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European Accounting Review

Vol. 20, No. 2, 289– 319, 2011

A Theoretical Analysis of the Impact

of Adopting Rolling Budgets,

Activity-Based Budgeting and

Beyond Budgeting

STEPHEN C. HANSEN

Department of Accountancy, School of Business, The George Washington University, Washington,

DC, USA

(Received: February 2009; accepted April 2010)

ABSTRACT Budgeting accomplishes many goals in an organization and evaluating the

potential impact of a change is difficult. I investigate the organization-wide effects of

three distinct budgeting alternatives (rolling budgets, activity-based budgeting and

beyond budgeting) using a model that incorporates three important budgeting functions:

forecasting, operational planning and performance evaluation. From the perspective of

the whole organization, each budgeting alternative improves profits. I then examine the

department preferences for each alternative when each function is under the control of a

different department and each department has its own, department-specific performance

metric. Forecasting is judged on the variance of the base demand forecast, operational

planning on the expected unit capacity costs and performance evaluation on the

salesperson’s expected action. In my model all departments always favor rolling

forecasts, while only one department always favors beyond budgeting (or activity-based

budgeting). For beyond budgeting and activity-based budgeting, the preferences of the

two other departments vary depending upon the model parameters.

1. Introduction

Although budgeting is an important control system for most organizations

(Simons, 1995; Armstrong et al., 1996; Ekholm and Wallin, 2000), many managers are dissatisfied with their current systems and are actively considering

Correspondence Address: Stephen C. Hansen, Department of Accountancy, School of Business,

The George Washington University, 2201 G St. NW, Washington, DC, 20052, USA. E-mail:

shansen@gwu.edu

0963-8180 Print/1468-4497 Online/11/020289–31 # 2011 European Accounting Association

DOI: 10.1080/09638180.2010.496260

Published by Routledge Journals, Taylor & Francis Ltd on behalf of the EAA.

290

S. C. Hansen

changes (Comshare, 2001; Neely et al., 2001). One aspect of budgeting complicates the evaluation of potential alternatives. The budgeting system is used for

many different purposes,1 and each organization designs their system to

address its most important problems. For instance, a steel mill’s budgeting

process may focus on operational planning, whilst a telemarketing organization’s

process may focus on performance evaluation.

In parallel with the many different purposes of the budget, proposed budgeting

modifications/alternatives affect the different purposes (termed functions) in

different ways.2 This paper examines three distinct budgeting alternatives that

focus on changing different functions. Rolling budgets generate improved forecasts and change the forecasting function (Comshare, 2001; Serven, 2002).

Beyond budgeting switches employee compensation from budget-based to relative performance contracts (Ekholm and Wallin, 2000; Hope and Fraser, 2003)

and changes the performance evaluation function. Finally, activity-based budgeting increases the sophistication of the operational planning system (Ansari et al.,

1999; Hansen and Torok, 2004) and changes the operational planning function.

Since the budgeting system may perform multiple functions, and different

alternatives focus on changing different functions, an important question is:

How will introducing a specific budgeting alternative affect the individual functions of the organization? For instance, if rolling budgets improve the forecasting/planning function, will it lead to an improvement or a decline in the

operational planning function?

In addition to clarifying what each alternative actually achieves, the answer to

this question will provide guidance into the potential areas of resistance for

implementing these new alternatives. If forecasting, operational planning and

performance evaluation reside in different departments and each has their own

department-specific performance measure, then reducing the performance

measure of a particular department will create resistance to change. Anticipating

later results, conditional on the performance measures, all departments will favor

rolling budgets, while only one department will always favor beyond budgeting

(activity-based budgeting). The preferences of the remaining departments vary

depending upon the model parameters.

There are many potential approaches to analyzing this research question, from

empirical analysis to experiments. I use a stylized mathematical model as a

means of simplifying the setting and separating out the individual effects. I hybridize the newsvendor problem with the Linear-Exponential-Normal (LEN) model

with the added twist that production is non-negative. While my model is generic

and can be interpreted in many fashions, I believe that it captures the essence of

the budgeting process and the impact of the distinct budgeting alternatives.

In the model an organization produces and sells output in a competitive market.

Demand for the organization’s product contains two elements: sales generated by

external macroeconomic factors, termed base demand input; and sales generated

by the action of the salesperson, termed salesperson input. Both inputs combine

via a Cobb – Douglas production function to generate total demand. At the start of

Rolling Budgets, Activity-Based Budgeting and Beyond Budgeting

291

the period the organization decides how much information to purchase about the

upcoming base demand and then generates a base demand forecast. The base

demand forecast influences both the operational planning and performance evaluation functions. Each unit of output requires one unit of capacity, and at the start

of the period the organization uses the base demand forecast to determine the

amount of ‘hard’ capacity to purchase. Hard capacity is comparatively cheap,

but must be paid for even if unused. In addition, the organization uses the base

demand forecast to design the compensation contract for the salesperson. The

compensation contract can use two monitors of the salesperson’s action: an external signal of the salesperson’s action and an indirect measure based on total

output and the base demand forecast. Once the compensation contract is

signed, the salesperson decides how much effort to exert to generate sales.

After the salesperson’s effort is expended, total demand and the external signal

are observed. The organization can then purchase expensive additional ‘soft’

capacity to make up any capacity shortfall. Soft capacity can be purchased

when needed, but is more expensive than hard capacity. I assume that the

output is sufficiently lucrative that the organization always finds it profitable to

purchase soft capacity. Production now takes place, products are delivered and

the salesperson is paid.

The model, summarized in Figure 1, captures the essence of three important

functions of the budgeting process:

(a) a common forecast used in other functions (the base demand forecast),

(b) operational planning (the hard capacity decision) and

(c) performance evaluation (designing the salesperson’s compensation

contract).

Although my model operates at a high level and does not incorporate detailed

business processes or procedures, I can examine the effect of implementing each

budgeting alternative in an indirect fashion. The proponents of each budgeting

alternative have identified what they feel are the benefits of their approach. I

identify which of my model parameters will be changed by the proponent’s

stated benefits and then perform comparative statics on that parameter.

Each of the three budgeting alternatives could affect several parameters and I

pare down the list to one for each technique. Rolling budgets generate improved

forecasts and this is modeled as reducing noise in the base demand signals.

Activity-based budgeting increases the sophistication of the operational planning

system and generates greater flexibility in responding to unforeseen events,

modeled as reducing the cost of soft capacity. Finally, the beyond budgeting

approach involves changing the ways that employees are compensated and

thereby improving performance evaluation, modeled as reducing the noise in

the external signal.

I use three performance metrics to judge improvement in the individual functions. I will say that reducing the variance in the base demand forecast improves

292

S. C. Hansen

Figure 1. The organization’s choices and the causal links between functions.

forecasting, while reducing the unit cost of capacity improves operational planning. The performance evaluation function improves when there is an increase

in the salesperson’s effort. My research question is how each budgeting alternative (each comparative static) affects the individual performance measures for

each function.

My analysis shows that different budgeting alternatives lead to different effects

on the performance measures of the organization’s budgetary functions.

Conditional on the performance measures, all departments will favor rolling

budgets, while only one department will always favor beyond budgeting

(activity-based budgeting). The preferences of the other departments vary depending upon the model parameters.

The remainder of the paper proceeds as follows. Section 2 reviews related literature, while Section 3 presents the model. Section 4 derives the equilibrium.

The three budgeting alternatives are examined in Section 5, Section 6 discusses

empirical implications and Section 7 concludes.

2.

Related Literature

My analysis of the interaction between different budgeting functions (purposes)

is similar to research devoted to understanding the tradeoffs between the multiple

purposes of accounting information. One tradeoff is between the stewardship and

performance evaluation roles of accounting (summarized in Lambert, 2001, Sect.

3.3.5). My model has a similar conflict between using the accounting system to

Rolling Budgets, Activity-Based Budgeting and Beyond Budgeting

293

make decisions and reward employees, but I focus on how the tradeoff changes

with each budgeting alternative. The second tradeoff is between the pricing and

capacity planning decisions of organizations (surveyed in Balakrishnan and

Sivaramakrishnan, 2002). My model also examines the capacity decisions, but

adds in the performance evaluation dimension.

The link between performance evaluation and forecasting also has been

extensively addressed in the principal agent budgeting literature (surveyed in

Covaleski et al., 2003). My innovations are that I add in a capacity decision

and I examine the impact of budgeting alternatives on the performance of

individual functions.

3. The Model

My model is a hybrid between the newsvendor and LEN models with the added

feature that total output is non-negative. The details follow.

The organization is risk neutral and maximizes the value of revenues minus

all costs. The total amount of sales, Y, is determined by two inputs: Y1 is

the base input which reflects current economic conditions, while Y2 is the

salesperson’s input which captures the impact of the salesperson’s action.

Total sales are non-negative and are determined by the Cobb – Douglas production function

Y = Y1l1 Y2l2

(1)

where Y1 , Y2 . 0 and 1 . l1 , l2 . 0.

One important feature of the Cobb – Douglas production function is that taking

the natural log of each side generates a linear expression. In particular, taking the

log of both sides of (1) yields

y = l1 y1 + l2 y2

(2)

where y = ln(Y), y1 = ln(Y1 ) and y2 = ln(Y2 ). The linear transformation (2)

allows the information assumptions of the LEN model to be used on the log

inputs.

Turning to the individual sales components, the base demand input is lognormally distributed as Y1 = ey1 where y1 N( y1 , s2y1 ).

The salesperson’s input is more complex than the base demand input. The

salesperson takes action, a, which generates a stochastic log factor

y2 = a + d 2

where d2 N(0, s2y2 ).

Therefore, the salesperson’s input is log-normally distributed as Y2 = ey2 with

y2 N(a, s2y2 ).

294

S. C. Hansen

After the salesperson takes his action, the organization observes a noisy,

external signal of the action. Mathematically, the external signal is

ŷ2 = a + 12

where 12 is normally distributed with mean 0 and variance s212 . The measurement

error is independent of all other sources of error in the model.

Since the log variables are normally distributed, equation (2) shows that

the total demand, Y, is log-normally distributed as Y = ey with

y N(l1 y1 + l2 a, l21 s2y1 + l22 s2y2 ).

The timeline for the model is given in Figure 2. At the beginning of the period

the organization has the opportunity to purchase signals of the log of anticipated

base demand. The organization selects m signals, each with a cost of t . 0. Each

signal consists of the actual log base demand plus noise

ŷ1i = y1 + 11i

i = 1, . . . , m.

The noise terms, 11i , are independent and identically distributed normal variables with mean 0 and variance s211 . Using Bayes formula, the organization’s

forecast of log base demand, y1 , given the m signals is

E[y1 |ŷ1 , m] ; y1 +

Figure 2. The timeline.

ms2y1

(ŷ1 − y1 )

(ms2y1 + s211 )

Rolling Budgets, Activity-Based Budgeting and Beyond Budgeting

295

where ŷ1 = (1/m) m

i=1 ŷ1i . The log base demand forecast has a normal

distribution with mean y1 and variance ŝy21 (m) ; (s2y1 s211 )/ (ms2y1 + s211 ).

Since the log signals are multi-normally distributed, the variance of the conditional distribution [the base demand forecast] does not depend upon the

actual forecast ŷ1 .

The salesperson observes the number of signals, m, that the firm purchases,

but does not observe the base demand forecast. The assumption of unobservable

forecasts is made to ensure mathematical tractability.3

Given that m signals of log base demand have been purchased and observed

and that the salesperson selects action a, the distribution of the log of total

demand is normal, denoted f (y|ŷ1 , a, m), with mean

E[y| ŷ1 , a, m] ; l1 E[y1 |ŷ1 , m] + l2 a

and variance

s2y (m) ; l21

s2y1 s211

+ l22 s2y2 .

(ms2y1 + s211 )

After the total output has been observed, the value of the total output and the

forecast of base demand can be used to construct a second, indirect, measure of

the agent’s action. Specifically, the relationship y = l1 y1 + l2 y2 implies that an

alternate estimate of the salesperson’s log input y2 is

ỹ2 ; E[y2 |y, ŷ1 , m] =

y − l1 E[y1 |ŷ1 , m]

l2

which has a normal distribution with mean a and variance s2y (m)/l22 . Since the

indirect measure is constructed from the base demand forecast, it shares the

property that the variance of ỹ2 is independent of the value of the base demand

forecast ŷ1 .

Returning to the properties of the total output, the distribution f (y|ŷ1 , a, m)

describes the log of total output. However, the firm’s profits depend upon the

distribution of total output. The distribution of total output, Y, is

g(Y|ŷ1 , a, m) = ey(ŷ1 ,a,m)

where y(ŷ1 , a, m) N(E[y|ŷ1 , a, m], s2y (m)).

Every unit of demand is sold at price p . 0 and requires v . 0 dollars of variable costs. Each unit requires one unit of capacity in order to be produced.

Capacity is of two types: cheap, ‘hard’ capacity which is purchased at the start

of the period, and more expensive, ‘soft’ capacity which can be purchased

once demand is known.

296

S. C. Hansen

The organization chooses the amount of hard capacity, x, after observing the

base demand forecast. Each unit of hard capacity costs a, and therefore the

entire amount of hard capacity costs ax. If realized demand is greater than the

organization’s hard capacity, the organization can pay a premium to purchase

additional units of soft capacity. Each unit of soft capacity costs b, where

b . a . 0.4 In order to generate clear comparative statics, I assume that the

soft capacity is at least twice as expensive as hard capacity, specifically

b . 2a. In addition, I assume that the organization’s product is sufficiently

lucrative that it is always profitable to purchase soft capacity, that is,

(p − v − b) . 0.

In parallel with determining the amount of hard capacity, the organization

also designs a compensation contract for the salesperson, which has a structure

similar to the classic LEN model (Holmstrom and Milgrom, 1987; Feltham

and Xie, 1994).

The salesperson is risk averse with personal cost of effort C(a) = a2 /2 and a

negative exponential utility function of −e−rz , where r is the absolute risk aversion parameter and z is the salesperson’s net compensation. The salesperson’s

compensation contract uses an indirect measure inferred from the log of total

observed demand and the base demand forecast, ỹ2 , and a direct measure

provided by the external signal, ŷ2 .

Contracts are restricted to the linear form

s0 + s1 ỹ2 + s2 ŷ2

where s0 , s1 and s2 are constants chosen by the organization. The salesperson

must be paid a minimum expected net wage, w0 . Since the measurement error

in the external signal is uncorrelated with all other errors in the model, the covariance between the two measures is zero, cov(ỹ2 , ŷ2 ) = 0. After the salesperson has

observed the number of base demand signals, the joint distribution of the two

action measures is

ỹ2

ŷ2

⎛

⎛ 2

⎞⎞

sy (m)

0

a

2 ,

⎠⎠.

, ⎝ l2

Normal⎝

a

0,

s212

The salesperson observes the number of base demand signals and the compensation contract and then decides on their optimal action. The salesperson does not

see the base demand forecast before making their decision. The salesperson’s

action and base demand stochastically produce the organization’s realized total

demand. At that point, the organization purchases any necessary soft capacity,

produces and sells the products, observes the direct action measure (the external

signal), calculates the indirect action measure and pays the salesperson according

to the specified contract.

Rolling Budgets, Activity-Based Budgeting and Beyond Budgeting

297

4. Analysis

The solution concept is sub-game perfect Nash equilibrium and the model is

solved by working backwards from the end of the timeline.

Once the organization has selected the amount of data, m, and has observed the

signals of log base demand and generated the log base demand forecast, ŷ1 , it

determines the amount of hard capacity, the salesperson’s contract and

(indirectly) the salesperson’s action by solving the following program.

The Capacity and Contract Program

+1

x

(p−v)Yg(Y|ŷ1 ,a,m)dY +

max

x,s1 ,s2

−1

[(p−v− b)(Y −x)+(p−v)x]g(Y|ŷ1 ,a,m)dY

x

+1 +1 +1

(s0 +s1 ỹ2 (y, ŷ1 )+s2 ŷ2 )f (y, ŷ1 , ŷ2 |a,m)dydŷ1 dŷ2 − ax

−

−1 −1 −1

subject to

(a) the salesperson’s participation constraint

+1+1+1

exp(−r[s0 + s1 ỹ2 (y, ŷ1 ) + s2 ŷ2 − a2 /2])f (y, ŷ1 , ŷ2 | a, m) dy dŷ1 dŷ2

−

−1−1−1

≥ − exp(−rw0 ) and

(b) the salesperson′ s optimal action solves

+1 +1 +1

max −

exp(−r[s0 + s1 ỹ2 (y, ŷ1 ) + s2 ŷ2 − a2 /2])f (y, ŷ1 , ŷ2 | a, m)dy dŷ1 dŷ2 .

a

−1 −1 −1

4.1. The Capacity Decision Problem

Differentiating the Capacity and Contract Program objective with respect to x

provides the expression

+1

a = b

g(Y|ŷ1 , a, m) dY.

(3)

x

Equation (3) is the standard solution to the newsvendor problem with a twist

from the LEN model: the distribution of demand depends upon the salesperson’s

action, a.

298

S. C. Hansen

Using the properties of the normal and log-normal distribution, equation (3)

can be rewritten as

a

x = exp E[y|ŷ1 , a, m] + sy (m)F−1 1 −

b

(4)

where F(.) is the cumulative unit normal distrib …

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