Managerial performance evaluation for capacity investments

See, for instance, Balakrishnan and Sivaramakrishnan (2002), Carlton and Perloff (2005), Kaplan (2006), and Pittman (2009).

Buildings would be another example of an asset where degradation appears to be primarily time-driven.

This finding dates back to Arrow (1964).

The initial investment then effectively constitutes a private good to the extent that the investment enables an overall amount of output (operating hours) to be delivered. In contrast, if asset degradation is time-driven, the initial capacity investment enables a given stream of future outputs and, in that sense, constitutes a public good.

The same informational assumption is maintained in the earlier studies of Reichelstein (2000), Dutta and Reichelstein (2005), Baldenius and Ziv (2003), Bareket and Mohnen (2007), Friedl (2005), Pfeiffer and Schneider (2007), Wei (2004), and Johnson (2010).

If \(t<T\), the investment history becomes \(\varvec{I}_{t}=(I_{t-1},I_{t-2},\ldots ,I_{0},0,\ldots ,0)\).

As argued below, this informational assumption can be relaxed.

Since \(BV_{t}=BV_{t-1}-D_{t}+v\cdot I_{t}\), there is no need to include the current asset values \(BV_{t}\) in the performance measure.

See, for example, Rogerson (1997).

See, for instance, Nezlobin (2012).

This depreciation rule is consistent with the treatment of the right-of-use assets in Type B leases proposed by the IASB in its Exposure Draft #ED/2013/6.

See, for instance, Ehrbar (1998) and Young and O’Byrne (2000). Rajan and Reichelstein (2009) examine investment incentives under alternative depreciation rules if residual income is used as a performance measure.

Another possible reason is that firms may view it as costly to deviate from GAAP in designing their internal performance measures. See Young and O’Byrne (2000), pp. 267–268.

This depreciation rule is also known as the units-of-production method. Proportional depreciation appears to be a natural way to meet the IAS 16 requirement that “the depreciation method used shall reflect the pattern in which the asset’s future economic benefits are expected to be consumed by the entity.” In our model, the pattern of revenues generated by an asset may differ from the pattern according to which its capacity is consumed. We note that the proportional depreciation rule reflects the schedule of capacity consumption and not that of revenue generation, and therefore it is consistent with the IASB’s Exposure Draft #ED/2012/5, which emphasizes that depreciation rules should reflect the temporal pattern of consumption benefits inherent in the asset and that revenue is generally not a valid proxy for consumption.

Corollary 1 stands in contrast to the findings in Nezlobin (2012), who shows in the context of an equity valuation model that financial statements prepared using straight-line depreciation do not provide sufficient information for valuation purposes when assets have one-hoss shay productivity. Replacement cost accounting is effectively the only accounting rule that aggregates information about a firm’s past investments so that investors can still precisely value the firm based on the most recent financial statements. This uniqueness result is based on the observation that, to estimate the firm’s value, investors need to have information about its latest economic profits as well as the replacement cost of its assets in place. In contrast, we show that goal congruence only requires the owner to observe the firm’s current economic profit. The replacement cost of assets in place can be viewed as the value of “pre-paid” future capital costs, and, while knowing this quantity is necessary for equity valuation purposes, it is not necessary for incentive purposes.

The coefficient on book values, \(u_{bv}^{*}\left( \hat{r}\right)\), is equal to zero only when \(\hat{r}=0\). In that case, \(u_{d}^{*}\left( 0\right) =-\frac{\varvec{x\cdot 1}}{\varvec{x\cdot \gamma }}\).

See Dutta and Reichelstein (2010) for further details. Baldenius et al. (2014) study managerial performance evaluation in a model where firms can be subject to excess capacity for multiple periods.

See Observation 2 below.

The problem formulation in (9) reflects that the entire capacity investment must be made upfront. Models with a single investment opportunity are commonly considered in the economics literature [see, for example, Chapters 5 and 6 in Dixit and Pindyck (2002)]. In most environments, the need for an upfront capital investment is likely to originate from an incompleteness in the market for capacity services. In particular upfront fixed costs associated with the installation of assets (incurred in addition to the variable cost of \(v\cdot K_{0}\)) or a minimum capacity size come to mind as reasons for capacity investments to be inherently lumpy. Conceivably, the owner has sufficient information about the class of possible environments \(\{R_{t}(\cdot )\}_{t=1}^{T}\) to know that investments are profitable within a certain range, but making multiple investments is impractical due to the the minimum capacity constraint.

There may be multiple maximizers of \(V_{0}\). Our notion of goal congruence implies that the manager would be indifferent among any of these maximizers.

This asset valuation rule is conceptually similar to Hotelling’s (1931) rule for the price path of an exhaustible resource. In Hotelling’s formulation, there is no upfront investment expenditure but instead the firm must incur a periodic cost to extract the resource from the ground.

The arguments underlying Proposition 2 are related to Step 1 of the proof of Proposition 5 in Baldenius and Reichelstein (2005). In their model, asset values (inventories) are, by construction, independent of past utilization rates, that is, independent of the past \(\{s_{t}\}\). While this specification is plausible in the context of inventory valuation, our context of capacity assets suggests that depreciation charges may depend on the history of past production levels.

See, for instance, Ehrbar (1998), Ehrbar and Stewart (1999), Stewart (1991), and Young and O’Byrne (2000).

Models with multiplicative shocks to revenue functions are common in the economic literature on investment under uncertainty: see, for instance, Dixit and Pindyck (2002), p. 359. While the assumption of a multiplicative shock obviously entails a loss of generality, there is no further restriction entailed in assuming that the expected value of \(\tilde{\epsilon }\) is equal to one. We also note that our result in Proposition 3 can be extended to settings with multiple permanent shocks, possibly a new one arriving in each period.

For example, electricity is frequently generated by a combination of baseload and peaktime power plants. Baseload power plants (e.g., coal-fired plants) are usually represented as “one-hoss shay” type assets whose practical capacity is available uniformly for 40 years (NETL 2007). They tend to produce cheaper electricity than gas-powered peaker plants. As the name suggests, peaker plants can be turned on and off at short notice, and their remaining capacity is frequently rated in terms of output produced, which is highly correlated with the number of times the power generating unit has been activated.

Our model here can also be interpreted as one of a single asset the capacity of which declines with time and usage. Specifically, let \(K_{t}\) denote the total remaining capacity of the asset at date \(t\):We then have \(K_{t+1}=K_{t}-K_{0}^{b}-q_{t+1}^{s}.\) Thus capacity declines by \(K_{0}^{b}\) units in each period, plus by another \(q_{t+1}^{s}\) units due to “abnormal” usage in periods when \(q_{t+1}^{s}>0\). Over the asset’s useful life, the total abnormal usage has to satisfy

If \(v_{b}/T>v_{s}\), our model essentially reduces to the one with usage-driven asset degradation. On the other hand, if \(v_{b}<v_{s}\), it will never be optimal to invest in surge capacity, and the hybrid model reduces to the one with time-driven asset degradation.

Like in Rogerson’s (1997) framework, the common knowledge of the cost of investment implies that the marginal revenue at the optimal investment level is known at the outset, though only the better informed agent is in a position to determine that investment level.

Note that it follows from Eq. (28) that \(v^{b}\) exceeds \(v^{s}\cdot \left| \mathcal {T}^{*}\right|\).

Poterba and Summers (1992) demonstrate that internal hurdle rates used for capital budgeting purposes tend to exceed a firm’s actual cost of capital. See also Christensen et al. (2002) , Baldenius et al. (2007), Pfeiffer and Schneider (2007) and Johnson et al. (2013) for studies that capture the link between the underlying agency problem and the optimal capital charge rate.