (North-Holland)

190 M. K. Mantrala, K, Raman / Accurate sales forecasting and performance

by sales force participation in forecasting have led some firms to establish special organiza- tional systems to monitor and reward the sales forecasting accuracy of their salespeople, e.g., Ampertif (Sales and Marketing Management, 1987). Other companies have attempted to devise sales force compensation schemes that incorporate incentives for forecast accuracy, for example, Miracle Adhesive Corporation (White, 1984). Moynahan (1981) outlines the challenges in structuring such incentive schemes and concludes they may be difficult to overcome. However, Gonik (1978) introduced a relatively simple bonus scheme used by IBM Brazil that aims to reward a salesperson for self-selecting a demanding forecast that becomes his quota as well as reward the actual performance relative to this quota. It turns out that this scheme has also appeared as the New Soviet Incentive Model in the Economics Literature (see, e.g., Weitz- man, 1976). * Despite possessing some rather interesting features, the Gonik scheme has received little attention in subsequent sales force compensation research (see, e.g., Basu, Lal, Srinivasan and Staelin, 1985; La1 and Staclin, 1986).

The objective of this paper is to elucidate the properties of the Gonik scheme and its implementation in the sales force context. We first specify the desired features or requirements to be met by an incentive scheme that includes a reward for forecast accuracy. We next describe the Gonik scheme and then analyze the response it would elicit from a risk-neutral salesperson who is uncertain about the realizable sales. Specifically, we first consider the case of a risk-neutral salesperson with fixed selling effort and show how his quota selection is affected by the parameters of the incentive plan. Further, we demon- strate how the firm can manipulate the plan

’ An early reference to the equivalence of the Gonik scheme and the New Soviet Incentive System is found in Albers (1982).

parameters to induce a quota that has a desired probability of fulfillment. We then ex- tend the analyses to the case of a risk-neutral salesperson who can vary his selling effort but associates a cost with effort. Next, we address the case of the risk-averse salesperson and highlight some general results and remaining problems in analyzing this case. Finally, we discuss the implementation of the Gonik scheme in practical settings. We close with conclusions and a search directions.

statement of further re-

2. Requirements of sales forecast accuracy bonus schemes

Commonly seen sales quota-bonus structures are of little help if management wishes to guard against biased sales estimates from sales representatives. For example, consider the offer of a fixed bonus, 3, upon fulfillment of a quota, 4, selected by the salesperson. 2 Let B denote the actual bonus awarded upon achievement of sales of q by the end of the period. Thus B = 0 for q < 4 and B= 3 for q a 4. Clearly, the salesperson has an incentive to understate his estimate of realizable sales under this scheme. Further, the plan does not encourage sales in excess of the quota, i.e., overfulfillment.

Although overfulfillment as well as underfulfillment of targets are costly at aggregate levels, most sales managers are inclined to reward sales in excess of a quota. First, it is normal management practice to encourage salespeople to stretch their performance rather than restrain their output. Second, there is always some uncertainty about the actual fulfillment of a quota and management may

2 We use the words “quota”, “target”, and “forecast” inter- changeably in the rest of this paper. A salesperson’s as- signed quota is assumed to be the same as the forecasted sales for his territory. This is often the case in practice (Churchill, Ford and Walker, 1990, p. 242).

M. K. Mantrala, K. Raman / Accurate sales forecasting and performance 191

believe that overfulfillment by some salespeople may compensate for underfulfillmen; by others (Moynahan, 1981). Now the above bonus plan is easily modified to provide an incentive for overfulfillment, for example, let

B = B+a(q-4)

i

forq2q^,

0 for q < 4,

where a > 0. However, such a change would reinforce the salesperson’s incentive to understate his sales expectations. Thus, there is tension between the encouragement of higher performances and elicitation of unbiased estimates of realizable sales.

Management could attempt to overcome the bias toward understatement by providing incentive pay that increases with the self- selected quota level, for example, let

B=bq^+a(q-4) forq>O,

where b> 0, a > 0, and we require b > a. However, this plan now provides an incentive to overstate the expected sales level. There- fore, any reward for forecast “ambitiousness” must be accompanied by some penalty for actual sales less than the self-selected quota.

Summarizing, the necessary requirements to be met by a forecast accuracy incentive scheme are as follows:

The salesperson should find: (1) it is more rewarding to choose and

fulfill a higher quota (forecast) than choose and fulfill a lower quota;

Table 1 Examples of payment grid based on Gonik (1978) formulae

to overfulfill any fulfill the chosen

(2) it is more rewarding chosen quota than merely quota;

(3) it is more rewarding to choose and fulfill a lower quota than underfulfill a higher selected quota;

(4) it is more rewarding to choose and fulfill a higher quota than overfulfill a lower selected quota.

Requirement (1) implies the more am- bitious the self-selected quota the higher should be the reward while requirement (2) implies the reward increases with overfulfillment. However, requirement (3) is a guard against overstatement of the expected sales to gain from the reward for ambitiousness while requirement (4) is a guard against understatement of expected sales to gain from the reward for overfulfillment. Devising an incentive scheme that meets all these requirements is puzzling. and understandably viewed with some skepticism in the sales management literature (see, e.g., Moynahan, 1981). How- ever, these requirements are indeed met by the Gonik (1978) incentive plan.

3. The Gonik scheme

The sales force incentive scheme presented by Gonik (1978) ties a salesperson’s bonus income, B, to (a) a tentative quota, q, chosen

0 0.5 1.0

m t’ 1.5 I 2.0 2.0 3.0

0

0.5 30 60 30 1.0 60 90 120

1.5 90 120 150 2.0 120 150 180 2.5 150 180 210 3.0 180 210 240

” Salesperson’s forecast divided by planner’s objective. ’ Actual sales divided by planner’s objective.

-

90 60 30 -

180 150 120 90 210 240 210 180 240 270 300 270 270 300 330 360

192 M. K. Mantrala, K. Raman / Accurate sales forecasting and performance

by the firm; (b) the sales forecast, 4, sub- mitted by the salesperson; and (c) the actual sales, 4, realized by the end of the accounting period. The plan requires management to first communicate 4 as well as the bonus payment formulae, or a payment grid as shown in Table 1, to the salesperson before the com- mencement of the period. 3 After getting this information, the salesperson selects 4. At the end of the period, the salesperson is paid a bonus according to the following formulae: 4

B = i@/ij) for 4 = 4, 0) - 3q-ij B+j -

( 1 4 for q<Q, (2)

. B - = ;B q+g

( ) 4 for q>J. (3)

The formulae imply 3 is the bonus payment when the salesperson concurs with management’s choice of quota, i.e., sets 4 = q and then exactly achieves this level.

3 The tentative quota, ij, that management communicates to the salesperson informs him about what management knows and expects with regard to sales in his/her territory. The salesperson can either concur or revise this forecast based on his own updated knowledge.

4 These formulae are presented in Exhibit II (p. 119) of the article by Gonik (1978). The numerical values in that exhibit can be recovered by setting B = 120.

With some algebraic manipulation of’ (l), (2), and (3), the formulae can be rewritten in a more instructive form:

B=B,=B+b(ij-if)+y(q-4)

for q<t&

B=B,=B+P(q^-ij)+a(q-4)

(4)

for q 2 4,

where

B, > 0, B, > 0

and

for q > 0

(9

p = (B/g), ar = (B/2q) and

y = (3i?/2q).

Therefore, the salesperson is penalized (rewarded) at the rate /? per unit by which his forecast is lower (higher) than if. The salesperson also gets penalized for underfulfillment of 4j at a rate y per unit sales short of 6 and gets rewarded for overfulfillment at the rate QL per unit sales in excess of 4. Finally, note that

y>p%Y>o. (6)

The Gonik scheme is therefore a piecewise linear function of actual sales output with a kink discontinuity at the self-imposed quota

B=B + p (6 - ij) =a

Fig. 1. The Gonik reward scheme.

M. K. Mantrara, K. Raman / Accurate sales forecasting and performance 193

of the salesperson (Fig. 1). Readers familiar with the Economics literature will recognize that this plan is the same as the New Soviet Incentive Model (Weitzman, 1976; Snow- berger, 1977).

Given that the plan parameters satisfy conditions (6), it is easily verified that the Gonik plan meets the above four plan requirements if the salesperson is bonus maximizing and knows his realizable sales with certainty. ’ However, in reality sales are stochastic as well as affected by the salesperson’s level of selling effort. Further, it is reasonable to assume the salesperson has a disutility or cost associated with each unit of effort. (Indeed if this were not the case, there is little reason to be con- cerned about salespeople “ low-balling” their forecasts.) We consider these factors in the following analysis of the salesperson’s response to the Gonik scheme and the benefits offered by it to the firm.

4. Analysis

Let u be the selling effort of the salesperson in, for example, hours per period, and 4 be the dollar sales per period. We assume the price of the product to be fixed and outside of the control of the salesperson. Further, marginal costs of production are assumed to be constant and the gross margin as a frac- tion of price is set equal to one, Sales are stochastically related to effort, i.e.,

q=g(u)+e,

5 The particular set of numerical values of these parameters used by Gonik (1978) is just one of many possible sets of values that can be used. The important point is that the parameter values must satisfy (6) for the plan to have the desired features. In the remainder of the paper we allow for any values of y, p, cy that satisfy (6).

where g(u) is the expected sales response to effort function reflecting decreasing returns to effort, i.e.,

g’(u) ’ 0, g”(U) < 0. 6

(The primes denote derivatives with respect to the argument of the function.) The random disturbance affecting sales is denoted by e with expected value E(e) = 0 and E( e2) > 0. Let F(X) denote the distribution function of e, i.e., F(X) = Prob( e c x). We assume that the probability distribution of sales is con- tinuous and differentiable so that F’(x) = f(x) is the probability density function (pdf). The salesperson knows this probability distribution but management does not. Manage- ment may only know that sales output q lies in some interval 0 < q1 < q < q2 < 60. (There would be no need for the Gonik scheme if management and the salesperson possessed the same information about the probability distribution of sales.) Finally, the salesperson associates a cost ($) with effort level u given bY wh

c’(u) > 0, P(u) > 0.

To facilitate the discussion, we begin with the case of the risk-neutral salesperson who has a fixed effort level and then proceed to the case where the risk-neutral salesperson can vary his effort. All the insights obtained in the first case carry over to the second case.

Case I: Risk-neutral salesperson with fixed effort

We now derive the choice of 4 by a risk- neutral salesperson who maximizes the expected value of his income. Let the fixed effort be denoted by uf and

4f

6

=gbrL cr” C(Uf).

The assumption that effort and the random disturbance have additively separable effects considerably simplifies the analyses. This assumption is frequently made in the analytical sales force compensation research literature (see, e.g.. Lal and Steelin, 1986).


The salesperson’s problem is therefore given as

max E[B-C,]. ci

(8)

Given that effort is fixed, the problem becomes

max E[B] =I*& dF(e) + Je’BZ dF(e), (i e1 *

(9)

where

e, =ql -qf, e2=q2-qf, * =4-qf,

and B, and B, are given by (4) and (5), respectively. The salesperson’s choice of 6 must therefore satisfy the first-order condition ’

wY~[fl*kF(ed]

+(P-4[F(e,)-F(*)] =o (10)

or

(a-y)F(*)+(p-a)=O. (11)

The first-order condition reduces to

P Prob(ecq-q,)=s.

Alternatively,

Y-P Prob(qaq^) = Y. -

(12)

(13)

The value of 4 that satisfies (10) maximizes the salesperson’s expected income if the second-order condition, given below, holds:

!a-yiF’@-qf) 0. (14)

Equation (14) is satisfied when y > (Y > 0. It then follows that j3 > QL and y > p in (12) and (13). In short, we require y 4 /? > a, = 0 to induce the salesperson to choose 4 that maximizes KS expected income. These conditions are met by t’ e Gonik scheme.

Equation (13) indicates that the salesperson chooses a 4 which has a probability of

’ The first-order condition is obtained by applying the Leib- nitz rule.

being at least fulfilled given by the relative magnitudes of the plan parameters set by the sales planner. Thus, by manipulating (Y, fi, y, the planner can induce the salesperson to submit a quota with a knoavn probability of being at least fulfilled. For example, the plan parameter values used by Gonik (1978) are such that

y - p = gy - a)*

In this case the representative’s choice of 4 is such that it has a 50% chance of fulfillment, i.e., it is set at the median of the probability distribution of sales. The planner can set y - j? greater (less) than i( y - (u) if a higher (lower) probability of fulfillment than 50% is desired. In this connection note that

(15)

and &j/ap > 0 while aq/aa < 0 and &j/a-f < 0. Therefore, the planner can alter any of the three parameters to affect the salesperson’s choice but must accept a lower (higher) 3 for a higher (lower) probability of fulfillment. However, whatever be the level of the selected target, the bonus always increases with actual sales. Consequently, the Gonik scheme pre- serves the salesperson’s incentive to obtain the highest possible level of sales during the course of the accounting period.

The above discussion raises an interesting question: What is the sales estimate and/or its probability of fulfillment that management desires to elicit from the salesperson? To answer this question, we consider the problem from the firm’s viewpoint. Specifically, we assume that the firm wants the sales representative’s choice of 4 to maximize its expected gains, E( ?T), given by

E[r] =E[q-B-L(q, a>]* (16) In (16), B is the salesperson’s bonus as per the Gonik plan while L(q, 6) is a function denoting the losses (costs) incurred by the firm when actual sales deviate from the level predicted by the salesperson, for example,


stock-out and excess inventory costs. Note that if there is no loss function, any choice of 2 that maximizes the salesperson’s expected income under the Gonik scheme will mini- mize the firm’s expected gains. Therefore, it is not in the firm’s interest to use a Gonik type incentive scheme when there are no costs attached to salespeople’s prediction errors. We now consider two special examples of the loss function.

(i) Quadratic loss function, i.e.,

L(q, t)=k(q-q^)2, k>O.

Losses due to under- and overfulfillment are weighted equally by this commonly applied lossfunction in the stochastic control theory of the firm (see, e.g., DeGroot, 1970).

The firm would therefore like the salesperson to choose 6 that maximizes

E[ln] =E(q)-E(B)-E(k(q-e)2). (17)

Differentiating (17) with respect to Q, we obtain the following first-order condition:

-(((Y-Y)F(B-q/)+(p-a))

-(-2k(E(q)-q^)}=O. (18)

Given that the salesperson chooses 6 so as to maximize his expected income, the first term in (18) is equal to zero. Therefore the second term must also equal zero. Hence, 4 should satisfy

6= E[q] =qf. 8 (19)

Now the second-order condition for a maximum is -

(( vy)F’(&-qf)) -2k<O.

This implies

(20)

(y-a)F’(cj-qf) <2k. (21)

Equation (21) indicates that the firm with a quadratic loss function must be cautious in setting the range y - (Y. If the range is set too

’ This result is derived without makir,g :hs z:;sumption thut

the firm knows the probability distribution function.

high relative to 2k, then the second-order condition will not be satisfied and the firm will end up with a minimum. Unfortunately, the firm does not know the probability &St& bution function and therefore faces an am- biguous situation. We can only say that the firm should keep y - (Y well below 2k. AS-

suming this is the case and the second-order condition is met, the firm requires the salesperson’s choice of target to be the mean of the probability distribution of sales. If this distribution is symmetric, i.e., its mean and medil;n coincide, the firm should set

y - p = i(y - cy).

On the other hand, if the distribution is skewed so that the mean is less (greater) than the median, then y - j? should be set greater (less) than $( y - cy). Clearly, these directions can be taken only when the firm has some idea of the shape of the probability distribution.

(ii) Asymmetric loss function, i.e.,

L= (k*(4-9) for9M

\k,(q-4) forq>,$.

In this loss function, kl is the cost per unit underfulfillment of the planned sales 4, for example, the holding cost per unit of excess inventory. Similarly, k, is the cost per unit overfulfillment of 4, for example, the unit stock-out cost. The costs k, and k, may or may not be equal. In our view, this is a more natural and flexible expression of the firm’s loss function than the quadratic form.

Taking the same approach as in the previ-

ous example, the firm now requires 4 satisfy the firs t-order condition

+k, s

“(q-4) dF(e) =O, + 1

J

where the notation is the same as that used in (9) .


The above expression reduces to

kl l-F(kd= k,+k,’ (22)

The second-order condition for a maximum is

-((~-Yy)FI(B-qj-~j

- {(k, +k,>F’(d-e)) co9 (23) i.e.,

Y --<kk,+k,. (24)

Therefore, the firm must ensure that the range Y- cy is less than k, + k, in minimizing result. Assuming met, the firm can assure 4 setting

order to avoid a this condition is satisfies (22) by

Y-P kl - = k, + k, l Y-a

(25)

Equations (24) and (25) imply that k, is an upper bound on the range y - /?. Therefore, if the cost per unit underfulfillment, k,, equals the cost per urnit overfulfillment, k,, the optimal choice of 4 for the firAm is the median (rather than the mean as in the previous example) of the probability distribution. This implies setting

y - p = i(y - a).

On the other hand, if k, is greater (less) than kZ, then y - /3 should be greater (less) than $( y - cy). Note that the shape of the probability distribution now does not affect the firm’s need to set the plan parameters according to (24) and (25). Thus, the ambiguities facing the firm with a quadratic loss function are much reduced when the loss function takes the form in this example.

Case II: Risk-neutral salesperson with variable effort

In this case the sales representative must determine his optimal 6 as well as the optimal level of selling effort for the accounting period. We assume that the salesperson

simultaneously makes these decisions when submitting 4. 9 Therefore, the salesperson’s problem is

max E[B-c(u)]. 4. u

(26)

The first-order condition with respect to 4 is

(P-Y)[F(a-g(u))-F(e,)l

+(P-~)[F(e,)-F(B-g(u))] =O, (27)

and the first-order condition with respect to u is

g’(u)[u(F(B - g(u)))

+a(1 - F(q^-g(u))}] = C’(u). (28)

As before, equation (27) reduces to

F(d-g(u))=E. (29)

Substituting (29) in (28) and simplifying, we get

Pg’(u) = c’(u). (30)

Further, from (29), we see that

(31)

where u* is the effort level that satisfies (30). Thus, the optimal quota level is affected by the effort decision. We now provide an example to illustrate the impact of the salesperson’s cost of effort on his optimal 4.

Example Let

g(u) = a, + a2 In u, c(u) = +c,u”,

9 This is a significant departure from analyses of economists, for example, Snowberger (1977) that treat quota and effort selections as sequential decisions. Such analyses assume that uncertainty prcscnt at the time of quota selection is eliminated before the effort decision is made. This assump tion is unrealistic in the selling context where uncertainty is never completely eliminated. A salesperson must decioe the effort level at the time of quota selection and it seems more appropriate to model these as simultaneous decisions under uncertainty.


and assume the probability distribution of e is uniform over the range [ - i, 31. Then from the first-order condition for u we get pa/u = COu, i.e., u* = (&/C#/’ and, therefore,

g( u*) = a, + ia2 ln(pa,&).

For the given distribution,

F-‘[(p-4/(y-a)] =(p-*)/(y-*)-5,

and therefore using (31) we see that

P a2 /?-a 1 ~=a,++a,ln-6_+~-~.

0

For example, when (p - cw)/(y - a) is set equal to 4, the salesperson sets the 6 equal to his expected sales given the optimal level of effort, i.e., g( u * ). Note that the optimal effort decreases as the cost of effort parameter, Co, increases. On the other hand, effort increases as p increases.

All the insights obtained under Case I still hold in the present case. The firm can impact the salesperson’s choice of 4 in the same way as before. Specifically, the following com- parative statics results hold for all concave

Fig. 2. Choices of y and (Y given p (y = 2fi - 01).

sales response functions and convex cost of effort functions:

au* >() !!z,, ap 3 ap 3

The probability of at least fulfilling 4 may also be impacted in a similar manner to that described in Case I. However, an additional advantage is seen in the present case that considers the salesperson’s effort as a decision variable. Specifically, /3 is the only plan parameter that affects u *. Hence, the firm can increase u* and thereby 4 through an increase in /3 and still maintain a desired probability of fulfillment by appropriately ad- justing (Y and y. This advantage was not available in Case I where an increase in 6 could only be accomplished by allowing the probability of fulfillment to fall. For example, consider the case of the firm with the cost per unit underfulfillment, ki, equal to the cost

lo Proofs available from authors.

a


per unit overfulfillment, kZ. Let ki = k2 = k. As we saw earlier, this firm should set

Y - P = ‘i(Y - 4

to induce the salesperson to select the median of the sales distribution given the optimal level of effort u*(p). Therefore, for any given p, the other two parameters should satisfy the condition y = 2p - (I[. Further, we require that y>p>cw>O (and (y-a)<2k; (y-p)< k). Therefore, referring to Fig. 2, for any j3, all combinations of y and at on the straight line segment (O,, OZ) with slope - 1 and intercept 2/? will maintain the desired probability of fulfillment.

Case III: The risk-averse salesperson

The previous analyses assumed the salesperson is risk-neutral and therefore maximizes his expected income in responding to the Gonik scheme. Our analyses of Cases I and II indicate the salesperson’s quota effort selection decisions are influenced

and bY

the parameters (Y, p, and y but remain unaf- fected by B and @ However, the latter parameters do affect the choices of a salesperson who is risk-averse rather than risk-neutral. The risk-averse salesperson maximizes the expected utility rather than the expected value of his income. Specifically, the salesperson’s problem is

maxE(U(B) - C(u)>, 6. u (32)

where U(B) denotes the utility for income function such that U’(B) > 0, U”(B) < 0.

It can be shown that the salesperson’s optimal choices of 6 and u must satisfy the following inequalities, derived from the first- order conditions: ‘I

l-F(q^-g(u))+ -

” Proofs available from authors.

(33)

and

g’(u)[BU’(B+P(q^-q))] 2 C’(u)* (34)

Equation (33) implies the probability of at least fulfilling the self-selected quota now is not known exactly but is greater than or equal to the ratio of the differences y - p and y - LY. This suggests a more conservative quota selection by the risk-averse salesperson as compared with the risk-neutral type who faces the same parameter values. The second condition, inequality (34), indicates the marginal utility of effort is greater than or equal to the marginal cost of effort, where the marginal utility and marginal cost are evaluated at the expected level of effort needed to achieve the chosen quota. Note that once again the parameters (Y and y do not impact the risk- averse salesperson’s effort-selection decision. However, both the effort-selection and quota-selection decisions are affected by p as well as the parameters 3 and 4. Unfor- tunately, the probability of at least fulfilling the quota as well as the effects of the plan parameters cannot be exactly determined without more specific knowledge of the salesperson’s utility function. The mathemati- cal derivation of such results is rather intrac- table and likely to involve approximations even when the utility functions are specified (see Snowberger, 1977; Ekern, 1979, for related work). We therefore do not pursue the analysis of the risk-averse salesperson’s response any further but instead turn to the practical questions that remain in connection with the implementation of the Gonik scheme.

5. Implementation issues

The above analyses have provided several theoretical insights with regard to the risk- neutral and risk-averse salesperson’s response to the Gonik scheme as well as some practical directions for setting the: parameters (x, p, and y. The analysis of the risk-neutral

M.K. Mantrala, K. Raman / Accurate sales forecasting and performance

salesperson with variable effort reveals the crucial role played by the parameter p but leaves unanswered the question of how the

B + & 4 - 4). Therefore, using assumption (A3). we require

B + PMu*(P)) - 4) = mu*(P), (35) where m is the known market wage rate. In (35) we have set 4 = g( u*(p)), which is the expected sales given the optimal effort. Pro- ceeding on the assumption that the salesperson exactly fulfills whatever quota he selects, the expected profits for the firm are given by

EM = tdu*m

199

firm should pick a specific value of /3. How- ever once this parameter value is set, we have indicated how ar and y may be manipulated to maintain a desired probability of at least fulfilling the quota. As we have shown, the desired probability of fulfillment depends on the relative magnitudes of the known costs per unit underfulfillment and overfulfillment.

Any approach for setting the value of fl must be based on management’s prior information and expectations about the salesperson and his territory. We now outline one such approach that leads to a benchmark value of /3. The approach is based on the following assumptions.

(Al) The salesperson is risk-neutral. l2 (A2) The salesperson will exactly fulfill

whatever quota he selects. (A3) In order to keep the salesperson on

the job, he must be guaranteed a minimum payment equal to the market wage rate (dol- lars per hour) times the effort expended (hours per period).

Given these initial assumptions, management may exploit the result that the salesperson’s optimal choice of effort must satisfy the condition &‘(M) = C’(u). :zi order to do so, management must develop its own estimates of the expected sales response function g(u) for the sales territory and the cost of effort function C(u) of the salesperson. Past data and managerial judgments may be used in assessing these functions. Once these functions are estimated, the salesperson’s optimal effort rule, u*(p), can be derived from the above optimality condition for his effort decision. Now assumption (A2) implies that the ultimate payment to the salesperson is simply

We confine our implementation suggestions to the risk-neutral case due to the lack of exact theoretical results and guidelines in the case of the risk-averse salesperson.

-[~+Pbdu*WH)]. (36) Therefore, substituting (35) in (36), the best choice of P is the solution to the problem

rnF E[lr] =g(u*(p)) -mu*(P). (37)

The “optimal” value of p may be substituted in (35) to determine 3. Note that q does not affect the choice of p but does influence the level of 3. Specifically,

g=mu*(p*) -/S*g(u*(p*)) -/3*ij, (38)

where p* is the solution to (37). Therefore the assumption of a minimum income requirement for the salesperson means the firm must be conservative in its selection of 4 although q does not affect the risk-neutral salesperson’s quota and effort selection decisions. l3

After setting p, management must consider the possibilities of under- and overfulfillment and appropriately set ar and y. These parameter values would be based on the known costs per unit of under- and overfulfillment which determine the desired probability of fulfillment. Suppose the firm uses an asymmetric loss function as earlier described. The costs would determine the upper bound on the

” Management could in fact dispense with setting cf in the case of the risk-neutral salesperson as this parameter neither affects the salesperson’s quota and effort selection decisions nor the choice of j3, (x, and y. However, q may have an informative role as indicated in footnote 2. Kotler (1970) describes several approaches that management may use to set q.

200 M. K. Mantrala, K. Raman / Accurate sales forecasting end performance

range for y - cy as well as the ratio ( y - a)/( y - fl). Given p, the particular values of y and 0 may be chosen as indicated in Fig. 2.

5.1. Exterrsion to multiple salespeople

We have so far treated the problem as if the firm had only a single salesperson. In reality it is large firms with many salespeo@e that are likely to be interested in using a Gonik type scheme. Typically such firms set one plan that applies uniformly to all sales representatives in order to avoid sales force conflicts and morale problems (see, e.g., Darmon, 1979). In such circumstances, our suggested approach for setting p may be modified to determine the value that maximizes the sum over all individual salespeople’s contributions to expected profits, i.e., for i = 1 9”.9 n salespeople,

n

(39)

Once p is chosen according to (39), the proce- dure for setting cy and y is the same as in the single salesperson case, assuming the costs per unit underfulfillment and overfulfillment are the same across all sales territories. How- ever, the firm would have to adopt some reasonable rule for setting the same B for all salespeople. Considering (38), one possible approach is to adjust the individual q’s up or down until everyone receives the same 3 that is consistent with their individual minimum income constraints. l4 Thus we see a very useful role for the individual q’s in situations where the firm intends to set the same bonus plan parameters for all salespeople.

Summarizing, we have outlined a workable approach for setting all the parameters of the Gonik plan, i.e., p, y, QL, 7?, and q. We do not claim that the various steps lead to optimal parameter values. Indeed, management can-

I4 The level of B itself would depend on the firm’s budget for bonus payments, i.e., its bonus fund for the sales force.

not really set optimal values when it is operat- ing with less information than the sales representatives. However, our approach does consider the salesperson’s optimal responses to the plan. Further, the plan structure does induce salespeople to report sales estimates with the probabilities of fulfillment desired by management. Finally, the plan induces salespeople to sell as much as they can by the end of the accounting period. Thus, the informational and motivational advantages remain in place.

The assumption of risk-neutral salespeople is a limitation of our suggestions for setting the Gonik plan. However structuring a plan that accounts for individual risk-aversion characteristics is a formidable task in practice. Indeed it seems rather impractical to conduct such an exercise when there is asymmetric information and a common plan is to be set for salespeople with varying risk attitudes. The assumption of risk-neutrality greatly facilitates understanding and simplifies the structuring of the plan. Once benchmark parameter values are derived, management can later adjust them if necessary to accommodate individual cases of highly risk-averse salespeople. It is also worth pointing out that it is really the firm’s loss function associated with prediction errors rather than individual sales representatives’ risk attitudes that is a dominant concern underlying the use of the Gonik plan. The loss function, in a sense, represents management’s own risk preferences and these are being transferred to the salespeople via the parameter settings of the Gonik plan.

The last point serves as a reminder that it is advantageous for the firm to use the Gonik scheme when there are significant costs associated with sales prediction errors. In the absence of such costs, it is more appropriate to use regular sales quota-bonus plans that do not include rewards for the accuracy of salespeople’s self-selected quotas. However, the optimal design of regular quota-bonus


plans is still a difficult task due to the problem of asymmetric information. These diffi- culties have been addressed in the operational models for optimising quota-bonus plans using salespeople’s inputs developed by Darmon (1979, 1987) and Mantrala, Sinha and Zoltners (1988).

6. Conclusion

Sales force incentive structures such as the Gonik (1978) bonus scheme have so far received little attention in sales force compensation research. This paper has described the properties of the Gonik scheme that aims to reward a salesperson for self-selecting a demanding sales forecast/quota as well as the actual fulfillment of that quota. We have presented several results with respect to a risk- neutral as well as risk-averse salesperson’s optimal responses to this incentive plan in a stochastic environment. In deriving these results, we have established that the Gonik scheme is useful when salespeople possess better information about their own sales prospects than central planners and there are significant costs associated with under- and overfulfillment of sales forecasts. These costs define the nature of the sales estimate that central planners seek from the salesperson. Specifically, the relative magnitudes of the costs per unit underfulfillment and overfulfillment determine the desired probability of at least fulfilling the forecast given by the salesperson. We have shown how the plan parameters may be manipulated to ensure that a salesperson submits a demanding sales forecast with the desired probability of fulfillment. Finally, we have provided directions for setting the plan parameters in practical situations where salespeople are assume to be risk-neutral.

There are several issues to investigate in future research on Gonik type sales force incentive schemes. First, a more complete

analytical treatment of the risk-averse salesperson’s responses is needed. Second, the analyses in this paper are limited to a static, i.e., one-period setting of the incentive plan. There are important questions with respect to the effectiveness and design of such incentive schemes over multi-period horizons. In particular, management’s selections of tentative quotas over time may be driven by “ratchet” rules (see, e.g., Weitzman, 1980). Such quota- setting rules may result in dynamic incentive planning problems that have not been addressed in this paper. The effectiveness of Gonik type sales force incentive schemes in coping with such problems remains to be examined (see Snowberger, 1977; Miller and Thornton, 1978, for related work). There is also a need for more systematic empirical research on salespeople’s motivation, behavior, and responses when asked to participate in sales forecasting and quota-setting. Little work has been done in this area since the study by Wotruba and Thurlow (1976). Such work would be immensely useful in verifying the assumptions underlying the use and design of Gonik type incentive schemes. Finally, it is necessary to conduct more research on actual implementations of the Gonik scheme such as that reported by Albers (1990).

Acknowledgment

The authors wish to thank Barton Weitz, Anne Coughlan, Alan Sawyer, John Lynch, Siinke Albers (editor of this Special Issue) and two anonymous reviewers for their help- ful comments on earlier versions of the paper.

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Analysis of a sales force incentive plan for accurate sales forecasting and performance