Residual Income, Depreciation, and Empire Building Anil Arya Ohio State University Tim Baldenius ...

15 Pages·2003·0.03 MB·English

Residual Income, Depreciation, and Empire Building
Anil Arya
Ohio State University
Tim Baldenius
Columbia University
Jonathan Glover
Carnegie Mellon University
December 1999
1. Introduction
Residual income has received a great deal of recent attention in the practitioner and
academic literatures on performance evaluation. In the practitioner literature, residual
income often goes under the label of economic value added (Stewart, 1991). Assuming the
charge for capital used to calculate residual income is equal to the discount rate, the
discounted stream of residual income has the following properties. One, it does not depend
on accounting choices.1 Two, it is equal to the net present value (NPV) of the project.
However, local managers are often the source of project proposals, and these managers
may discount at a rate different than firm owners. In this case, a goal incongruence may
arise between managers and owners. The difference in discount rates also implies that
accounting choices matter. This opens the door for accounting choices to be used to
alleviate the goal incongruence.
Consider a typical textbook problem on residual income (e.g., Anthony and
Govindarajan, 1998, pp. 259-262). A project has an initial cash outflow followed by an
annuity of cash inflows. If a standard depreciation schedule is used (straight-line or
accelerated), the residual income of the project increases over time. This is because the
capital charge decreases over time and the depreciation charge decreases or remains
constant over time. The increasing residual income appears to indicate constantly
improving profitability, whereas there has actually been no real change in profitability after
the project has been undertaken.
A solution to the problem is to use annuity depreciation, which produces a constant
residual income in each year. In the constant cash inflow case, annuity depreciation is
decelerated. The capital charge is decreasing over time and an offsetting depreciation
charge increases over time. From an incentive perspective, annuity appreciation has the
particularly appealing property that the present value of the residual income is positive if
1 By accounting choices, we mean those that affect the timing of income recognition but
not the total amount of income recognized over the firm's life.
2
and only if the NPV of the project is positive, regardless of the manager's discount rate
(Reichelstein 1997, Rogerson 1997). However, annuity depreciation is rarely used in
practice (Reece and Cool, 1978). In this paper, we provide one possible explanation for
the use of non-annuity and, in particular, non-decelerated depreciation. When used in
conjunction with residual income, non-decelerated depreciation curbs the manager's
tendency for empire-building.
Agency costs have been used to explain many observed institutional practices. For
example, a manager's desire to consume perquisites can make it optimal for a budget center
to use a hurdle rate higher than the firm's cost of capital in evaluating projects (Antle and
Eppen, 1985). Other traits of managers can lead to agency problems. For example, the
manager may have a preference for large projects--he may want to build an empire
(Berkovitch and Israel, 1998; Harris and Raviv, 1996; Jensen, 1986; Mueller, 1969; Stulz,
1990). Also, managers sometimes exhibit a short-term orientation/impatience
(Reichelstein, 1997; Zimmerman, 1995).
In our model, the manager prefers larger projects to smaller projects and has a
higher discount rate than the firm's cost of capital. The former reflects the manager's
tendency to empire-build; the latter reflects the manager's impatience. The reason for the
manager's higher discount rate could be that, relative to firm owners, his access to capital
markets is more constrained and/or he faces an exogenous probability of changing jobs
each period (a horizon problem).2
Empire building introduces a force that has the manager accepting some negative
NPV projects. The optimal depreciation schedule is chosen so as to introduce a
counterbalancing force. Because of his impatience, the manager place a greater weight on
the first-period (relative to the second-period) residual income than does the firm's owner.
2 Suppose the manager and the firm owner both discount future cash flows at the rate r,
but the manager retains his job with probability p in each period. Then the manager
effectively discounts future compensation (associated with retaining his job) at a rate of
(1+r)/p - 1, which is greater than r.
3
By choosing a depreciation schedule that makes the first-period residual income less than
the second-period residual income, the value of the residual income stream when
discounted by the manager declines. The optimal depreciation schedule is chosen so that
the decline in discounted residual income for the agent exactly offsets his benefit from
empire-building. That is, one managerial trait (impatience) is used to keep another trait
(empire building) in check. When the manager's desire to empire build is strong enough,
the optimal depreciation schedule is non-decelerated. When projects are independent, this
results in the manager undertaking a project if and only if its NPV is positive. In the case
of mutually exclusive projects, the manager undertakes the project with the highest
(positive) NPV.
Our focus is on the use of an accounting instrument, depreciation. According to
Davidson (1957), "[d]epreciation is probably the most discussed and most disputatious
topic in all accounting." Depreciation is traditionally viewed as a way of matching
expenses with revenues (Paton and Littleton, 1940). Other views include depreciation as a
reserve for asset replacements, as matching physical deterioration, and as a statistic for an
unknown long-run variable (Brief and Owen, 1970; Sunder 1997). In this paper, we
develop a view of (non-decelerated) depreciation as a way of introducing a bias to counter
managers' empire-building tendencies. The idea that accounting conventions can be used
to offset undesirable managerial traits is not new. For example, conservatism is often
discussed as a way of countering managers' tendency toward optimism.
Non-accounting instruments can also be used to achieve goal congruence. We also
study how depreciation can be used in conjunction with other instruments (capital charge
and the scale of production) to achieve goal congruence in models of adverse selection.
The remainder of the paper is organized into four sections. Section 2 presents the
model. The main result is presented in Section 3. Section 4 studies an extension. Section
5 concludes the paper.
4
2. Model
Consider a firm whose participants are a risk-neutral principal (owner) and a risk-
neutral agent (manager). The firm faces a two-period investment opportunity with an initial
investment of I and a cash inflow of c at the end of each period. There is uncertainty
_
regarding c. It is common knowledge that c is drawn from the interval [c_,c], with a
probability distribution function f(c).
All cash in- and outflows are received (issued) directly by the principal. The
agent's compensation is assumed to be proportional to residual income. Denote by d and
(1-d) the depreciation rate in period one and period two, respectively, 0 ≤ d ≤ 1. In period
one, residual income is RI = c - dI - r I; in period two, it is RI = c - (1-d)I - r (1-d)I. In
1 p 2 p
the expression for residual income, the first term is the cash revenue, the second term is the
depreciation expense, and the third term is the capital charge computed using the principal's
discount rate r . Residual income is computed (and compensation is paid) at the end of
p
each period using the actual cash flows.
The sequence of events is as follows. First, the agent privately observes c.
Second, the agent decides whether or not to undertake the project.3 Third, if the agent
decides to undertake the project, the principal provides funding of I. Finally, c is realized
at the end of periods one and two.
The principal would like the agent to undertake the project if and only if its net
present value (NPV) is non-negative. That is, the agent should undertake the project if and
only if -I + c(1+r )-1 + c(1+r )-2 ≥ 0. To make the problem interesting, we assume the
p p
_
NPV computed at c_ is negative and at c is positive.
The agent's preferences over projects are given by RI (1+r )-1 + RI (1+r )-2 + eI.
1 a 2 a
The first two terms are the present value of residual income computed using the agent's
3 We have assumed that the decision rights for project approval reside with the agent.
Given the compensation arrangement and the fact that the agent can misstate the future
cash flows associated with the project, this setting is equivalent to one in which the
agent proposes projects and the principal makes project approval decisions.
5
discount rate, r . The last term reflects the fact that the agent derives utility from the size of
a
the project--the agent is an empire-builder. e is the agent's marginal rate of substitution of
size for discounted residual income. A higher value of e implies that the agent is more of
an empire-builder. The principal knows the agent's characteristics e and r .
a
There are two reasons the agent may choose to accept or reject projects differently
than the principal would. First, because of taste for empire building, the agent is willing to
accept some negative NPV projects. Second, the agent's discount rate r is greater than the
a
principal's discount rate r --the agent is impatient. The question we ask is: is it possible to
p
use the accounting instrument of depreciation to induce goal congruence between the
principal and the agent?
3. Result
Consider two benchmark cases.
No empire building (e = 0)
With e = 0, the only reason the principal and the agent value projects differently is
because of their different discount rates. If r = r , the present value of residual income is
a p
equal to the NPV of the project and is free of the depreciation choice. If r ≠ r , goal
a p
incongruence can be eliminated by an appropriate choice of depreciation. The trick is to
choose a depreciation schedule that produces a constant residual income, RI = RI . The
1 2
depreciation schedule that achieves this objective is called annuity depreciation (or relative
benefit depreciation). Annuity depreciation ensures that the residual income in each period
is positive if and only if the project has a positive NPV. Hence, the discount rate becomes
irrelevant (Reichelstein, 1997; Rogerson, 1997).
Observation 1. In the absence of empire building, goal congruence can be
1
achieved by setting d = .
2+r
p
6
Two comments. First, in the case of constant cash inflows, the optimal
depreciation schedule is decelerated (d < 1/2). Second, the depreciation schedule does not
_
depend on r , c_, c, or f(c).
a
No managerial impatience (r = r )
a p
With r = r , the only reason the principal and the agent value projects differently is
a p
because of the agent's tendency to empire-build. The present value of residual income is
independent of depreciation choice. Hence, for all depreciation schedules, the agent's
utility for a project is NPV + eI. Now, the agent will take on all projects with a NPV of -eI
and above.
Observation 2. In the case of identical discount rates, goal congruence cannot be
achieved by the choice of depreciation method.
Empire building and managerial impatience (e > 0 and r > r )
a p
We now return to the case that the agent is both an empire-builder and impatient.
Our result is that goal congruence can sometimes be achieved by using a depreciation
schedule that is more accelerated than annuity depreciation. The idea is to curb the agent's
empire-building tendency by designing a depreciation schedule that exploits his impatience.
One undesirable trait of the agent is used to keep his other undesirable trait in check.
_
Proposition. For all e, 0 ≤ e ≤ e, goal congruence can be achieved by setting
1 e(1+r )2 _ (r -r )(1+r )
d = d* = + a , where e = a p p .
2+r (r -r ) (1+r )2(2+r )
p a p a p
Proof of the Proposition. Denote the value of c for which the project has a
zero NPV by c*. c* is the solution to the equation -I + c(1+r )-1 + c(1+r )-2 = 0. Hence,
p p
c* = I(1+r )2(2+r )-1.
p p
7
Goal congruence is achieved if the agent also uses c* as the cutoff in making
investment decisions, i.e., the agent's utility is positive if c > c* and negative if c < c*.
The optimal depreciation rate, d*, is chosen such that the agent's utility is 0 when c =
c*. d* is the solution to the equation [c* - dI - r I](1+r )-1 + [c* - (1-d)I - r (1-
p a p
d)I](1+r )-2 + eI = 0. Substituting for c* and solving for d yields d*. As e increases,
a
so does d*. The upper bound on e is the value of e at which d* = 1.
The optimal depreciation rate is made up of two parts. The first part is the annuity
depreciation rate. The second part is an adjustment to curb the agent's empire building
tendencies. This part is free of distributional assumptions but, unlike annuity depreciation,
does depend on r (and e).
a
As the agent's desire to empire build increases, the depreciation schedule becomes
more accelerated. The intuition for the result is as follows. Empire building introduces a
force that has the agent accepting projects more often than the principal would. The
depreciation schedule is chosen so as to introduce a counterbalancing force, one that has the
agent rejecting projects more often than the principal would. Because of his impatience, the
agent values the first-period residual income relative to the second-period residual income
more than the principal does. By choosing a depreciation schedule that makes the first-
period residual income less than the second-period residual income, the value of the
residual income stream, when discounted by the agent, declines. The optimal depreciation
schedule is chosen so that the decline in discounted residual income for the agent exactly
offsets his benefit from empire-building.
The upper bound on e reflects the requirement that depreciation be nonnegative in
each period (0 ≤ d ≤ 1). If we allowed for depreciation greater than the initial investment in
period one and negative depreciation in period two, goal congruence could always be
achieved.
8
Not surprisingly, if the agent's tendency to empire-build is large enough, the
optimal depreciation method is non-decelerated (d ≥ 1/2).
(r -r )r (r -r )(1+r )
Corollary 1. For all e, a p p < e < a p p , the depreciation
2(1+r )2(2+r ) (1+r )2(2+r )
a p a p
schedule that achieves goal congruence is non-decelerated.
Proof of Corollary 1. The upper and lower bounds on e are found by
equating the expression for d* to 1/2 and 1, respectively, and solving for e.
Mutually exclusive projects
So far we have considered the case of a single investment opportunity. Clearly,
multiple projects that are independent can be dealt with in the same way. As it turns
out, even if projects are mutually exclusive, the depreciation rate proposed in the
proposition leads to goal congruence. That is, the agent undertakes the project with the
highest (positive) NPV.
_
Corollary 2. For all e, 0 ≤ e ≤ e, the agent's utility is linearly increasing in the
NPV of the project if d = d*.
Proof of Corollary 2. The agent's utility is [c - dI - r I](1+r )-1 + [c - (1-
p a
d)I - r (1-d)I](1+r )-2 + eI . Plugging d = d* into this expression yields:
p a
2+r 1+r
( a) ( p)2 NPV.
2+r 1+r
p a
Varying depreciation and the capital charge
So far in the paper, we studied the role of depreciation in achieving goal
congruence. There are other instruments that can be used. For example, the capital charge
can be varied. Ewert and Wagenhofer (pp. 528-532, 1997) curtail an agent's empire-
building tendency by using a capital charge higher than the principal's discount rate. We
9
do not wish to single out any single instrument. In general, depreciation can be viewed as
one in a portfolio of instruments that can be used to curb empire building.
While in the previous setting, cost of capital could also be used to achieve goal
congruence, there are settings in which having multiple instruments available is critical.
We present an example in which both the capital charge and depreciation can be varied.
For the particular setting studied, the unique optimal choice of these two instruments is to
compute the capital charge at the principal's discount rate and to use the depreciation rate
given in the proposition.
Suppose there are two types of agents. A type 1 agent has the same preferences as
the principal--he discounts at the same rate as the principal and is not an empire-builder. A
type 2 agent is the same as in the previous section of the paper--he is impatient and an
empire-builder. The principal does not know the agent's type.
Here, we give the principal the flexibility of choosing both the capital charge, k,
and the depreciation rate, d. The principal's objective is to maximize the expected NPV of
the project subject to the constraints that the cutoffs c and c the principal intends a type 1
1 2
and type 2 agent to implement are incentive compatible. The only other constraints are that
depreciation be a proper allocation scheme and that the cutoffs are within the set of possible
cash inflows.
_
Corollary 3. For all e, 0 ≤ e ≤ e, goal congruence can be achieved if and only if
the principal sets k = r and d = d*.
p
Proof of Corollary 3. The best the principal can do is to implement c = c
1 2
= c*. Suppose the principal sets k = r and d = d*. Because a type 1 agent discounts at
p
r , the present value of residual income is invariant to depreciation and is equal to the
p
NPV of the project. Setting c = c* is incentive compatible for a type 1 agent. From
1
_
the Proposition, we know that as long as e < e, it is also incentive compatible for a type
2 agent to set c = c*.
2