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Performance-based bonuses for investment and abandonment decisions
Accepted Manuscript
Performance-based bonuses for investment and abandonment decisions Hwa-Sung Kim PII: DOI: Reference:
S1544-6123(16)30044-7 10.1016/j.frl.2016.04.009 FRL 508
To appear in:
Finance Research Letters
Received date: Revised date: Accepted date:
26 September 2015 23 March 2016 3 April 2016
Please cite this article as: Hwa-Sung Kim, Performance-based bonuses for investment and abandonment decisions, Finance Research Letters (2016), doi: 10.1016/j.frl.2016.04.009
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Highlights • We derive optimal performance-based bonuses for investment and abandonment decisions
decisions
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• Compensation optimal for investment generates agency confliicts in abandonment
• Shareholders should adjust the bonus contract for investment to mitigate any agency problems in the abandonment decision
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CE
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bonus for abandonment decisions
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• Managers are concerned only with their effort costs if they receive the optimal
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Performance-based bonuses for investment
Hwa-Sung Kim†
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March 2016
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and abandonment decisions∗
Abstract
This paper examines whether a performance-based bonus for a manager’s invest-
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ment influences her abandonment decision. First, we derive optimal performancebased bonuses for investment and abandonment decisions. Second, we show that
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there could be a discrepancy between the managers abandonment timing and that of the shareholders, even though an appropriate performance-based bonus
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was compensated to mitigate agency conflicts in the investment decision. Third, we also show that as long as the manager is contracted to receive the optimal
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performance-based bonus for the abandonment decision, only the effort costs that she incurs affect the abandonment timing.
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Keywords: Real option; Investment decision; Abandonment decision; Agency problem; Performance-based bonus JEL classification: D81; D86; G31; J33
∗
I would like to the anonymous reviewer, Scott Erdahl, and Brian Lucey (the editor) for their valuable and helpful comments. This work was supported by the National Research Foundation of Korea Grant funded by the Korean Government (NRF-2014S1A5A2A01017497). † School of Management, Kyung Hee University, 26 Kyungheedae-ro, Dongdaemun-gu, Seoul, 02447, Korea. Phone: +82-2-961-0499, E-mail: [email protected].
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1
Introduction
In the literature on corporate decision making, researchers tend to pay consistent attention to the latest findings on both investment and abandonment options. The reason for this consistent attention is that these two real options are associated with the beginning
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and the end of decision-making for a firm’s investment (e.g., Brennan and Schwartz, 1985). Moreover, the identity of the investment and abandonment decision-maker is important to consider. The firm’s decision-making is delegated to the manager with a special knowledge of investment projects. However, agency conflicts exist, that is, a
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manager does not always pursue the interest of the shareholders when making investment and abandonment decisions (e.g., Jensen, 1986; Berger et al., 1996). To attenuate agency conflicts, the shareholders utilize several mechanisms, for example, an appropriate compensation package.
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While much research deals with the impact of the agency problem on the investment decision, there are relatively few studies that examine the influence of agency conflicts
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on the abandonment decision.1 Recently, several papers examine this subject and draw various results. For instance, Morellec (2004) demonstrates that overinvestment by the
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manager results in late abandonment when she has the control rights over the abandonment policy. Lambrecht and Myers (2007) show that late abandonment is caused by the
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manager’s reluctance to relinquish her rents. This paper is motivated by the following question: is compensation for alignment in
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investment decisions still effective in mitigating agency conflicts when the manager makes the abandonment decision? As stated previously, existing papers show that overinvestment by the manager or unwillingness to relinquish managerial rents is an important factor in affecting the manager’s abandonment decision-making. In addition to these 1
Recent examples of research on an abandonment option of a firm include the firm’s risk management behavior (Wong, 2006) and operating leverage (Wong, 2009) in the presence of abandonment options. However, these papers do not consider agency conflicts between the shareholders and the manager.
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factors, we examine whether the manager’s abandonment decision is influenced by the compensation for the investment decision. Our examination, as in the Cardoso and Pereira (2015) model, considers a performance-based bonus as compensation dependent on the state of the investment revenue.
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In this paper, we show that the performance-based bonus for the manager to induce compliance with the investment timing of the shareholders is not effective in mitigating agency conflicts when the abandonment decision is made. This implies that to align the manager’s abandonment timing with that of the shareholders, the performance-based bonus should be adjusted once the investment is made.
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The remainder of this paper is organized as follows: the following section presents the model to derive the optimal performance-based bonus as well as the investment and abandonment thresholds. Section 3 examines how executive compensation is related to
The model
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2
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investment and abandonment timing. Section 4 concludes the paper.
To develop a model where the performance-based bonus is linked to the investment
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and abandonment decisions, we extend a traditional real-options model (e.g., Dixit and
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Pindyck, 1994). Consider a firm with both investment and abandonment options. The firm can exercise the investment option by paying a fixed cost of I. After the investment
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option is exercised, the firm obtains revenue R by incurring a fixed production cost C per unit of time.2 Once the investment is made, the firm’s revenue evolves as follows:
dR = µRdt + σRdW (t),
(1)
2 We can consider the revenue subtracted from the production cost as a project value as in Dixit and Pindyck (1994).
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where µ is the growth rate of the revenue, σ is the volatility of the revenue, and W (t) is a standard Brownian motion at time t. Here, µ and σ are constant. The firm’s operating profit, which is the revenue minus the production cost, is taxed at rate τ . Let r be the risk-free rate that is greater than the growth rate of the revenue.
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The shareholders hire a manager to invest effectively. However, the investment is not verifiable and so it is likely that the manager will choose the investment timing so as to maximize her wealth. As in Cardoso and Pereira (2015), we assume that the shareholders compensate the manager for implementing the investment with a fixed wage, w per unit of time as well as a performance-based bonus, the payment of which is a proportion φ (0
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≤ φ ≤ 1) of an after-tax operating profit. As in a standard principal-agent model (e.g., Holmstrom and Milgrom, 1987, 1991), this paper considers the linear contract for the manager. Although we do not consider the general type of the managerial compensation, a linear contract is a good approximation for nonlinear contracts (e.g., Jin, 2002). Under
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the linear sharing rule between the manager and the shareholders, this paper focuses on the impact of performance-based bonuses on both the investment and abandonment
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decisions.
While implementing the investment, the manager incurs an effort cost, e per unit of
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time, until the abandonment decision is made. Additionally, we assume that the manager leaves or loses her current job and receives severance pay, s, when the abandonment
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option is exercised. In the next subsection, we first investigate the optimal proportion
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of the performance-based bonus when the abandonment decision is made.
2.1
Abandonment decision
First, we examine the abandonment threshold chosen by the manager. The wealth of the manager consists of a wage and a performance-based bonus, excluding effort costs. Before the abandonment decision is made, the value of the managerial wealth, W (R), 5
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satisfies the following equation: 1 2 2 ∂ 2W ∂W σ R − rW + φ(R − C)(1 − τ ) + w − e = 0. + µR 2 2 ∂R ∂R
(2)
According to Dixit and Pindyck (1994), we obtain the general solution for the value of
W (R) = A1 R
β1
+ A2 R
β2
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the managerial wealth as follows:
R C w−e +φ − (1 − τ ) + , r−µ r r
(3)
where A1 and A2 are constants to be determined, and the constants β1 and β2 are as
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follows:
β2
1 µ = − 2− 2 σ
s
1 µ − 2 2 σ
1 µ − 2 2 σ
2
2
+
2r , σ2
(4)
+
2r . σ2
(5)
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β1
1 µ = − 2+ 2 σ
s
Note that β1 exceeds unity, and β2 is negative. The general solution must satisfy the fol-
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lowing three boundary conditions: (i) limR→∞ W (R)/R < ∞ (no-bubble condition); (ii) M M M ) = s (value-matching condition at RA ); (iii) W 0 (RA ) = 0 (smooth-pasting conW (RA
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M M dition at RA ), where RA represents the abandonment threshold at which the manager’s
wealth is maximized. The first condition implies that the coefficient A1 in equation (3)
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must be zero. The second condition represents the severance pay for the manager when the abandonment option is exercised. The third condition demonstrates that the manager chooses the abandonment threshold to maximize her wealth rather than that of the shareholders. After some calculations, we obtain the abandonment threshold chosen by
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the manager as follows: M RA
−β2 r − µ φC w−e = (1 − τ ) − +s . 1 − β2 φ(1 − τ ) r r
(6)
When the manager controls the abandonment decision, her wealth is R C w−e +φ − (1 − τ ) + , r−µ r r
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W (R) = AO
M
M (R; RA )
(7)
where AOM represents the value of the abandonment option when the manager is in control. AOM is given by M (R; RA )
M β2 RA C R w−e −φ − (1 − τ ) . = s− M r r−µ r RA
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AO
M
(8)
Next, to examine how different the manager’s abandonment timing is from the share-
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holders’s abandonment timing, we consider the shareholders’ abandonment threshold.
following equation:
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Before the investment is abandoned, the value for the shareholders, V (R) satisfies the
(9)
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∂V 1 2 2 ∂ 2V σ R + µR − rV + (1 − φ)(R − C)(1 − τ ) − w = 0. 2 2 ∂R ∂R
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The general solution to equation (9) is given by
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V (R) = B1 R
β1
+ B2 R
β2
R C w + (1 − φ) − (1 − τ ) − , r−µ r r
(10)
where B1 and B2 are constants to be determined. The wealth of the shareholders equals
the value of the abandonment option plus the present value of the after-tax operating profit net of the performance-based bonus minus the present value of the fixed wage, which is a cost to the shareholders until the investment is abandoned. We also consider
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the investment to be partially reversible. If the notation θ (0 ≤ θ ≤ 1) denotes the degree of the reversibility of the investment, the shareholders can recover a partial amount of θI.3 The boundary conditions to solve equation (10) are (i) limR→∞ V (R)/R < ∞ S S (no-bubble condition); (ii) V (RA ) = θI − s (value-matching condition at RA ); (iii) S S S V 0 (RA ) = 0 (smooth-pasting condition at RA ), where RA denotes the abandonment
(10) into the three boundary conditions delivers S (R; RA )
C w R − (1 − τ ) − , + (1 − φ) r−µ r r
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V (R) = AO
S
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threshold at which the value for the shareholders is maximized. Substituting equation
(11)
where AOS represents the value of the abandonment option under the control of the shareholders. The abandonment option value is given by S (R; RA )
β2 S C w R RA − (1 − τ ) + . = θI − s − (1 − φ) S r−µ r r RA
(12)
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AO
S
The abandonment threshold chosen by the shareholders is
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r−µ (1 − φ)C w −β2 (1 − τ ) + + θI − s . = 1 − β2 (1 − φ)(1 − τ ) r r
(13)
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S RA
Equation (13) shows that the abandonment threshold increases with the degree of re-
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versibility, θ. We observe that the abandonment threshold also rises with the amount of wage, w, but it decreases with severance pay, s.
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We derive the optimal proportion for a performance-based bonus to align the man-
ager’s abandonment threshold with that of the shareholders. Proposition 1. To induce the manager to choose the abandonment threshold of the shareholders, the shareholders should compensate the manager with a performance-based 3
We can include the case where the investment is irreversible if θ is set to be zero.
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bonus by the proportion φ∗A : φ∗A =
rs − w + e . rθI + e
(14)
Proof. Equating equation (6) to equation (13) delivers the optimal proportion of the
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performance-based bonus. The proportion φ∗A represents the optimal performance-based bonus for alignment between both parties in the abandonment decision. Note that the optimal proportion φ∗A is similar to the proportion derived by Cardoso and Pereira (2015) in that the proportions are determined by the manager’s wage and effort cost. Equation (14) shows that φ∗A is
2.2
Investment decision
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also affected by severance pay and the degree of reversibility of the investment.
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We investigate the performance-based bonus to mitigate agency conflicts when the manager makes the investment decision. The firm has an investment option, which is worth
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F (R). As in the case of the abandonment decision, we also consider the investment decisions made by both the manager and the shareholders. We first derive the invest-
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ment threshold under the manager’s control. Before the investment decision is made,
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the value of the investment option satisfies the following equation: ∂F 1 2 2 ∂ 2F σ R + µR − rF = 0. 2 2 ∂R ∂R
(15)
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The general solution of equation (15) is F (R) = C1 Rβ1 + C2 Rβ2 ,
(16)
where C1 and C2 are constants and can be determined by the three boundary conditions: (i) limR→0 F (R) = 0; (ii) F (RIM ) = W (RIM ); (iii) F 0 (RIM ) = W 0 (RIM ), where RIM denotes 9
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the investment threshold at which managerial wealth is maximized. The first condition implies that the investment option value becomes worthless if the revenue approaches zero. The equation for the investment threshold chosen by the manager is:
(17)
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C 1 φ(1 − τ ) M β2 w−e M 0= 1− RI + 1 − AOM (RIM ; RA ) − φ (1 − τ ) + , β1 r−µ β1 r r
where AOM is given by equation (8). We can calculate numerically RIM in equation (17). Next, we derive an equation for the investment threshold chosen by the shareholders, RIS , if we replace the boundary conditions (ii) and (iii) with the following two equations:
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(ii0 ) F (RIS ) = V (RIS ) − I and (iii0 ) F 0 (RIS ) = V 0 (RIS ). Analogously, the equation for the investment threshold chosen by the shareholders is given as
w β2 C 1 (1 − φ)(1 − τ ) S S RI + 1− AOS (RIS ; RA )−(1−φ) (1−τ )− −I, (18) 0 = 1− β1 r−µ β1 r r
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where AOS is provided in equation (12). From equation (18), RIS can be calculated
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numerically.
We derive the optimal proportion of the performance-based bonus that allows for
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alignment between both parties in the investment decision. Proposition 2. Let φ∗I be the proportion of the performance-based bonus to match the
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manager’s investment threshold to the shareholders’ investment threshold. By the following system of equations, we obtain the proportion φ∗I : β1 −1 φ∗I (1−τ ) ∗ RI β1 r−µ
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0= 0=
β1 −β2 β1
M AOM (RI∗ ; RA ) − φ∗I Cr (1 − τ ) + w−e , r β1 −1 (1−φ∗I )(1−τ ) ∗ S 2 RI + β1β−β AOS (RI∗ ; RA ) − (1 − φ∗I ) Cr (1 − τ ) − β1 r−µ 1
+
w r
(19) − I.
Proof. We can find the proportion φ∗I of the performance-based bonus for the manager by setting RIM and RIS equal to RI∗ in equations (17) and (18).
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From the perspective of the shareholders, the proportion φ∗I represents the optimal performance-based bonus in the investment decision. The investment threshold RI∗ associated with φ∗I represents the optimal investment threshold. We draw some implications on the relationship between a performance-based bonus and the abandonment timing
3
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using the two propositions.
The effects of performance-based bonus on aban-
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donment decisions
This section investigates the relationship between a performance-based bonus and investment and abandonment decisions. We select the following parameter values as the base case: C = $0.75, I = $5, θ = 0.5, τ = 20%, r = 5%, µ = 3%, σ = 25%, w = 0.04, e = 0.15, and s = 0.2.4 First, we examine the optimal proportions of the
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performance-based bonus, φ∗I and φ∗A in the base case.
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[Table 1 is about here]
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Panel A of Table 1 shows that in the base case, the shareholders should establish a performance-based bonus that provides approximately 26% of the operating profit to tie
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the manager’s investment timing to that of the time at which they want to invest. On the contrary, once an investment is made, if the shareholders want to induce the man-
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ager to select their optimal abandonment time, then they should compensate her with approximately 44% of the operating profit. Importantly, a discrepancy in abandonment S M timings between the shareholders (RA = 0.224) and the manager (RA = 0.296) may
occur if the shareholders maintain the performance-based bonus at around 26% of the 4
We select base-case parameter values similar to Mauer and Sarkar (2005).
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operating profit until the abandonment decision is made. Based on this analysis, we obtain the following implication. Implication 1. Although the shareholders provided the appropriate performance-based bonus to align their investment timing with that of the manager, the performance-based
the shareholders want to abandon the investment.
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bonus should be adjusted so as to match the manager’s abandonment timing to the time
Additionally, similar to Cardoso and Pereira (2015), Panel B of Table 1 shows that the changes in µ and σ do not affect the optimal proportion of the performance-based
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bonus for the abandonment decision, that is, φ∗A takes the value of 0.436 irrespective of the values of µ and σ.
Furthermore, we observe the impacts of the manager’s effort cost, fixed wage, and severance pay on the abandonment timing. To do so, we determine the abandonment
threshold at φ∗A :
rθI + e −β2 r − µ C (1 − τ ) + , = 1 − β2 1 − τ r r
(20)
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∗ RA
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threshold at φ∗A . Substituting equation (14) into equation (6) delivers the abandonment
∗ where RA denotes the optimal abandonment threshold. Equation (20) shows that if
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the shareholders provide φ∗A proportion of the performance-based bonus, the optimal abandonment threshold becomes irrelevant to the levels of the manager’s wage and
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severance pay. The manager is concerned only with effort costs when the abandonment
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decision is made. We confirm this from Panel B of Table 1. Implication 2. If the shareholders compensate the manager with the performance-based bonus to align their abandonment timing with that of the manager, the manager is concerned only with the effort costs when making the abandonment decision. However, if the proportion of the performance-based bonus is held at φ∗I until the abandonment decision is made, the manager makes an abandonment decision that de12
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viates from what the shareholders wish. To explain in more details, it is worth comparing the abandonment thresholds in two cases. The first is when there are managershareholder conflicts. The second is when the manager acts in the interests of the shareholders in abandonment decision-making.
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First, we examine the abandonment decision in the presence of agency conflicts. M The abandonment threshold, RA of equation (6), represents the manager’s optimal
abandonment threshold in her best interest. We expect several relationships between the manager’s optimal abandonment decision and her wage and severance pay. As the level of her wage is higher, the manager tends to delay abandonment. This is because the
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manager prefers late abandonment to enjoy the high level of wage as much as possible. We support this inference by the following comparative static:
M ∂RA ∂w
< 0. Additionally,
holding other variables fixed, a high level of severance pay induces the manager to abandon early because she wants to enjoy the high level of severance pay as soon as
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possible. We also confirm this relationship by the comparative static:
M ∂RA ∂s
> 0.
∗ when Second, we investigate the result concerning the abandonment threshold, RA
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the manager acts in the best interests of the shareholders. This case implies that the manager does not pursue her own private benefits when making the abandonment de-
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cision. This is because the optimal performance-based bonus, φ∗A of equation (14) is contracted, which leads to an alignment between the abandonment decisions of the
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manager and the shareholders. Each combination of wage or severance pay determines an optimal level of performance-based bonus accordingly so that the manager makes
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an abandonment decision in the shareholders’ interests. For example, we confirm from equation (14) that a low wage and a high performance-based bonus balance out:
∂φ∗A ∂w
< 0.
Therefore, the manager is not concerned with her level of wage or severance pay when making the abandonment decision as long as the optimal performance-based bonus, φ∗A
is contracted. In contrast, the manager’s effort cost affects the abandonment threshold
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even in the absence of manager-shareholders conflicts. As with the fixed wage and severance pay, the optimal performance-based bonus is affected by the effort costs. Moreover, the manager’s effort costs do not influence the shareholder’s value of equation (9) but do influence the managerial wealth of equation (3). Additionally, because the shareholders provide the manager with the optimal performance-based bonus, they share the same
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∗ abandonment threshold, RA , which is affected by the values of both parties. Conse∗ quently, the agreed abandonment threshold, RA , becomes a function of the manager’s
effort costs when there is no agency problem.
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[Table 2 is about here]
Up to now, we have examined the optimal performance-based bonuses for the investment and abandonment decisions. We have shown that the shareholders should adjust the optimal performance-based bonus associated with the investment decision
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in order to match the manager’s abandonment timing to their optimal abandonment timing. We consider an alternative case where the shareholders provide the identical
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performance-based bonus for both the investment and abandonment decisions without
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any adjustment to the bonuses.5
To mitigate the agency conflicts in both decisions, suppose that the shareholders
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are willing to choose an equally weighted average of two optimal performance-based bonuses associated with each decision. Let φmid denote the equally weighted average of
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φ∗I and φ∗A . At φmid , the shareholders’ and the manager’s investment (abandonment) S,mid M,mid ) and RIM,mid (RA ). Since φ∗A is greater than thresholds are denoted by RIS,mid (RA
φ∗I , φmid is greater than φ∗I . Therefore, this average of the optimal performance-based bonuses will be more effective when the shareholders consider stronger inducements to the manager to commence the investment. We confirm this from the observation that 5
I am thankful to the reviewer for suggesting this alternative case.
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the equally weighted average of the two optimal performance-based bonuses, φmid leads to early investment by the manager relative to the optimal investment threshold, that is, RIM,mid is lower than RI∗ . Moreover, the equally weighted average of the two optimal performance-based bonuses, φmid induces the manager to choose the abandonment M,mid M ∗ threshold, RA , that is closer than RA to the optimal abandonment threshold, RA .
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Table 2 shows that the average of the optimal performance-based bonuses reduces the gap between the abandonment thresholds chosen by the shareholders and the manager. S,mid M,mid ∗ M In the base case, at φmid , RA and RA are 0.232 and 0.262, whereas RA and RA
are 0.243 and 0.296, respectively. From Table 2, we also obtain the following results: the
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S,mid M,mid difference between the two thresholds, RA and RA at φmid is smaller as the fixed
wage is higher or severance pay is lower. The difference in the two thresholds declines
4
Conclusion
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as the effort costs are lower.
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This paper demonstrates that even compensation that is optimal for aligning the investment timing between the shareholders and the manager could lead to a conflict in
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abandonment timing. We show that although the shareholders compensate the manager with an appropriate performance-based bonus for the alignment in the investment de-
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cision, they should adjust the performance-based bonus to mitigate agency conflicts in the abandonment decision. We also show that as long as the manager is contracted to
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receive the optimal performance-based bonus for the abandonment decision, the abandonment timing is influenced not by the level of wage and severance pay, but only by effort costs. This paper shows the difference in optimal performance-based bonuses for investment and abandonment decisions using a linear contract for the manager. Future research could include how the optimal performance-based bonus for the two decisions is determined under more general compensation. 15
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References [1] Berger, P. G., Ofek, E., Swary, I., 1996. Investor valuation of the abandonment option. Journal of Financial Economics 42, 257-287.
Journal of Business 58, 135-157.
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[2] Brennan, M. J., Schwartz, E. W., 1985. Evaluating natural resource investments.
[3] Cardoso, D., Pereira, P. J., 2015. A compensation scheme for optimal investment decisions. Finance Research Letters 14, 150-159.
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[4] Dixit, A., Pindyck, R., 1994. Investment under Uncertainty. Princeton University Press, New Jersey.
[5] Holmstrom, B., Milgrom, P., 1987. Aggregation and linearity in the provision of
M
intertemporal incentives. Econometrica 55, 303-328.
[6] Holmstrom, B., Milgrom, P., 1991. Multi-task principal agent analysis: linear con-
tion 7, 24-52.
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tracts, asset ownership and job design. Journal of Law, Economics, and Organiza-
PT
[7] Jensen, M. C., 1986. Agency costs of free cash flow, corporate finance and takeovers.
CE
American Economic Review 76, 323-329. [8] Jin, L., 2002. CEO compensation, diversification, and incentives. Journal of Finan-
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cial Economics 66, 29-63. [9] Lambrecht, B. M., Myers, S. C., 2007. A theory of takeovers and disinvestment. Journal of Finance 62, 809-845.
[10] Mauer, D. C., Sarkar, S., 2005. Real options, agency conflicts and optimal capital structure. Journal of Banking and Finance 29, 1405-1428.
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[11] Morellec, E., 2004. Can managerial discretion explain observed leverage ratios? Review of Financial Studies 17, 257-294. [12] Wong, K. P., 2006. The effects of abandonment options on operating leverage and forward hedging. International Review of Economics and Finance 15, 72-86.
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[13] Wong, K. P., 2009. The effects of abandonment options on operating leverage and
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CE
PT
ED
M
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investment timing. International Review of Economics and Finance 18, 162-171.
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Table 1. Optimal performance-based bonuses and thresholds for investment and abandonment decisions Panel A
φ∗I Base case 0.257
Abandonment at φ∗I
φ∗A
S RA
M RA
0.436
0.224
0.296
0.243
Optimal abadonment
RI∗
φ∗A
∗ RA
2.136
0.436
0.243
1.881
0.436
0.284
2.965
0.436
0.153
0.240
2.150
0.436
0.343
µ = 4%
0.270
2.101
0.436
0.128
w = 0.02
0.305
2.135
0.509
0.243
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Optimal investment
w = 0.08
0.162
2.137
0.291
0.243
e = 0.1
0.157
2.032
0.311
0.229
e = 0.2
0.337
2.240
0.523
0.256
θ = 0.20
0.252
2.155
0.600
0.222
θ = 0.60
0.260
2.129
0.400
0.250
s = 0.1
0.260
2.137
0.418
0.243
s = 0.4
0.253
2.134
0.473
0.243
φ∗I
Base case
0.257
σ = 20%
0.266
σ = 40%
0.231
µ = 2%
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Parameter
CE AC
∗ RA
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Panel B
Abadonment at φ∗A
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Optimal proportions
Table 1 illustrates the optimal performance-based bonuses and thresholds for investment and abandonment decisions for varying parameter values.
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Table 2. Equally weighted average of the optimal performance-based bonuses and thresholds for investment and abandonment decisions Investment at φmid φmid
Base case 0.347
RIS,mid
RIM,mid
S,mid RA
M,mid RA
2.256
1.909
0.232
0.262
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Parameter
Abadonment at φmid
0.351
1.981
1.695
0.272
0.306
σ = 40%
0.334
3.160
2.572
0.146
0.168
µ = 2%
0.338
2.283
1.887
0.327
0.375
µ = 4%
0.353
2.210
1.900
0.123
0.138
w = 0.02
0.407
2.285
1.916
0.230
0.262
w = 0.08
0.226
2.210
1.886
0.236
0.264
e = 0.1
0.234
2.109
1.776
0.222
0.249
e = 0.2
0.430
2.400
2.027
0.242
0.276
θ = 0.20
0.426
2.423
1.788
0.205
0.245
θ = 0.60
0.330
2.220
1.943
0.241
0.267
M
0.339
2.241
1.931
0.233
0.260
0.363
2.285
1.869
0.229
0.266
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s = 0.4
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s = 0.1
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σ = 20%
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CE
Table 2 illustrates the equally weighted average of the optimal performance-based bonuses and thresholds for investment and abandonment decisions for varying parameter values.
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Performance-based bonuses for investment and abandonment decisions Hwa-Sung Kim PII: DOI: Reference:
S1544-6123(16)30044-7 10.1016/j.frl.2016.04.009 FRL 508
To appear in:
Finance Research Letters
Received date: Revised date: Accepted date:
26 September 2015 23 March 2016 3 April 2016
Please cite this article as: Hwa-Sung Kim, Performance-based bonuses for investment and abandonment decisions, Finance Research Letters (2016), doi: 10.1016/j.frl.2016.04.009
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Highlights • We derive optimal performance-based bonuses for investment and abandonment decisions
decisions
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• Compensation optimal for investment generates agency confliicts in abandonment
• Shareholders should adjust the bonus contract for investment to mitigate any agency problems in the abandonment decision
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CE
PT
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bonus for abandonment decisions
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• Managers are concerned only with their effort costs if they receive the optimal
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Performance-based bonuses for investment
Hwa-Sung Kim†
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March 2016
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and abandonment decisions∗
Abstract
This paper examines whether a performance-based bonus for a manager’s invest-
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ment influences her abandonment decision. First, we derive optimal performancebased bonuses for investment and abandonment decisions. Second, we show that
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there could be a discrepancy between the managers abandonment timing and that of the shareholders, even though an appropriate performance-based bonus
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was compensated to mitigate agency conflicts in the investment decision. Third, we also show that as long as the manager is contracted to receive the optimal
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performance-based bonus for the abandonment decision, only the effort costs that she incurs affect the abandonment timing.
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Keywords: Real option; Investment decision; Abandonment decision; Agency problem; Performance-based bonus JEL classification: D81; D86; G31; J33
∗
I would like to the anonymous reviewer, Scott Erdahl, and Brian Lucey (the editor) for their valuable and helpful comments. This work was supported by the National Research Foundation of Korea Grant funded by the Korean Government (NRF-2014S1A5A2A01017497). † School of Management, Kyung Hee University, 26 Kyungheedae-ro, Dongdaemun-gu, Seoul, 02447, Korea. Phone: +82-2-961-0499, E-mail: [email protected].
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1
Introduction
In the literature on corporate decision making, researchers tend to pay consistent attention to the latest findings on both investment and abandonment options. The reason for this consistent attention is that these two real options are associated with the beginning
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and the end of decision-making for a firm’s investment (e.g., Brennan and Schwartz, 1985). Moreover, the identity of the investment and abandonment decision-maker is important to consider. The firm’s decision-making is delegated to the manager with a special knowledge of investment projects. However, agency conflicts exist, that is, a
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manager does not always pursue the interest of the shareholders when making investment and abandonment decisions (e.g., Jensen, 1986; Berger et al., 1996). To attenuate agency conflicts, the shareholders utilize several mechanisms, for example, an appropriate compensation package.
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While much research deals with the impact of the agency problem on the investment decision, there are relatively few studies that examine the influence of agency conflicts
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on the abandonment decision.1 Recently, several papers examine this subject and draw various results. For instance, Morellec (2004) demonstrates that overinvestment by the
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manager results in late abandonment when she has the control rights over the abandonment policy. Lambrecht and Myers (2007) show that late abandonment is caused by the
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manager’s reluctance to relinquish her rents. This paper is motivated by the following question: is compensation for alignment in
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investment decisions still effective in mitigating agency conflicts when the manager makes the abandonment decision? As stated previously, existing papers show that overinvestment by the manager or unwillingness to relinquish managerial rents is an important factor in affecting the manager’s abandonment decision-making. In addition to these 1
Recent examples of research on an abandonment option of a firm include the firm’s risk management behavior (Wong, 2006) and operating leverage (Wong, 2009) in the presence of abandonment options. However, these papers do not consider agency conflicts between the shareholders and the manager.
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factors, we examine whether the manager’s abandonment decision is influenced by the compensation for the investment decision. Our examination, as in the Cardoso and Pereira (2015) model, considers a performance-based bonus as compensation dependent on the state of the investment revenue.
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In this paper, we show that the performance-based bonus for the manager to induce compliance with the investment timing of the shareholders is not effective in mitigating agency conflicts when the abandonment decision is made. This implies that to align the manager’s abandonment timing with that of the shareholders, the performance-based bonus should be adjusted once the investment is made.
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The remainder of this paper is organized as follows: the following section presents the model to derive the optimal performance-based bonus as well as the investment and abandonment thresholds. Section 3 examines how executive compensation is related to
The model
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2
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investment and abandonment timing. Section 4 concludes the paper.
To develop a model where the performance-based bonus is linked to the investment
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and abandonment decisions, we extend a traditional real-options model (e.g., Dixit and
CE
Pindyck, 1994). Consider a firm with both investment and abandonment options. The firm can exercise the investment option by paying a fixed cost of I. After the investment
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option is exercised, the firm obtains revenue R by incurring a fixed production cost C per unit of time.2 Once the investment is made, the firm’s revenue evolves as follows:
dR = µRdt + σRdW (t),
(1)
2 We can consider the revenue subtracted from the production cost as a project value as in Dixit and Pindyck (1994).
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where µ is the growth rate of the revenue, σ is the volatility of the revenue, and W (t) is a standard Brownian motion at time t. Here, µ and σ are constant. The firm’s operating profit, which is the revenue minus the production cost, is taxed at rate τ . Let r be the risk-free rate that is greater than the growth rate of the revenue.
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The shareholders hire a manager to invest effectively. However, the investment is not verifiable and so it is likely that the manager will choose the investment timing so as to maximize her wealth. As in Cardoso and Pereira (2015), we assume that the shareholders compensate the manager for implementing the investment with a fixed wage, w per unit of time as well as a performance-based bonus, the payment of which is a proportion φ (0
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≤ φ ≤ 1) of an after-tax operating profit. As in a standard principal-agent model (e.g., Holmstrom and Milgrom, 1987, 1991), this paper considers the linear contract for the manager. Although we do not consider the general type of the managerial compensation, a linear contract is a good approximation for nonlinear contracts (e.g., Jin, 2002). Under
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the linear sharing rule between the manager and the shareholders, this paper focuses on the impact of performance-based bonuses on both the investment and abandonment
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decisions.
While implementing the investment, the manager incurs an effort cost, e per unit of
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time, until the abandonment decision is made. Additionally, we assume that the manager leaves or loses her current job and receives severance pay, s, when the abandonment
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option is exercised. In the next subsection, we first investigate the optimal proportion
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of the performance-based bonus when the abandonment decision is made.
2.1
Abandonment decision
First, we examine the abandonment threshold chosen by the manager. The wealth of the manager consists of a wage and a performance-based bonus, excluding effort costs. Before the abandonment decision is made, the value of the managerial wealth, W (R), 5
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satisfies the following equation: 1 2 2 ∂ 2W ∂W σ R − rW + φ(R − C)(1 − τ ) + w − e = 0. + µR 2 2 ∂R ∂R
(2)
According to Dixit and Pindyck (1994), we obtain the general solution for the value of
W (R) = A1 R
β1
+ A2 R
β2
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the managerial wealth as follows:
R C w−e +φ − (1 − τ ) + , r−µ r r
(3)
where A1 and A2 are constants to be determined, and the constants β1 and β2 are as
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follows:
β2
1 µ = − 2− 2 σ
s
1 µ − 2 2 σ
1 µ − 2 2 σ
2
2
+
2r , σ2
(4)
+
2r . σ2
(5)
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M
β1
1 µ = − 2+ 2 σ
s
Note that β1 exceeds unity, and β2 is negative. The general solution must satisfy the fol-
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lowing three boundary conditions: (i) limR→∞ W (R)/R < ∞ (no-bubble condition); (ii) M M M ) = s (value-matching condition at RA ); (iii) W 0 (RA ) = 0 (smooth-pasting conW (RA
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M M dition at RA ), where RA represents the abandonment threshold at which the manager’s
wealth is maximized. The first condition implies that the coefficient A1 in equation (3)
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must be zero. The second condition represents the severance pay for the manager when the abandonment option is exercised. The third condition demonstrates that the manager chooses the abandonment threshold to maximize her wealth rather than that of the shareholders. After some calculations, we obtain the abandonment threshold chosen by
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the manager as follows: M RA
−β2 r − µ φC w−e = (1 − τ ) − +s . 1 − β2 φ(1 − τ ) r r
(6)
When the manager controls the abandonment decision, her wealth is R C w−e +φ − (1 − τ ) + , r−µ r r
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W (R) = AO
M
M (R; RA )
(7)
where AOM represents the value of the abandonment option when the manager is in control. AOM is given by M (R; RA )
M β2 RA C R w−e −φ − (1 − τ ) . = s− M r r−µ r RA
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AO
M
(8)
Next, to examine how different the manager’s abandonment timing is from the share-
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holders’s abandonment timing, we consider the shareholders’ abandonment threshold.
following equation:
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Before the investment is abandoned, the value for the shareholders, V (R) satisfies the
(9)
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∂V 1 2 2 ∂ 2V σ R + µR − rV + (1 − φ)(R − C)(1 − τ ) − w = 0. 2 2 ∂R ∂R
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The general solution to equation (9) is given by
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V (R) = B1 R
β1
+ B2 R
β2
R C w + (1 − φ) − (1 − τ ) − , r−µ r r
(10)
where B1 and B2 are constants to be determined. The wealth of the shareholders equals
the value of the abandonment option plus the present value of the after-tax operating profit net of the performance-based bonus minus the present value of the fixed wage, which is a cost to the shareholders until the investment is abandoned. We also consider
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the investment to be partially reversible. If the notation θ (0 ≤ θ ≤ 1) denotes the degree of the reversibility of the investment, the shareholders can recover a partial amount of θI.3 The boundary conditions to solve equation (10) are (i) limR→∞ V (R)/R < ∞ S S (no-bubble condition); (ii) V (RA ) = θI − s (value-matching condition at RA ); (iii) S S S V 0 (RA ) = 0 (smooth-pasting condition at RA ), where RA denotes the abandonment
(10) into the three boundary conditions delivers S (R; RA )
C w R − (1 − τ ) − , + (1 − φ) r−µ r r
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V (R) = AO
S
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threshold at which the value for the shareholders is maximized. Substituting equation
(11)
where AOS represents the value of the abandonment option under the control of the shareholders. The abandonment option value is given by S (R; RA )
β2 S C w R RA − (1 − τ ) + . = θI − s − (1 − φ) S r−µ r r RA
(12)
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AO
S
The abandonment threshold chosen by the shareholders is
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r−µ (1 − φ)C w −β2 (1 − τ ) + + θI − s . = 1 − β2 (1 − φ)(1 − τ ) r r
(13)
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S RA
Equation (13) shows that the abandonment threshold increases with the degree of re-
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versibility, θ. We observe that the abandonment threshold also rises with the amount of wage, w, but it decreases with severance pay, s.
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We derive the optimal proportion for a performance-based bonus to align the man-
ager’s abandonment threshold with that of the shareholders. Proposition 1. To induce the manager to choose the abandonment threshold of the shareholders, the shareholders should compensate the manager with a performance-based 3
We can include the case where the investment is irreversible if θ is set to be zero.
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bonus by the proportion φ∗A : φ∗A =
rs − w + e . rθI + e
(14)
Proof. Equating equation (6) to equation (13) delivers the optimal proportion of the
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performance-based bonus. The proportion φ∗A represents the optimal performance-based bonus for alignment between both parties in the abandonment decision. Note that the optimal proportion φ∗A is similar to the proportion derived by Cardoso and Pereira (2015) in that the proportions are determined by the manager’s wage and effort cost. Equation (14) shows that φ∗A is
2.2
Investment decision
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also affected by severance pay and the degree of reversibility of the investment.
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We investigate the performance-based bonus to mitigate agency conflicts when the manager makes the investment decision. The firm has an investment option, which is worth
ED
F (R). As in the case of the abandonment decision, we also consider the investment decisions made by both the manager and the shareholders. We first derive the invest-
PT
ment threshold under the manager’s control. Before the investment decision is made,
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the value of the investment option satisfies the following equation: ∂F 1 2 2 ∂ 2F σ R + µR − rF = 0. 2 2 ∂R ∂R
(15)
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The general solution of equation (15) is F (R) = C1 Rβ1 + C2 Rβ2 ,
(16)
where C1 and C2 are constants and can be determined by the three boundary conditions: (i) limR→0 F (R) = 0; (ii) F (RIM ) = W (RIM ); (iii) F 0 (RIM ) = W 0 (RIM ), where RIM denotes 9
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the investment threshold at which managerial wealth is maximized. The first condition implies that the investment option value becomes worthless if the revenue approaches zero. The equation for the investment threshold chosen by the manager is:
(17)
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C 1 φ(1 − τ ) M β2 w−e M 0= 1− RI + 1 − AOM (RIM ; RA ) − φ (1 − τ ) + , β1 r−µ β1 r r
where AOM is given by equation (8). We can calculate numerically RIM in equation (17). Next, we derive an equation for the investment threshold chosen by the shareholders, RIS , if we replace the boundary conditions (ii) and (iii) with the following two equations:
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(ii0 ) F (RIS ) = V (RIS ) − I and (iii0 ) F 0 (RIS ) = V 0 (RIS ). Analogously, the equation for the investment threshold chosen by the shareholders is given as
w β2 C 1 (1 − φ)(1 − τ ) S S RI + 1− AOS (RIS ; RA )−(1−φ) (1−τ )− −I, (18) 0 = 1− β1 r−µ β1 r r
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where AOS is provided in equation (12). From equation (18), RIS can be calculated
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numerically.
We derive the optimal proportion of the performance-based bonus that allows for
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alignment between both parties in the investment decision. Proposition 2. Let φ∗I be the proportion of the performance-based bonus to match the
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manager’s investment threshold to the shareholders’ investment threshold. By the following system of equations, we obtain the proportion φ∗I : β1 −1 φ∗I (1−τ ) ∗ RI β1 r−µ
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0= 0=
β1 −β2 β1
M AOM (RI∗ ; RA ) − φ∗I Cr (1 − τ ) + w−e , r β1 −1 (1−φ∗I )(1−τ ) ∗ S 2 RI + β1β−β AOS (RI∗ ; RA ) − (1 − φ∗I ) Cr (1 − τ ) − β1 r−µ 1
+
w r
(19) − I.
Proof. We can find the proportion φ∗I of the performance-based bonus for the manager by setting RIM and RIS equal to RI∗ in equations (17) and (18).
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From the perspective of the shareholders, the proportion φ∗I represents the optimal performance-based bonus in the investment decision. The investment threshold RI∗ associated with φ∗I represents the optimal investment threshold. We draw some implications on the relationship between a performance-based bonus and the abandonment timing
3
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using the two propositions.
The effects of performance-based bonus on aban-
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donment decisions
This section investigates the relationship between a performance-based bonus and investment and abandonment decisions. We select the following parameter values as the base case: C = $0.75, I = $5, θ = 0.5, τ = 20%, r = 5%, µ = 3%, σ = 25%, w = 0.04, e = 0.15, and s = 0.2.4 First, we examine the optimal proportions of the
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performance-based bonus, φ∗I and φ∗A in the base case.
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[Table 1 is about here]
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Panel A of Table 1 shows that in the base case, the shareholders should establish a performance-based bonus that provides approximately 26% of the operating profit to tie
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the manager’s investment timing to that of the time at which they want to invest. On the contrary, once an investment is made, if the shareholders want to induce the man-
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ager to select their optimal abandonment time, then they should compensate her with approximately 44% of the operating profit. Importantly, a discrepancy in abandonment S M timings between the shareholders (RA = 0.224) and the manager (RA = 0.296) may
occur if the shareholders maintain the performance-based bonus at around 26% of the 4
We select base-case parameter values similar to Mauer and Sarkar (2005).
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operating profit until the abandonment decision is made. Based on this analysis, we obtain the following implication. Implication 1. Although the shareholders provided the appropriate performance-based bonus to align their investment timing with that of the manager, the performance-based
the shareholders want to abandon the investment.
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bonus should be adjusted so as to match the manager’s abandonment timing to the time
Additionally, similar to Cardoso and Pereira (2015), Panel B of Table 1 shows that the changes in µ and σ do not affect the optimal proportion of the performance-based
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bonus for the abandonment decision, that is, φ∗A takes the value of 0.436 irrespective of the values of µ and σ.
Furthermore, we observe the impacts of the manager’s effort cost, fixed wage, and severance pay on the abandonment timing. To do so, we determine the abandonment
threshold at φ∗A :
rθI + e −β2 r − µ C (1 − τ ) + , = 1 − β2 1 − τ r r
(20)
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∗ RA
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threshold at φ∗A . Substituting equation (14) into equation (6) delivers the abandonment
∗ where RA denotes the optimal abandonment threshold. Equation (20) shows that if
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the shareholders provide φ∗A proportion of the performance-based bonus, the optimal abandonment threshold becomes irrelevant to the levels of the manager’s wage and
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severance pay. The manager is concerned only with effort costs when the abandonment
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decision is made. We confirm this from Panel B of Table 1. Implication 2. If the shareholders compensate the manager with the performance-based bonus to align their abandonment timing with that of the manager, the manager is concerned only with the effort costs when making the abandonment decision. However, if the proportion of the performance-based bonus is held at φ∗I until the abandonment decision is made, the manager makes an abandonment decision that de12
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viates from what the shareholders wish. To explain in more details, it is worth comparing the abandonment thresholds in two cases. The first is when there are managershareholder conflicts. The second is when the manager acts in the interests of the shareholders in abandonment decision-making.
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First, we examine the abandonment decision in the presence of agency conflicts. M The abandonment threshold, RA of equation (6), represents the manager’s optimal
abandonment threshold in her best interest. We expect several relationships between the manager’s optimal abandonment decision and her wage and severance pay. As the level of her wage is higher, the manager tends to delay abandonment. This is because the
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manager prefers late abandonment to enjoy the high level of wage as much as possible. We support this inference by the following comparative static:
M ∂RA ∂w
< 0. Additionally,
holding other variables fixed, a high level of severance pay induces the manager to abandon early because she wants to enjoy the high level of severance pay as soon as
M
possible. We also confirm this relationship by the comparative static:
M ∂RA ∂s
> 0.
∗ when Second, we investigate the result concerning the abandonment threshold, RA
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the manager acts in the best interests of the shareholders. This case implies that the manager does not pursue her own private benefits when making the abandonment de-
PT
cision. This is because the optimal performance-based bonus, φ∗A of equation (14) is contracted, which leads to an alignment between the abandonment decisions of the
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manager and the shareholders. Each combination of wage or severance pay determines an optimal level of performance-based bonus accordingly so that the manager makes
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an abandonment decision in the shareholders’ interests. For example, we confirm from equation (14) that a low wage and a high performance-based bonus balance out:
∂φ∗A ∂w
< 0.
Therefore, the manager is not concerned with her level of wage or severance pay when making the abandonment decision as long as the optimal performance-based bonus, φ∗A
is contracted. In contrast, the manager’s effort cost affects the abandonment threshold
13
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even in the absence of manager-shareholders conflicts. As with the fixed wage and severance pay, the optimal performance-based bonus is affected by the effort costs. Moreover, the manager’s effort costs do not influence the shareholder’s value of equation (9) but do influence the managerial wealth of equation (3). Additionally, because the shareholders provide the manager with the optimal performance-based bonus, they share the same
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∗ abandonment threshold, RA , which is affected by the values of both parties. Conse∗ quently, the agreed abandonment threshold, RA , becomes a function of the manager’s
effort costs when there is no agency problem.
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[Table 2 is about here]
Up to now, we have examined the optimal performance-based bonuses for the investment and abandonment decisions. We have shown that the shareholders should adjust the optimal performance-based bonus associated with the investment decision
M
in order to match the manager’s abandonment timing to their optimal abandonment timing. We consider an alternative case where the shareholders provide the identical
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performance-based bonus for both the investment and abandonment decisions without
PT
any adjustment to the bonuses.5
To mitigate the agency conflicts in both decisions, suppose that the shareholders
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are willing to choose an equally weighted average of two optimal performance-based bonuses associated with each decision. Let φmid denote the equally weighted average of
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φ∗I and φ∗A . At φmid , the shareholders’ and the manager’s investment (abandonment) S,mid M,mid ) and RIM,mid (RA ). Since φ∗A is greater than thresholds are denoted by RIS,mid (RA
φ∗I , φmid is greater than φ∗I . Therefore, this average of the optimal performance-based bonuses will be more effective when the shareholders consider stronger inducements to the manager to commence the investment. We confirm this from the observation that 5
I am thankful to the reviewer for suggesting this alternative case.
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the equally weighted average of the two optimal performance-based bonuses, φmid leads to early investment by the manager relative to the optimal investment threshold, that is, RIM,mid is lower than RI∗ . Moreover, the equally weighted average of the two optimal performance-based bonuses, φmid induces the manager to choose the abandonment M,mid M ∗ threshold, RA , that is closer than RA to the optimal abandonment threshold, RA .
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Table 2 shows that the average of the optimal performance-based bonuses reduces the gap between the abandonment thresholds chosen by the shareholders and the manager. S,mid M,mid ∗ M In the base case, at φmid , RA and RA are 0.232 and 0.262, whereas RA and RA
are 0.243 and 0.296, respectively. From Table 2, we also obtain the following results: the
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S,mid M,mid difference between the two thresholds, RA and RA at φmid is smaller as the fixed
wage is higher or severance pay is lower. The difference in the two thresholds declines
4
Conclusion
M
as the effort costs are lower.
ED
This paper demonstrates that even compensation that is optimal for aligning the investment timing between the shareholders and the manager could lead to a conflict in
PT
abandonment timing. We show that although the shareholders compensate the manager with an appropriate performance-based bonus for the alignment in the investment de-
CE
cision, they should adjust the performance-based bonus to mitigate agency conflicts in the abandonment decision. We also show that as long as the manager is contracted to
AC
receive the optimal performance-based bonus for the abandonment decision, the abandonment timing is influenced not by the level of wage and severance pay, but only by effort costs. This paper shows the difference in optimal performance-based bonuses for investment and abandonment decisions using a linear contract for the manager. Future research could include how the optimal performance-based bonus for the two decisions is determined under more general compensation. 15
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References [1] Berger, P. G., Ofek, E., Swary, I., 1996. Investor valuation of the abandonment option. Journal of Financial Economics 42, 257-287.
Journal of Business 58, 135-157.
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[2] Brennan, M. J., Schwartz, E. W., 1985. Evaluating natural resource investments.
[3] Cardoso, D., Pereira, P. J., 2015. A compensation scheme for optimal investment decisions. Finance Research Letters 14, 150-159.
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[4] Dixit, A., Pindyck, R., 1994. Investment under Uncertainty. Princeton University Press, New Jersey.
[5] Holmstrom, B., Milgrom, P., 1987. Aggregation and linearity in the provision of
M
intertemporal incentives. Econometrica 55, 303-328.
[6] Holmstrom, B., Milgrom, P., 1991. Multi-task principal agent analysis: linear con-
tion 7, 24-52.
ED
tracts, asset ownership and job design. Journal of Law, Economics, and Organiza-
PT
[7] Jensen, M. C., 1986. Agency costs of free cash flow, corporate finance and takeovers.
CE
American Economic Review 76, 323-329. [8] Jin, L., 2002. CEO compensation, diversification, and incentives. Journal of Finan-
AC
cial Economics 66, 29-63. [9] Lambrecht, B. M., Myers, S. C., 2007. A theory of takeovers and disinvestment. Journal of Finance 62, 809-845.
[10] Mauer, D. C., Sarkar, S., 2005. Real options, agency conflicts and optimal capital structure. Journal of Banking and Finance 29, 1405-1428.
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[11] Morellec, E., 2004. Can managerial discretion explain observed leverage ratios? Review of Financial Studies 17, 257-294. [12] Wong, K. P., 2006. The effects of abandonment options on operating leverage and forward hedging. International Review of Economics and Finance 15, 72-86.
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[13] Wong, K. P., 2009. The effects of abandonment options on operating leverage and
AC
CE
PT
ED
M
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investment timing. International Review of Economics and Finance 18, 162-171.
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Table 1. Optimal performance-based bonuses and thresholds for investment and abandonment decisions Panel A
φ∗I Base case 0.257
Abandonment at φ∗I
φ∗A
S RA
M RA
0.436
0.224
0.296
0.243
Optimal abadonment
RI∗
φ∗A
∗ RA
2.136
0.436
0.243
1.881
0.436
0.284
2.965
0.436
0.153
0.240
2.150
0.436
0.343
µ = 4%
0.270
2.101
0.436
0.128
w = 0.02
0.305
2.135
0.509
0.243
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Optimal investment
w = 0.08
0.162
2.137
0.291
0.243
e = 0.1
0.157
2.032
0.311
0.229
e = 0.2
0.337
2.240
0.523
0.256
θ = 0.20
0.252
2.155
0.600
0.222
θ = 0.60
0.260
2.129
0.400
0.250
s = 0.1
0.260
2.137
0.418
0.243
s = 0.4
0.253
2.134
0.473
0.243
φ∗I
Base case
0.257
σ = 20%
0.266
σ = 40%
0.231
µ = 2%
ED
M
Parameter
CE AC
∗ RA
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Panel B
Abadonment at φ∗A
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Optimal proportions
Table 1 illustrates the optimal performance-based bonuses and thresholds for investment and abandonment decisions for varying parameter values.
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Table 2. Equally weighted average of the optimal performance-based bonuses and thresholds for investment and abandonment decisions Investment at φmid φmid
Base case 0.347
RIS,mid
RIM,mid
S,mid RA
M,mid RA
2.256
1.909
0.232
0.262
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Parameter
Abadonment at φmid
0.351
1.981
1.695
0.272
0.306
σ = 40%
0.334
3.160
2.572
0.146
0.168
µ = 2%
0.338
2.283
1.887
0.327
0.375
µ = 4%
0.353
2.210
1.900
0.123
0.138
w = 0.02
0.407
2.285
1.916
0.230
0.262
w = 0.08
0.226
2.210
1.886
0.236
0.264
e = 0.1
0.234
2.109
1.776
0.222
0.249
e = 0.2
0.430
2.400
2.027
0.242
0.276
θ = 0.20
0.426
2.423
1.788
0.205
0.245
θ = 0.60
0.330
2.220
1.943
0.241
0.267
M
0.339
2.241
1.931
0.233
0.260
0.363
2.285
1.869
0.229
0.266
PT
s = 0.4
ED
s = 0.1
AN US
σ = 20%
AC
CE
Table 2 illustrates the equally weighted average of the optimal performance-based bonuses and thresholds for investment and abandonment decisions for varying parameter values.
19