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Creating Intangible Capital
Robin Dottling1, Tomislav Ladika2 and Enrico Perotti3
1Rotterdam School of Management, Erasmus University2University of Amsterdam
3University of Amsterdam, CEPR and Tinbergen Institute
July 3, 2019Preliminary Draft
Abstract
We propose a new framework for intangible capital creation by the joint investment of firm
resources and skilled human capital, subject to a double moral hazard. First, key employees
are free to leave with some intangibles, so firms must reward them in deferred form, creating
uninsurable risk. Thus high-intangible firms require less upfront funding and have larger
free cash flow, yet still follow a prudent financial policy to insure unvested claims. Second,
firm spending on intangible investment is easily diverted. Promising large payoffs to human
capital exacerbates moral hazard, as diversion prompts skilled employees to depart and
forfeit unvested claims. Balancing incentives requires firms to have more cash in good states
(to reduce the cost of compensation), and more inside equity to avoid diversion risk. The
model can explain several puzzling trends and generates new implications for measuring
investment, firm value, and returns to labor.
Keywords. Technological change, intangible assets, cash holdings, human capital, corpo-
rate leverage, equity grants, deferred equity, share vesting.
JEL classifications. G32, G35, J24, J33
*We thank Fernando Anjos, Patrick Bolton, Lauren Cohen, Esther Eiling, Mariassunta Giannetti, Dirk
Jenter, Paige Ouimet, Per Stromberg, Shusen Qi, Luke Taylor, Annette Vissing-Jørgensen, David Yer-
mack, and seminar participants for helpful input.Send correspondence to Enrico Perotti, [email protected].
Creating Intangible Capital
July 3, 2019
Abstract
We propose a new framework for intangible capital creation by the joint investment of firm
resources and skilled human capital, subject to a double moral hazard. First, key employees
are free to leave with some intangibles, so firms must reward them in deferred form, creating
uninsurable risk. Thus high-intangible firms require less upfront funding and have larger
free cash flow, yet still follow a prudent financial policy to insure unvested claims. Second,
firm spending on intangible investment is easily diverted. Promising large payoffs to human
capital exacerbates moral hazard, as diversion prompts skilled employees to depart and
forfeit unvested claims. Balancing incentives requires firms to have more cash in good states
(to reduce the cost of compensation), and more inside equity to avoid diversion risk. The
model can explain several puzzling trends and generates new implications for measuring
investment, firm value, and returns to labor.
Keywords. Technological change, intangible assets, cash holdings, human capital, corpo-
rate leverage, equity grants, deferred equity, share vesting.
JEL classifications. G32, G35, J24, J33
1. Introduction
Technological advances since 1980 have transformed corporate investment, leading to a rising
share of intangible assets relative to physical plant and other tangible capital (Corrado and
Hulten, 2010). This major shift in asset composition (see Figure 1) has concurred with sev-
eral puzzling trends, such as a sharp decline in tangible investment and in its correlation with
measures of expected profitability (Philippon and Gutierrez, 2016; Lee et al., 2016).
Figure 1: Growth of Intangibles to Total Capital
Existing research carefully documents how high intangibles usage can limit access to finance,
highlighting the need for a prudent financial policy. Firms with a higher ratio of intangible
to total capital may be financially constrained because their assets are less pledgeable due to
moral hazard (Holmstrom and Tirole, 1997) or because they face higher costs of financial distress
(Opler et al., 1999). The evidence is consistent with a reduced debt capacity (Bates et al., 2009).
Indeed as intangible assets have risen, net corporate leverage has fallen across a wide range of
sectors (Falato et al., 2018; Pinkowitz et al., 2016; Graham and Leary, 2018), as Figure 3 shows.
This paper offers a general framework for intangible capital creation as the joint investment of
firm resources and mobile human capital. A key distinction of the approach is a view of highly
skilled employees as co-creators of intangible assets, whose reward should include a share of the
payoffs. Building on this insight, the model provides a novel rationale for low measured invest-
ment and external financing demand. It can shed light on recent developments in corporate
1
finance, even in the absence of a traditional precautionary motive.
The paper’s first insight is that intangible assets derive their value largely from skilled human
capital. Successful companies rely on advanced capabilities developed by talented employees,
for a wide range of modern tasks such as product design, data analysis, software and techno-
logical development, innovative distribution and brand marketing (Eisfeldt and Papanikolaou,
2013). Unlike firms’ upfront capital expenditures on tangible assets, the application of human
capital involves few cash outlays and hence is not recorded in financial statements.
While firms can directly acquire physical assets and a few intangible assets,1 they cannot
own human capital. Employees are free to leave (Hart and Moore, 1994) even once they have
developed intangible capital for a better outside option or to escape financial distress (Ashwini
and Matsa, 2013; Babina, 2016). Ensuring commitment of human capital requires deferred com-
pensation such as tenure, career prospects, or time-vesting shares. As a result, while intangible
investment is difficult to fund externally, it is largely self-financed as the bulk of compensation
for human capital investment is deferred.
These insights are consistent with the evolution of free cashflow and financing over time and
across firms. A growing reliance on intangible assets across sectors has reduced measured in-
vestment spending for all firms. In particular, while high-intangibles (henceforth HINT) firms
generate similar operating (pre-investment) cashflows as low-intangibles (LINT) firms, since
1980 they have consistently spent a lower proportion on investment (see Figure 2). LINT firms’
outlays historically required external financing, but HINT firms spend less than 80% of the cash
they generate.
We formally examine these insights in a three-period model, in which a firm insider has
access to a profitable investment opportunity and contracts with a risk-averse employee and
risk-neutral outside investors. The firm’s investment is characterized by its technological re-
liance on tangible versus intangible capital. Tangible collateral is easily assessed and can be
assigned by outsiders, but spending on intangibles may be diverted for the insider’s own private
benefit. Moreover, intangible investment requires less upfront investment spending by the firm
as it is supported by the employee’s human capital.
1Firms can directly establish property rights on a few intangible assets, such as patents and licenses
2
Figure 2: Cash Flow Use for Across Firms and Over Time
In the interim period, the firm may face a net financial need for re-investment (Holmstrom
and Tirole, 1998), as well as the risk that the employee chooses to leave (Oyer, 2004). These two
motives shape financial and compensation policies, which in turn affect insider moral hazard.
The baseline model abstracts from external financing. To retain the employee, the firm offers
the bulk of compensation (besides basic wages) in the form of deferred equity that fully vests
after output is realized in the final period. While fixed deferred wages provide better insur-
ance to risk-averse employees, they leave high rents in bad states of the world, where outside
options are weak. Stock compensation reduces those rents, as it is correlated with industry
performance and hence the value of outside options (Oyer, 2004). The firm insider chooses the
optimal compensation by trading off these two forces.
A key result is that the firm can provide insurance not only by offering deferred wages, but also
by hoarding safe resources. The employee’s stock compensation is a risk-sensitive claim on the
firm’s value that cannot be hedged, so a conservative financial policy increases its utility value.
Hence, the model highlights a retention motive for a prudent financial policy, distinct from the
traditional precautionary motive associated with the lower debt capacity of intangible assets.
3
Interestingly, the retention motive induces firms to insure against good states of the world,
where outside options are strong. This contrasts with the traditional precautionary motive for
firms to insure spending needs in bad states of the world. These results show that negative
leverage may be optimal also for financially unconstrained firms, and rationalize the puzzling
observation that successful innovative and unconstrained firms appear to hoard most cash.2
However, a prudent financial structure raises governance concerns. Even in the absence of
external financing, deferred employee compensation may induce insiders to divert resources.
This is because diversion leads to the early departure of skilled employees, allowing insiders
to capture their unvested share of existing assets. This compensation overhang effect is more
pronounced among firms that rely more on human capital. Interestingly, to prevent diversion
the firm may need to offer even more stock compensation, as this reduces employees’ rents from
fixed compensation in bad states of the world, when insiders are most tempted to divert.
Governance concerns become even more prevalent when insiders do not have sufficient re-
sources (inside equity) to fund their investment needs internally. The extended model introduces
external financing, and shows how debt and external equity have different effects on risk bearing
for human capital. The need to provide insurance to employees makes risky debt unattractive
relative to granting equity. On the other hand, insiders with a small equity stake may choose
to divert resources. The result highlights a critical conflict between insuring employees and
conveying proper incentives against insider moral hazard. Corporate cash offers insurance for
physical and intangible investment, but also allows inefficient intangible spending by managers
for their own benefit. The model shows how the optimal insider stake depends on the insider’s
initial wealth and intangible capital needs.
Another extension shows that corporate payout policy is affected since dividends paid to
vested shareholders reduce the value of deferred compensation.3 A payout policy based on re-
purchases avoids diluting unvested claims, and indeed HINT firms prefer them over dividends
(see Figure 4).
The paper makes several contributions to the literature on intangible investment and human
2Comparative static results show that this motive is particularly strong for firms with a lot of intangible invest-ment, since these firms rely most on human capital retention.
3This extension is work in progress.
4
capital. First, it offers a demand-driven explanation for several recent trends associated with
intangibles, such as weak measured investment (Gutierrez and Philippon, 2017), low net lever-
age (Bates et al., 2009; Begenau and Palazzo, 2017; Graham and Leary, 2018), and the puzzling
observation that funding no longer flows to firms with high Tobin’s Q (Lee et al., 2016). Second,
to the best of our knowledge the model is first to describe the dual moral hazard problem inher-
ent to intangible capital creation. This setup shows that corporate cash may be most valuable
when the firm is most successful, and compensation overhang can exacerbate diversion among
firms with the most talented employees. A third, broader implication is that the traditional
dichotomy between capital and labor may not apply to HINT firms. These firms’ financial
statements also may have reduced accuracy, since common accounting metrics do not properly
measure the amount of human capital investment or the value of claims on it.
Several authors have offered related insights on human capital and finance. Berk et al. (2010)
show that maintaining low leverage allows a firm to insure its employees against the human cost
of bankruptcy, as it reduces the likelihood of financial distress. We complement their work by
identifying an insurance mechanism that applies outside of distress. Acharya et al. (2011) show
that firms must retain internal resources to incentivize future managers. We add an insurance
motive and derive an optimal share of deferred equity and a minimum insider stake. We also
show that promising too much future value to employees can exacerbate insider moral hazard.
Similar to our paper, Bolton et al. (2019) show that an entrepreneur’s ability to hedge idiosyn-
cratic firm risk may be constrained by the inalienability of her human capital. Their findings
relate to our compensation overhang effect, which may force insiders to offer more stock com-
pensation, exposing the employee to more idiosyncratic risk. In Sun and Xiaolan (2018) firms
also finance investment through compensation contracts. The authors highlight how this may
crowd out future debt capacity, potentially exacerbating precautionary needs. Our setup nests
many of these papers’ results, in a setup with both insider moral hazard and risk-averse em-
ployees with inalienable human capital. Importantly, in our setup employees are co-investors,
explaining lower spending demand as intangible investment substitutes physical assets.
Our basic model assumes abundant inside equity and all tangible investment is durable. In re-
ality tangible assets are only partial collateral, and constrained firms may purchase less durable
5
assets as they are cheaper Rampini (2018).
After discussion motivating evidence in Section 2 consistent with our results we present the
basic model under no binding financial constraints in Section 3, and extensions on the moral
hazard costs of cash and the choice of debt versus equity in Section 4. Section ?? discusses pay-
out policy and Section 5 briefly discuss implications for measuring investment and evaluating
firm performance. Proofs are in Appendix C.
2. Motivating Evidence
This section presents empirical facts about intangibles, and reviews related work on corporate
finance developments. The figures are drawn from listed U.S. firm data used by Bates et al.
(2009).4 Intangible assets are measured following Peters and Taylor (2017) and Eisfeldt and
Papanikolaou (2013). Appendix A describes the data in detail.
Fact 1. HINT firms maintain lower net leverage
Figure 3 plots the evolution of net leverage over time for the median HINT and LINT firm,
and separately for HINT firms outside IT-related sectors. In each year, HINT firms are defined
as those with a ratio of intangibles to total assets in the highest tercile, while LINT firms are
in the lowest tercile.
HINT firms consistently maintained lower net leverage. Their net leverage has fallen over
time, becoming negative in the early 1990s across all sectors (though the IT sector has lower
leverage). In contrast, LINT firms’ net leverage was fairly stable at 35% of total assets until
2000. It declined moderately since as these firms’ intangible capital ratio also rose.
HINT firms’ lower net leverage reflects two key trends. First, HINT firms invest less and
raise less external financing relative to their capital base. Second, HINT firms retain a much
larger share of liquid resources on their balance sheets, as the right panel of Figure 3 shows.
Remarkably, the growth in cash holdings since 1980 is concentrated among HINT firms, while
LINT firms’ cash ratios have mostly remained below 10%. More recent evidence shows that
4The sample contains all Compustat U.S. firms excluding financials and utilities from 1980 to 2015, a period ofrapid adoption of IT technology.
6
Figure 3: Intangibles Usage, Net Leverage, and Cash Holdings
the aggregate rise in cash holdings is driven by innovative firms (Begenau and Palazzo (2017),
Graham and Leary (2018)).
Fact 2. HINT firms have higher free cash flow
Figure 2 (presented above) plots the median HINT and LINT firms’ capital expenditures,
outlays into production of intangibles, and free cash flow across five-year intervals. Overall,
HINT firms invest less of their cash flows, and consistently earn positive free cash flow, while
LINT firms historically have used net external financing to fund their larger investment spend-
ing. The distinction is increasingly less marked: As reliance on human capital spreads across
sectors, capital expenditures and total investment spending have fallen over time among both
HINT and LINT firms.
Importantly, lower investment spending by HINT firms is not due to lack of profitability.
In fact, during the sample period the median HINT firm is slightly more profitable than the
median LINT firm on a pre-investment basis. Its operating cash flow range from 18 to 26%
of total assets since 1980, compared to 17 to 20% for LINT firms. Moreover, all variables in
Figure 2 are scaled by operating cash flows, to control for differences in profitability.
Increasing substitution of physical capital with intangible assets may explain why companies
appear to invest less than they used to. Skilled employees’ human capital contributions produce
few observable cash outflows, and thus a significant amount of corporate activity may be un-
7
Figure 4: Intangibles Usage and Composition of Free Cashflows
recorded in financial statements. Peters and Taylor (2017) show that including firms’ spending
on human capital compensation in investment improves considerably its correlation with market
to book ratios. Finally, the model suggests that high share valuations may be associated with
large insider claims and a rising share dilution for outside investors (Eisfeldt and Papanikolaou,
2014).
Fact 3. HINT firms raise less external financing and more deferred equity
Figure 5 shows that HINT firms raise significantly less debt than LINT firms. In its place,
innovative firms grant to their employees a significant amount of deferred equity, with expected
market value equal to about 30% of total annual financing. In contrast, employee equity grants
amount to 12% of capital raised by LINT firms, though this percentage has grown over time.
Retained earnings (a form of capital implicitly raised from external shareholders) are similar
across HINT and LINT firms, while net debt issuance is twice as small. This latter fact is
consistent with the decline in external financing among high-Q firms (Lee et al. (2016)), many
of which also have high intangibles usage.
Fact 4. HINT firms retain more resources, and prefer repurchases over divi-
8
Figure 5: Intangibles Usage and Sources of Financing
dends
Figure 4 examines how HINT firms allocate their higher free cash flow. The median HINT
firm retains about 60% of free cash flow, and pays out the rest mostly through share repur-
chases. In contrast, LINT firms pay out most of their free cash flow, and until 2000 preferred
dividends to share buybacks.5
Fact 5. Less constrained firms behave similarly
A natural interpretation of facts 1, 3 and 4 is that HINT firms make more cautious financial
choices, as their intangible capital cannot be pledged to raise external financing in times of need.
We argue here that some additional explanation may be useful, as these patterns hold equally
for firms that are unlikely to be financially unconstrained.
Table 1 reports key corporate finance indicators separately for HINT and LINT firms that
paid dividends during the year, or were in the S&P 500. Firms that pay dividends typically
have large cash buffers, while S&P 500 firms have broad access to financial markets. The also
reports difference between the median HINT and LINT firms in these subsamples, as well as
across the entire sample.
The variation in financial choices among all HINT and LINT firms is similar to the differences
5Plots exclude repurchases of employee stock following option exercises, using the method of Fama and French(2001).)
9
Table 1: Corporate Policies among Dividend-Paying and S&P 500 Firms Firms
All Firms Dividend-Paying Firms S&P 500 FirmsHINT LINT Diff. HINT LINT Diff. HINT LINT Diff.
Net Leverage -0.03 0.32 -0.29 0.06 0.29 -0.23 0.06 0.30 -0.24Cash Holdings 0.15 0.07 0.08 0.10 0.06 0.04 0.12 0.05 0.07Free Cashflows 0.11 0.03 0.08 0.22 0.14 0.08 0.27 0.15 0.12Deferred Equity 0.16 0.04 0.12 0.06 0.03 0.03 0.11 0.04 0.07Retained Cashflows 1.00 0.86 0.14 0.44 0.41 0.03 0.46 0.35 0.11
between large or dividend-paying HINT and LINT firms. This indicates that the previously doc-
umented facts are not limited to firms that need to save cash for precautionary reasons.
2.1. Related work on recent trends in corporate financing
A rich literature has documented remarkable changes in corporate financial policy that concur
with rising intangibles usage. First, since 2000 U.S. corporate investment spending has sig-
nificantly lagged the level predicted by measures of growth opportunities (such as Tobin’s Q)
and profitability (Philippon and Gutierrez (2017), Alexander and Eberly (2018), Crouzet and
Eberly (2018)).6 Second, an even more striking finding is a recent negative correlation between
growth opportunities and external financing. Since 1996, firms and sectors with higher Q values
have raised less external funding and experienced larger net equity outflows (Lee et al. (2016)).
Third, since 1980 firms have accumulated cash at a historic rate, with levels rising from 8%
to 23% of total assets (Graham and Leary (2018)). Explanations include precautionary reserves
to avoid financing constraints (Kim et al., 1998; Almeida et al., 2004; Harford et al., 2014); U.S.
fiscal rules encouraging cash hoarding abroad (Foley et al., 2007; Harford et al., 2017; Faulk-
ender et al., 2019); and a reduction in the opportunity cost of holding cash (Azar et al. (2016)).
This trends raises concerns about rising agency costs of managerial discretion (Jensen (1986),
Pinkowitz et al. (2006), Dittmar and Mahrt-Smith (2007), Harford et al. (2008)). Notably, cash
held by R&D-intensive IPO firms has risen fourfold since 1980, and firms tend to reduce cash
holdings over their life cycle (Begenau and Palazzo, 2017). Faulkender et al. (2019) show that
6Consistent with this finding, (Dottling et al., 2017) document a relatively higher sensitivity of investment to Qin Europe, where market competition remains stable.
10
the increase in foreign cash holdings is driven by R&D-intensive firms, which can more easily
shift income abroad. Relatedly, Pinkowitz et al. (2016) document that among purely domes-
tic U.S. firms the increase in cash holdings is also concentrated among R&D-intensive firms,
suggesting a significant role for fundamental as well as fiscal reasons.
Explanations in the literature include that a secular reduction in market competition in the
United States has led to the decrease in investment (Philippon and Gutierrez, 2017). Another
is the precautionary view supported by Bates et al. (2009), who document a strong association
between cash reserves and cashflow volatility as well as R&D expenditures. The view that
intangibles reduce access to credit is also pursued by Falato et al. (2018).
Our paper contributes by offering a complementary view quite consistent with these trends,
which is based on the widespread adoption of information technology in all aspects of production
and distribution across all sectors.
3. Baseline Model
3.1. Setup
The model has three active periods t = 0, 1, 2, a firm that is managed by a risk-neutral insider,
and a risk-averse skilled employee who is hired by the firm. In the basic model the firm has no
outside investors.
3.1.1. Technology
The firm has access to an investment project that requires fixed investment expenditure of It in
t = 0, 1. The project is characterized by its technological intangible intensity η, defined as the
fraction of intangible capital used in production and requires investment of (1−η)It into tangible
assets and ηIt into intangibles.7 The firm must purchase tangible assets, but only needs to spend
a fraction α on intangible investment. Its total investment spending is Ift = [ηα + (1 − η)]It.
The remaining portion of intangible assets is created over time by the employee, who co-invests
her own human capital of Iwt = η(1− α)It by exerting effort. The firm’s intangible investment
7The fixed scale of tangible vs. intangible investment can be motivated by a Leontief production function.
11
includes purchases of lab equipment to support R&D or data and advertisements to build
marketing capacity, while the employee accumulates knowledge and develops ideas. Because the
employee’s human capital contribution involves no cash outlay, a significant amount of intangible
investment is unrecorded in financial statements, a point we discuss in greater detail in Section 5.
The project generates a stochastic cashflow Rit(η) in t = 1, 2. Cashflows vary with intangible
intensity and the state of the economy i ∈ {high, low}. For ease of exposition, we omit the
reference to η and express cashflows as simply Rit.
The firm’s investment spending mechanically decreases in η (∂Ift /∂η = (α− 1)It < 0), as the
employee co-invests a larger share of human capital when intangible assets are more important
for production. This choice of production technology is motivated by our empirical observation
that over time, HINT firms have had lower upfront cash outlays and earned higher free cashflows
than LINT firms.
3.1.2. Endowments and Preferences
The insider has an initial cash endowment W0, and chooses to contribute A0 ≤W0 of it to fund
the project. This endowment can be interpreted as initial insider equity or retained cashflows
from previous operations. The baseline model studies a firm that has sufficient resources to cover
all investment needs, i.e., the insider has W0 > I0 + I1. Section 4 considers the general case
with external financing. Cash can be saved across periods at a risk-free rate normalized to 0.
The insider is indifferent over the timing of consumption ct, and there is no discounting:
Uf = E[c0 + c1 + c2]
The employee is endowed with human capital that supports the creation of intangibles. She has
mean-variance preferences over consumption with risk-aversion parameter ρ:
Uw = E[cw0 + cw1 + cw2 ]− ρV ar[cw0 + cw1 + cw2 ],
where E and V ar denote the expectation and variance operators. The employee’s effort cost is
12
normalized to 0 for simplicity.
Following Hart and Moore (1994), the employee cannot commit up front to stay at the firm
through the project’s completion. After the firm makes its investment decision at t = 1, the
employee receives an outside offer proportional to her human capital, reflecting the option to
move to another firm or start an own venture. The offer provides a state-dependent utility value
s = η(1−α)si, where si = sh in the high state and sl < sh in the low state. As in Oyer (2004), the
value of the outside option is correlated with macroeconomic performance, for example because
industry peers compete more aggressively for talent when the overall economy is strong.
3.1.3. Contractability and Moral Hazard
All agents can verify tangible assets created by the firm and cash held on the balance sheet.
These assets are contractible and fully redeployable upon termination or completion of the
project, so that the collateral value of tangible assets is K2 = (1 − η)[I0 + I1] at t = 2. In
contrast, the insider can choose to direct the full amount of firm intangible spending αηI1 at
t = 1 toward generating an own private benefit with utility value αηI1.8
While outsiders can verify that the firm has invested into intangibles, only the insider and
employee can assess the quality of this investment, i.e., whether it is legitimate spending or
resource diversion. Diversion allows the insider to generate a private benefit, but it causes the
project to fail with certainty, undermining future cashflows.9
3.1.4. Timeline
Figure 6 summarizes the project’s evolution and agents’ actions and payoffs in different states.
At t = 0 the insider chooses how much cash A0 to contribute to the project, and uses a
portion of it to fund the project’s initial cost If0 , so that cash holdings at the end of the period
are C0 = A0−If0 . The firm also offers the employee a compensation contract (w, b), where w is a
fixed deferred salary paid once the final payoff is realized at t = 2 and b is a share grant that vests
8We can allow for a more general formulation of the utility value of the private benefit. What matters is that itincreases in the amount of intangible spending diverted.
9Introducing a loss on redeployed tangible assets does not affect the results.
13
Figure 6: Timeline of Baseline Model
High state
Cashflow 𝑅"# > 𝐼"&
Continuation
Re-invest −𝐼"&
Project succeeds• Final cashflow 𝑅( plus
recovery of 𝐶" and 𝐾( = (1 −𝜂)(𝐼0+𝐼")
• Employee receives 𝑤 +𝑏𝑉(• Insider receives 1 − b 𝑉(
Project fails• Recovery of 𝐶" plus
𝐾( = (1 − 𝜂)(𝐼0+𝐼")
Departs
NATURE INSIDER EMPLOYEE
𝑡 = 1 𝑡 = 2
𝑞
1−𝑞
𝑡 = 1.5
Receives outside offer 𝑠 = 1 −𝛼 𝜂𝑠=
DiversionClaim α𝜂𝐼" as private benefit
INSIDER
𝑡 = 0
• Contribute A0
• Invest 𝐼0&
• Grant (𝑤, 𝑏)Low state
Cashflow 𝑅"B < 𝐼"& Observes
diversion
Stays
NATURE
at t = 2.10 The outside option is not contractible, and we assume that contractual renegotiation
after t = 0 is not possible. Thus any wage promise must be honored in all states of the economy.11
We decompose all cashflows as the sum of a random variable θit plus the previous period’s
intangible spending: Rit = θit + αηIt−1. As will become clear below, this assumption ensures
that payoffs are independent of the firm’s intangible intensity η, so the project has the same net
payoff independent of its underlying technology.12 At t = 1, the state of the economy (industry)
becomes public knowledge. In the high state “H” (probability q) the project’s cashflow exceeds
required re-investment: Rh1 > If1 . In this state, the firm has sufficient resources to continue the
project regardless of its cash holdings. In contrast, in the low state (probability 1− q) Rl1 < If1 ,
such that the firm can only re-invest if it has retained sufficient resources. In the final period,
θ2 is distributed according to the CDF F (θ2) on the support [0,∞) and with variance σ2. In
the high state, E[θ2] = θh2 , and in the low state E[θ2] = θl2 < θh2 . Hence, in the high state not
10The employee’s utility function can be modelled to include a preference for smoothing consumption. In this casethe firm’s remuneration policy may involve a fixed wage at t = 0 or t = 1. Such payments would increase the up-front cost of hiring the employee, but would not affect retention since the outside offer arrives at the end of t = 1.
11Oyer (2004) considers the possibility of renegotiation. Adjusting compensation may be costly. Reducing wagesis hard, and raising rewards raises demands by others (Hart and Moore, 2008).
12The insider’s NPV from the project subtracts the employee compensation, which is endogenous. However theformulation ensures that for an entrepreneur contributing her own human capital, the payoff net of her outsideoption is independent of η.
14
only are intermediate cashflows higher, but also the outlook for final cashflows
Rh2 ≡ θh2 + αηI1 > Rl2 ≡ θl2 + αηI1.
The firm’s investment decision at t = 1 is observed by the employee, who also receives an
outside offer si. The employee can choose to remain and contribute human capital η(1 − α)I1
to complete the project. If she chooses to depart, the project fails and the firm recovers only
cash and the value of tangible assets K2 = (1− η)(I0 + I1), while intangible assets do not have
any collateral value in case of failure. Upon departing, the employee’s compensation expires
without vesting. The employee always departs if she observes diversion.
At t = 2 the final project payoff R2 is realized and the employee’s share grant vests. All cash
flows and asset holdings are sold and agents consume.
We assume that the project has a positive NPV given no diversion, so that a self-funded
insider would undertake it at t = 0.
Assumption 1. The project has positive NPV (net of the employee’s outside option value) at
t=0:
q[θh1 + θh2
]+ (1− q)
[θl1 + θl2
]≥ (1− α)ηsh (1)
The left-hand side of Eq. (1) is the total net payoff of the project, consisting of its expected
cashflows plus the collateral value of tangible assets, net of investment outlays. The right-hand
side is the highest wage the firm has to pay the employee in order to match her outside option
in all states.
Next we assume that the project’s payoffs are such that continuation at t = 1 is efficient in
either state when the employee receives no rents.
Assumption 2. The project has positive NPV (gross of the employee’s outside option value)
in states H and L:
θh2 ≥ (1− α)ηsh + ρσ2 (2)
(1− α)ηsh > θl2 ≥ (1− α)ηsl + ρσ2 (3)
15
The assumption that (1− α)ηsh > θl2 implies that the firm cannot simply offer a fixed wage
of (1− α)ηsh.
3.2. Solution
The model is solved backwards, starting with the employee’s decision whether to accept the
outside offer, followed by the insider’s choice whether to invest or divert resources at t = 1, and
finally the choice of compensation contract and cash holdings at t = 0.
3.2.1. Employee Participation
Employee compensation must be deferred until t = 2, otherwise it cannot ensure retention. The
employee remains at the firm as long as the expected utility value of her compensation (w, b)
at t = 1 matches the outside offer in states H and L:
w + bE1[V h2 ]− ρb2V ar1[V h
2 ] ≥ (1− α)ηsh, (PCh)
w + bE1[V l2 ]− ρb2V ar1[V l
2 ] ≥ (1− α)ηsl, (PCl)
where E1[V i2 ] and V ar1[V i
2 ] denote the expectation and variance of final firm value at the time
that the outside offer is made, for i = h, l:
E1[V i2 ] = A0 − If0︸ ︷︷ ︸
= C0
+ Ri1 − If1︸ ︷︷ ︸
Free Cashflow t = 1
+ Ri2 − w +K2︸ ︷︷ ︸Final Payoff and Recovery Value
= A0 + θi1 + θi2 − w (4)
V ar1[V i2 ] = σ2 (5)
3.2.2. Insider Re-investment
The insider’s choice of tangible investment (1 − η)I1 is easily assessed by outsiders, while the
choice of intangible capital αηI1 may be diverted for private benefit, in which case the project
fails to produce any further payoff and firm value at t = 2 only reflects financial slack at t = 1.
16
As the employee can see the choice of intangibles she will choose to leave. Her unvested payoff
then expires, adding to the gain from diversion.13
In order to mimic a non-diverting firm, the insider still has make the full investment If1 , and
hence earns
αηI1︸︷︷︸Private Benefit
+ C1 +K2︸ ︷︷ ︸Firm Value After Diversion
= A0 + θi1,
where C1 = C0 +Ri1 − If1 denote cash holdings at the end of t = 1. In contrast, the value from
continuation without diversion is (1− b)E1[V i2 ] = (1− b)[A0 + θi1 + θi2−w]. Comparing the two
yields the following incentive compatibility constraints for states H and L:
(1− b)[A0 + θh1 + θh2 − w] ≥ A0 + θh1 (ICh)
(1− b)[A0 + θl1 + θl2 − w] ≥ A0 + θl1 (ICl)
In the absence of external financing, the firm’s intangible intensity η does not directly show
up in the IC constraints.14 However, it may affect the moral hazard problem indirectly via
the firm’s compensation contract or cash holdings. If deferred compensation rises with η, then
intangible intensity affects insiders’ incentives to divert so as to avoid sharing firm value with
the employee. We refer to this effect as compensation overhang.
Lemma 1. Under Assumption 2, the insider prefers continuation to diversion for i = h, l if
the employee receives no rents in state i. That is:
• if (PCh) binds, then (ICh) is slack.
• if (PCl) binds, then (ICl) is slack.
We show below that in state H the insider does not allow the employee to accrue rents, and
therefore strictly prefers continuation to diversion. However, diversion may occur in state L
whenever the insider leaves rents to the employee in state L.
13Note that in the baseline model without external finance the net gain from the private benefit is zero. Thereason that the insider may divert is purely so that she does not need to share firm value with the employee.
14With external finance, there is an additional direct effect by which the firm’s intangible intensity affects themoral hazard problem, see Section 4.
17
3.2.3. Insider Financing Contribution
The insider offers a compensation contract (w, b) at t = 0 that satisfies the employee’s partic-
ipation constraint in both states, and chooses how much cash A0 to commit to the project.
Any cash left over after the initial investment C0 = A0 − If0 is saved until t = 1, for two pur-
poses. First, in the low state re-investment is only possible when the insider sets aside sufficient
precautionary cash savings:
C0 ≥ If1 −Rl1 ≡ CPREC (PREC)
The insider thus needs to contribute A0 ≥ CPREC + If0 ≡ APREC , as shown in detail below.
Second, when the employee owns a stake in the project (i.e., b∗ > 0) she is exposed to its
idiosyncratic cashflow risk. Because the employee is risk-averse, she requires a premium to bear
this risk. The insider can insure the employee by contributing part of her endowment as cash
savings, and thereby increasing the utility value of deferred compensation. The crucial insight
is that the employee has an indirect claim on the firm’s cash holdings through her deferred
equity grant. Thus next to the precautionary motive for holding cash, saving cash also reduces
the cost of hiring human capital.
3.3. Optimal Firm Financial and Compensation Policies
The insider chooses compensation and cash holdings to maximize her share of firm value, subject
to the employee’s participation constraints, incentive compatibility constraints, and precaution-
ary needs:15
maxA0,w,b
Uf = (1− b)E0[V2]−A0 (6)
s.t. (PCh), (PCl), (ICh), (ICl), (PREC)
15Note that choosing A0 is analogous to choosing C0, since investment scales are fixed.
18
where E0[V2] = q E1[V h2 ] + (1− q) E1[V l
2 ] is the expected final firm value from the viewpoint of
t = 0. This problem can be re-formulated as the following Lagrangian function:
maxA0,w,b
L = (1− b){A0 + q(Ah1 + Ah2) + (1− q)(Al1 + Al2)− w
}−A0 (7)
+ µh
{w + b[A0 + θh1 + θh2 − w]− ρb2σ2 − (1− α)ηsh
}+ µl
{w + b[A0 + θl1 + θl2 − w]− ρb2σ2 − (1− α)ηsl
}+ φh
{(1− b)[θh2 − w]− b[A0 + θh1 ]
}+ φl
{(1− b)[θl2 − w]− b[A0 + θl1]
}+ λ{C0 − CPREC
}
where µh, µl, φh, φl and λ are the Lagrange multipliers for the constraints (PCh), (PCl), (ICh),
(ICl), and (PREC), respectively.16
Problem (7) shows that numerous solutions are possible depending on which constraints bind.
To impose structure on the solution, we first note that the insider always matches the employee’s
outside option in the high state.
Lemma 2. A∗0, b∗, and w∗ are always set so that the employee’s participation constraint (PCh)
binds in the high state (µh > 0). It follows that (ICh) is always slack at the optimum (φh = 0).
The full proof is in Appendix C. The key intuition of the lemma is that granting more shares
to retain the employee is particularly costly to the insider in the high state, when cash flows
are high. Therefore, if (PCh) was slack, the insider could reduce the share grant to the point
where (PCh) binds, while still satisfying (PCl).17 From Lemma 1 it follows that (ICh) is slack,
as the insider chooses not to divert in state H when the employee receives no rents.
The model now produces two separate equilibrium regions, based on whether the insider’s
binding constraint is to contribute sufficient resources to retain the employee in all states or to
16Formally, the Lagrangian should also contain non-negativity constraints for C0, w and b. We omit these con-straints for readability.
17Mathematically, the left-hand side of (PCh) increases more in b than the left-hand side of (PCl), becauseE1[V h2 ] > E1[V l2 ] while V ar1[V h2 ] = V ar1[V l2 ].
19
ensure that re-investment is feasible in the low state. In the Retention Motive (RET) region the
firm is financially unconstrained in the traditional sense, but the project can only be completed
if the insider provides sufficient insurance to match the employee’s relatively high outside op-
tion. This region is characterized by optimal cash holdings C∗0 ≥ CPREC , and corresponds to
λ = 0 and a slack (PREC) constraint in the Lagrangian formulation (7).
In the traditional Precautionary Motive (PREC) region, the re-investment need in the low
state at t = 1 is high relative to the value of the employee’s outside option. In this region the
insider chooses C∗0 = CPREC , and the employee may receive more insurance than needed to
remain at the firm in state LV. This corresponds to λ > 0 and a binding (PREC) constraint.
To further impose structure on the problem, we first solve the model for cases in which the
insider does not divert, i.e., (ICl) is slack and hence φl = 0. Section 3.3.3 studies diversion with
φl > 0.18
3.3.1. Dominant Retention Motive
In the RET region the insider chooses three variables to satisfy two constraints, so the baseline
model is underdetermined. We start by examining the solution in which (PCl) binds (µl > 0)
in addition to (PCh), i.e., the employee receives no rents in either state.
Lemma 3. The optimal contract contains equity that vests at t = 2.
The intuition is as follows. When the insider grants no equity, a high wage of w∗RET =
(1−α)ηsh is necessary to retain the employee in the high state. Because this wage is also guaran-
teed in state L, the employee receives rents of (1−α)η(sh−sl). The insider strictly prefers a con-
tract (b′ > 0, w′ ≥ 0) that transfers less value to the employee but still satisfies both of her partic-
ipation constraints. Intuitively, a share grant is worth less in the low state, reducing the rent paid
to the employee in the low state (at the cost of exposing the employee to more risk) (Oyer, 2004).
A high wage may also encourage diversion by insiders. We discuss this friction more exten-
sively in Section 3.3.3.
18Breaking up the problem and solving it sequentially over different solution regions allows us to highlight each ofthe different economic forces in our model. Appendix B provides a general overview of all the cases that can arise.
20
When (PCl) binds, the optimal equity grant b∗RET can be derived by combining (PCl) and
(PCh):
b∗RET =(1− α)η∆s
∆θ(8)
where ∆s ≡ sh − sl and ∆θ ≡ [θh1 + θh2 ]− [θl1 + θl2].
The optimal equity grant is scaled up by the firm’s intangible intensity, offering a reward
based on the ratio of the employee’s incremental retention cost in the high state relative to the
incremental firm value. Thus the firm must grant a larger equity stake when the employee’s
outside option rises more in the high state than does the project value.
Next we solve for the optimal amount of insurance that the firm provides to the risk-averse
employee. Both cash holdings and wages can serve as insurance, since the employee receives
a fraction b∗RET of each unit of cash insiders put into the firm, and a net share (1 − b∗RET )
of wages. She thus receives the same utility value from the firm holding 1/b units of cash or
granting 1/(1− b) units of deferred salary w. We define the overall net level of insurance as:
INS(w,A0; b) ≡ bA0 + (1− b)w. (9)
Lemma 4. In the RET region there is an equivalence between providing insurance via cash
C0 ≥ CPREC or deferred wages w, as long as the overall level of insurance satisfies (PCh):
INS(w,A0; b) ≥ (1− α)ηsh + ρb2σ2 − b(θh1 + θh2 ). (10)
The equivalence between cash holdings and deferred wages is shown formally in the general
solution to the problem in Appendix B. From (PCh), the overall level of insurance needs to
match the employee’s outside option and cost of risk, net of the expected value of cashflows
earned by the employee. Optimal insurance INS∗RET is obtained by substituting b∗RET into Eq.
(10) and setting the inquality to bind.
The solution and comparative statics are summarized in the proposition below.
Proposition 1. When (PCh) and (PCl) bind, the insider’s optimal compensation and financ-
21
ing choices are characterized by:
b∗RET =(1− α)η∆s
∆θ,
INS∗RET =
(ρ(1− α)η∆sσ2
∆θ+sh∆θ
∆s− [θh1 + θh2 ]
)(1− α)η∆s
∆θ.
Both the optimal equity grant and overall level of insurance are increasing in intangible intensity:
∂b∗RET∂η
=(1− α)∆s
∆θ≥ 0
∂INS∗RET∂η
=ρ(1− α)∆sσ2
∆θb∗RET +
INS∗RETb∗RET
(1− α)∆s
∆θ≥ 0
The comparative static results show that the need to provide insurance and deferred stock
compensation to the employee is particularly strong for intangible-intensive firms. As high-skill
human capital plays a bigger role in their investment process, the employee has better outside
options.
Interestingly, in the RET region the firm requires more liquid resources in the high than low
state (C0 +θh1 versus C0 +θl1). Holding abundant cash in the high state is a cost-effective way for
the firm to retain a key employee, as the alternative of providing a large share grant is particu-
larly costly when expected firm value is high. This result implies that the most successful firms
may choose a conservative financial policy, even though they are likely financially unconstrained.
For completeness, we note that two additional solutions exist in the RET region. First, there
is a solution in which both the insider leaves the employee’s low participation constraint (PCl)
are slack. This happens when risk aversion is relatively high, so the insider prefers to leave
some rents to the employee in the low state, so that he can offer a lower share grant to limit
the employee’s exposure to firm risk. The economic insights are the same as in the case studied
here, and we present this alternative solution in Appendix B. The comparative static results in
Proposition 1 also hold in this case.
Another solution exists in which (PCl) is slack but the insider’s incentive compatibility con-
straint (ICl) binds. This region generates some interesting results on how the compensation
22
may interact with the insider’s moral hazard problem, and we discuss it in Section 3.3.3.
3.3.2. Traditional Precautionary Motive
In the PREC region the firm saves just enough cash to ensure that re-investment needs can
be met in state L. Optimal cash holdings are directly pinned down by (PREC), such that the
insider needs to contribute A0 = CPREC + If1 = APREC .
Because cash holdings in the PREC region are determined by the firm’s precautionary needs,
which are large relative to the value of the employee’s outside option, the firm does not provide
additional insurance via deferred wages.
Lemma 5. The optimal contract in the PREC region contains only equity and no deferred
wages.
The formal proof is in Appendix C. Financial constraints require the insider to save so much
cash towards the low state, that it is unnecessary to provide additional insurance to retain the
employee in the high state, so there is no further benefit to granting a deferred wage. This
point highlights an interesting complementarity between the traditional precautionary motive
and the retention motive. A prudent financial policy insures the firm’s investment spending in
bad states of the world, while also providing insurance to employees in good states of the world
when outside options are high.
The optimal equity grant can be derived by plugging C∗0,PREC into (PCh) and solving for b∗.
This yields a quadratic equation that implicitly defines the optimal equity grant:
b[(1− η)(I0 + I1) + αηI1 + θh1 − θl1 + θh2 ]− ρb2σ2 − (1− α)ηsh = 0. (11)
The smaller root to this equation, which we denote denote b∗PREC , is optimal as it minimizes
compensation cost. It can be expressed in closed form using the quadratic formula.
Because the insider’s choices are determined by precautionary needs rather than minimizing
the cost of employee retention, one of the participation constraints does not bind. By Lemma 2,
the insider leaves (PCl) slack and provides rents to the employee in state L.19 If these rents are
19The insider could bind (PCl) by granting a negative wage, but we assume this is not possible.
23
too high, the insider may divert resources in the low state. This occurs when the project’s low-
state continuation value is less than the employee’s rents, which the insider can re-claim through
diversion. Re-arranging (ICl), it is clear that (b∗PREC , C∗0,PREC) are only incentive-compatible
if
b∗PREC ≤θl2
θl1 + θl2 +A∗0,PREC.
The following proposition summarizes the solution for the (PREC) region.
Proposition 2. In the PREC region, the insider’s optimal compensation and financing choice
is characterized by:
b∗PREC implicitly defined as smaller root of Eq. (11)
w∗PREC = 0
A∗0,PREC = (1− η)(I0 + I1) + αηI1 − θl1
The project is abandoned at t = 0 if these values do not satisfy
b∗PREC ≤θl2
θl1 + θl2 +A∗0,PREC,
The optimal equity grant is increasing in intangible intensity while cash savings is decreasing:
∂b∗PREC∂η
> 0
∂A∗0,PREC∂η
= (α− 1)I1 − I0 < 0
The comparative statics for A∗0,PREC result from the fact that high-intangible firms require
a lower upfront funding contribution, as firm investment spending is lower and the employee
contributes human capital. This result is qualified once external financing is introduced in Sec-
tion 4. HINT firms have a lower safe debt capacity since intangible assets may be diverted, so
while own investment spending is smaller, a larger fraction needs to be funded internally.
24
3.3.3. Compensation Overhang
We now study the firm’s problem when (ICl) binds. Propostion 2 already shows that in the
PREC region the project may be abandoned if rents provided to the employee are too large.
In this case, the compensation and financing decisions by the firm tempt the insider to divert
resources in the low state. In the RET region, the insider also may prefer to leave rents to the
employee in the low state, so as to pay a smaller share grant and expose her to less risk (see
Appendix B).
(ICl) binds whenever minimizing compensation costs requires the insider to provide so much
rents to the employee in the low state that she cannot commit to avoid diverting resources.
This compensation overhang effect leads to the project failing in some states. The insider can
prevent this moral hazard problem by reducing the employee’s rents in the low state until (ICl)
is just satisfied. In this case, the optimal share grant follows from combining (PCh) and (ICl):
θl2 + b∆θ = ρb2σ2 + (1− α)ηsh. (12)
The optimal grant b∗RET -IC is the smaller root to this quadratic equation. As before, the opti-
mal level of insurance INS∗RET -IC follows from (PCh), and an equivalence exists between cash
holdings and deferred wages.
The following proposition summarizes the solution:
Proposition 3. If (ICl) binds in the RET region, the optimal share grant b∗RET -IC is the
smaller root to Eq. (12).20 The optimal level of insurance is given by
INS∗RET -IC =
((1− α)ηsh
b∗RET -IC+ ρσ2b∗RET -IC − [θh1 + θh2 ]
)b∗RET -IC .
20Applying the quadratic formula, b∗RET -IC =∆θ−[(∆θ)2−4ρσ2(1−α)η]1/2
2ρσ2
25
Both the optimal equity grant and overall level of insurance are increasing in intangible intensity:
∂b∗RET -IC∂η
≥ 0
∂INS∗RET -IC∂η
≥ 0
Moreover, the optimal equity grant is larger, and the optimal level of insurance is smaller, than
what the insider would offer if (ICl) were slack:
b∗RET -IC ≥ b∗RET ,
INS∗RET -IC ≤ INS∗RET .
As in Section 3.3.1, the optimal equity grant and insurance rise with the firm’s intangible
intensity. The key difference is that the insider offers a larger share grant and less insurance to
the employee than she would if (ICl) were slack. A higher share grant reduces the employee’s
rents in the low state, because shares have relatively less value in the low state. Thus, it reduces
the value of unvested equity that the insider could re-claim by engaging in diversion, alleviating
the moral hazard problem. The cost is that the insider needs to offer more compensation via
higher insurance than she would if diversion were not possible. This is shown formally in the
general solution in Appendix B.
4. External Financing
This section presents the extended model, relaxing the assumption that the insider’s initial
endowment W0 is sufficient to fund all investment needs. Because the insider’s maximum cash
contribution is less than If0 + If1 , she must raise external financing to complete the project. We
show how the possibility of diversion limits the insider’s capacity to raise external financing.
To enrich the setup, we further allow for an information asymmetry between insiders and
outside investors in the low state, as illustrated in the timeline in Figure 7. With probability p
the project has a positive payoff net of re-investment needs, as before: E[θ2] = θl2 > If1 . In this
26
Figure 7: Timeline of Extended Model
Good state
Cashflow 𝜃"# > 𝐼"&
Continuation
Re-invest −𝐼"&
Orderly termination• Recovery of 𝐶)+𝜃"+ − 𝐼)
& plus 𝐾" = (1 − 𝜂)𝐼)
• Employee departs
Departs
NATURE INSIDER EMPLOYEE
𝑡 = 1 𝑡 = 2
𝑞
1−𝑞
𝑝
1−𝑝
𝑡 = 1.5
Receives outside offer 𝑠 = 1 −𝛼 𝜂𝑠+
DiversionClaim α𝜂𝐼" as private benefit
Positive signal
INSIDER
𝑡 = 0
• Contribute 𝐶0• Invest 𝐼)
&
• Grant (𝑤, 𝑏)• Raise 𝐸) ,𝐷)
Negative signal
Bad state
Cashflow 𝜃"# > 𝐼"& Observes
diversion
Stays
NATURE
Project succeeds• Final cashflow 𝜃B+ plus
recovery of 𝐾B = (1 −𝜂)(𝐼)+𝐼")
• Employee receives 𝑤 +𝑏𝑉B+
• Insider receives (1 − b)𝑉B+
Project fails
• Recovery of 𝐶)+ 𝜃"+ − 𝐼)& − 𝐼"
&
plus 𝐾B = (1 −𝜂)(𝐼)+𝐼" )
state “LV”, the insider’s choice to continue or divert depends on her ownership in the firm and
the employee’s compensation. With probability 1 − p the insider learns that the project fails
with certainty: θ2 = 0 (“state LF”). In this state, the employee will then certainly leave, and the
insider recovers the value of all tangible assets K1 = (1− η)I0 and cash holdings. The baseline
model in Section 3 is nested in this generalized formulation, and corresponds to the case p = 1.
4.1. Extension Setup
At t = 0 or t = 1 the insider can issue debt Dt. At t = 0 the insider can also sell an equity stake
e in the project to raise E0 from risk-neutral outside investors. We discuss the case of equity
issuance at t = 1 in the Appendix. The required equity stake e and interest paid on debt are
set such that outside investors break even. Risk-free debt pays the safe rate of 0. We assume
for simplicity that all interest payments are due at t = 2, and denote r0 the total net interest
paid on debt raised at t = 0, and r1 the net interest paid on debt raised at t = 1.
External finance may introduce moral hazard, as an insider benefits from diverting intangible
investment for private benefit without bearing its full cost. We assume that outside investors at
t = 0 can constrain observable insider choices at t = 1, such as allowing only investment spending
in line with the firm technology, but cannot distinguish between valuable intangible investment
and diversion. Insider choices at t = 1 cannot be made contingent on employee retention since
27
the employee chooses to leave only after observing the quality of intangible investment.
4.1.1. Precautionary Savings and Financial Slack
With external financing, the firm’s budget constraints at t = 0 and t = 1 are respectively given
by
A0 + E0 +D0 = C0 + If0 ,
C0 +R1 +D1 = C1 + If1 ,
and hence its cash holdings are C0 = A0+E0+D0−If0 , and C1 = C0+R1+D1−If1 , respectively.
Similarly, the firm’s (PREC) constraint also reflects the possibility to raise funding at t = 1:
C0 +D1 ≥ If1 −Rl1. (PREC’)
Note that from the perspective of satisfying its precautionary constraint, the firm is indifferent
between raising funding at t = 0 and hold it as cash on balance sheet, or to wait until t = 1
to raise debt. As we show below, cash raised via debt cannot help to retain the employee, and
is thus only useful to satisfy precautionary needs, while risky debt may even harm employee
retention.
For the further analysis it is therefore useful to abstract from the firm’s choice of how much
safe debt to raise, and instead focus on its financial slack,21 which we define as cash holdings
plus the unencumbered safe collateral value of tangible assets:
S0 ≡ C0 + [(1− η)I0 −D0]︸ ︷︷ ︸Unused collateral capacity
= A0 + E0 − αηI0,
Si1 ≡ C1 + [(1− η)(I0 + I1)− (D0 +D1)]︸ ︷︷ ︸Unused collateral capacity
= A0 + E0 + θi1 − αηI1,
where the second equality follows from the firm’s respective budget constraints. Note that the
21In reality, safe debt may offer some benefits, such as reduced screening and enforcement costs next to fiscalsavings.
28
firm can always raise safe debt at a risk-free interest rate of 0 by pledging its tangible assets as
collateral. To abstract from the firm’s choice of how much safe debt to raise, we focus on slack,
and hence A0 and E0 as the firm’s decision variables. We simply note that as long as the firm
ensures that it has sufficient slack, it can fund all its investments by raising safe debt against
tangible collateral, and leave the exact choice how much debt to raise indeterminate. This allows
us to simplify the t = 0 budget constraint, as well as the precautionary constraints (PREC’) as
St ≥ 0, t = 0, 1.
In the remainder we assume that θl1 ≥ αηI1, so that S1 ≥ 0 and hence (PREC’) can always be
satisfied by pledging the collateral value of tangible assets. This assumption allows us to focus
on the more interesting and novel RET region, where the firm’s main concern is retaining the
employee.
4.2. RET Region
In the RET region, the insider’s key constraints are the employee’s participation constraints
(PCh) and (PCl). These constraints are the same as in the model without external financing
in Section 3, though the relevant firm value entering the constraints is now given by
E1[V i2 ] =
∫ ∞θ2
(C1 +Ri2 +K2 − w − (1 + r0)D0 − (1 + r1)D1
)dF (θ)
V ar1[V i2 ] = σ2 +X (13)
where θ2 ≡ D0 + D1 + r0D0 + r1D1 + w − C1 −K2 denotes the realization of θ2 such that for
θ2 < θ2 the firm defaults.
Proposition 4. Risky debt reduces incentives for employees to stay, i.e. risky debt is counter-
productive in terms of satisfying (PCh) and (PCl). Thus, the firm never raises risky debt
in the RET region ( (PREC’) slack). Safe debt has no effect on the employee’s participation
constraints.
29
The intuition for the result is straightforward. Risky debt financing increases the risk of
any form of employee compensation, which then requires a higher risk premium. Thus, in
the absence of any distinct benefit for debt financing, the insider prefers to issue equity to
risk-neutral investors to reduce compensation costs.
4.2.1. Moral Hazard and Limits to External Finance
In contrast to debt, outside equity can provide insurance to the employee. However, equity
funding may still worsen insider incentives to divert. To raise E0 in outside equity, insiders
need to promise a share e s.t.
eE0[V2] = E0,
where E0[V2] is the expected final firm value from the viewpoint of t = 0, given by
E0[V2] = E0[C1 +R2 +K2 − w −B0 −B1] = A0 + E0 + θ1 + θ2 − w,
where θ1 ≡ qθh1 + (1− q)θl1 and θ2 ≡ qθh2 + (1− q)θl2 denote the ex-ante (t = 0) expectation of
θ1 and θ2, respectively. Combining these two equation allows to express E0 as a function of e,
showing how much funding the firm can raise by promising a share e to investors:
E0 =e
1− e[A0 + θ1 + θ2 − w
]. (14)
External finance may exacerbate moral hazard, as an insider benefits from diverting intangi-
ble investment for private benefit without bearing its full cost. With a share e promised to
outsiders, insiders earn from diverting:
αηI1︸︷︷︸Private Benefit
+ (1− e) [C1 +K2]︸ ︷︷ ︸Firm Value After Diversion
= αηI1 + (1− e)[A0 + E0 + θi1]
= A0 + θi1 + e[αηI1 + θ1 − θi1 + θ2],
30
where the last line uses the pricing equation (14). In contrast to the model without external
financing (Section 3), the gain from diversion now increases in the share promised to insiders
e, as well as in the firm’s intangible intensity η, as insiders can divert intangible spending.
The value from continuation without diversion is
(1− e− b)E1[V i2 ] = (1− e− b)[A0 + E0 + θi1 + θi2 − w]
=
(1− b
1− e
)[A0 + θi1 + θi2 − w
],
where the second line uses the pricing equation (14). The gain from continuation decreases
both in e and in b, as insiders have to share more future firm value with outside investors and
employees.
Comparing the gain from diversion to the gain from continuation yields the following incentive-
compatibility constraints:
(1− b
1− e
)[A0 + θh1 + θh2 − w
]≥ A0 + θh1 + e[αηI1 + θ1 − θh1 + θ2] (IC ′h)(
1− b
1− e
)[A0 + θl1 + θl2 − w
]≥ A0 + θl1 + e[αηI1 + θ1 − θl1 + θ2]. (IC ′l)
Eqs (IC ′h) and (IC ′l) are the generalized versions of (ICh) and (ICl) in Section 3, and collapse
to (ICh) and (ICl) if e = 0. The key difference is that external finance exacerbates moral
hazard, so that the incentive compatibility constraints implicitly define an upper bound ei, s.t.
incentive-compatibility in state i = H,L is satisfied if and only if e ≤ ei.
4.3. Firm Problem with External Financing
Because equity is fairly priced, the firm’s objective function is equivalent to that in Section 3:
Uf = (1− b− e)E0[V2]− (A0 − E0) = (1− b)E0[V2]−A0.
31
The firm’s problem is given by
maxA0,E0,w,b
Uf = (1− b)E0[V2]−A0 (15)
s.t. (PCh), (PCl), (IC′h), (IC ′l), (PREC
′)
As we focus on parameters such that (PREC’) is slack, we solve the firm problem for the RET
region only. As we show next, the firm’s optimal choices are essentially the same as in Section 3
if the incentive-compatibility constraints are slack. In Section 4.3.2 below, we elaborate how
the firm’s optimal choices may change when the firm becomes constrained.
4.3.1. Slack Incentive-Compatibility Constraints
As in Section 3, we focus on the case in which both participation constraints bind, while the
solution with a slack (PCl) is shown in Appendix B. Relative to the model without external
financing, the key difference is that the firm needs to raise some of its cash holdings via outside
equity E0, so that the overall level of insurance is given by
INS(w,A0; b) ≡ b(A0 + E0) + (1− b)w. (16)
Note that because equity is fairly priced, the firm is still indifferent between providing insurance
via cash holdings, or by offering deferred wages (as described in Lemma 4 in Section 3). The
following proposition summarizes the firm’s optimal choices with slack incentive-compatibility
constraints:
Proposition 5. When (PCh) and (PCl) bind, and (IC ′h) and (IC ′l) are slack, the insider’s
optimal compensation choices are equivalent to those in the absence of external finance, as
outlined in Proposition 1:
b∗RET ′ =(1− α)η∆s
∆θ,
INS∗RET ′ =
(ρ(1− α)η∆sσ2
∆θ+sh∆θ
∆s− [θh1 + θh2 ]
)(1− α)η∆s
∆θ.
32
To fund the insurance, insiders contribute their entire endowment A∗RET ′ = W0, and raise
external equity
E∗RET ′ =1
b∗RET ′INS∗RET ′ −W0 −
(1− b∗RET ′)b∗RET ′
w,
offering a share e∗RET ′ to external investors
e∗RET ′ =E∗RET ′
E0[V2]=INS∗RET ′ − b∗RET ′W0 − (1− b∗RET ′)wINS∗RET ′ + b∗RET ′(θ1 + θ2)− w
.
4.3.2. Binding Incentive-Compatibility Constraints
4.4. Summary: External Financing
To summarize, issuing outside equity increases the firm’s incentives to divert, as now proceeds
from terminating need to be shared with others. A novel factor is the gain from inducing the
employee to leave, ensuring unvested claims expire and granting the insider a larger share of
existing assets.
The extension to external finance shows its impact on employee retention, moral hazard and
thus its cost of capital as a function of its technology. The need to provide insurance to em-
ployees generally makes risky debt unattractive. Outside equity allows a constrained insider to
raise adequate slack to ensure reinvestment and insure employees. However the insider’s moral
hazard problem becomes more serious once some firm value is promised to outside investors.
The result shows that external equity funding a firm with more intangibles is more expen-
sive, reflecting a higher degree of moral hazard. A larger insider share is required for HINT
firms to avoid a larger temptation to divert and the large losses associated with losing talented
employees. The analysis is consistent with the empirical evidence around funding intangibles,
and offers a broader interpretation relative to the classic precautionary motive.
5. Summary of Results
This section briefly summarizes our key results on financing intangibles, and also proposes a
revised view of corporate financial statements.
33
Table 2. Summary of Theory and Results
HINT Firms LINT Firms
I Require more human capital investment I Require more cash spending
I Compensation of HC deferred over time I Firm investment spending front-loaded
I Co-investment by risk-averse employees I Investment financed by risk-neutral outsiders
I Finance more with inside equity I Raise more external equity and debt
I Moral hazard reduces external financing capacity I Safe collateral raises external financing capacity
I Save more cash due to both I Save less cash overallprecautionary motive and to insure employees
I Prefer repurchases to dividend payouts I More likely to pay out dividends
Table 2 first lists our view on the differences between creating tangible and intangible assets.
Intangibles require a larger contribution of human capital to create. Because human capital
cannot be trapped inside a firm, its compensation must be deferred to ensure commitment until
the project’s completion. This leads to a key difference in the timing of cashflows: LINT firms
spend more cash upfront to purchase tangible assets, while HINT firms accumulate cash over
time until compensation vests. A third key difference is that intangibles are largely created by
risk-averse employees, while tangibles are funded by risk-neutral outsiders.
The main novel results are summarized in the bottom panel of the table. HINT firms fi-
nance investment in part by unvested equity, and need to secure a larger insider stake. LINT
firms can fund their larger share of investment spending with outside equity and debt. HINT
firms’ external financing capacity is lower because insiders can divert spending on intangibles,
which also makes it costlier. Next to incorporating intangible capital’s limited pledgeability,
our approach also reveals a novel “compensation overhang” effect, since an unvested share af-
fects insider moral hazard just as much as external financing. HINT firms choose hold more
cash to insure their employees and prefer repurchases to support the value of unvested claims.
Strikingly, the model predicts the most successful firms may hold more cash than those more
constrained, with the goal to minimize the equity share granted in the good state. These results
complement the traditional precautionary need for cash in bad times.
The implication of significant intangible capital and a structural retention motive has implica-
34
Figure 8: Revised View of Corporate Financials
Balance Sheet Market Value
tions for our interpretation of financial statements and the measurement of investment activity.
Intangible assets embedded in skilled human capital constitute much of an innovative firm’s
value, yet are largely unrecorded in financial statements. While accounting rules require firms
to classify spending on R&D, advertisements, marketing, and organizational capital as ordinary
business expenses, recent work recognizes part of this spending is an investment and adds it to
a firm’s capital stock (Peters and Taylor, 2017; Bellstam et al., 2017).22
Next to corporate goodwill investment, also skilled human capital contribution goes unac-
counted in financial statements, as it does not produce a measureable cash outlay.
As intangible assets embedded in skilled human capital cannot be reliably measured, their
contribution to firm value is difficult to quantify. HINT firms’ total investment activity may
have been strongly underestimated in recent years, at the same time that measurable investment
spending has declined (Philippon and Gutierrez (2017)).
Figure 8 puts forth a revised view of financial statements. It compares the balance sheet
and market values of HINT (η > 0) and LINT (η = 0) firms, mapping them to values from
22While conceptually it is clear that such spending enhances corporate goodwill, accounting rules do not recognizeits value until it is realized in an acquisition.
35
our model at t = 0. The capital that HINT firms record on the balance sheets may appear
to be smaller than that of LINT firms, because they acquire fewer tangible assets and much
of the firm’s intangible spending αηI0 is uncapitalized. Employees’ human capital contribution
(1− α)ηI0 is entirely unrecorded in corporate balance sheet.23
While HINT firms’ total investment exceeds traditional measures, their market capitalization
is in part not destined to current investors, as a significant amount is pledged to skilled em-
ployees, early investors and founders (see Figure 8). An interesting research challenge is also
to measure the degree of equity dilution created by large and steady share grants to critical
human capital. In principle, accounting measures that reports the scale and time distribution
of unvested equity is a valuable measure of anticipated dilution, and the profit division between
inside, outside and unvested equity.
6. Conclusions
The paper has studied the effect of evolving technology through the lens of its impact on the
composition of corporate investment. Our main contribution is a formal analysis of the creation
of intangible assets, which yields novel implications for corporate financing, risk management
and payout policy. Our simple model distinguishes firms in terms of their technological reliance
on intangibles.
We show that the specific nature of intangible capital implies two key differences. First,
while traditional firms rely on upfront purchases of physical capital, intangible capital is devel-
oped jointly by firm resources and creative employees contributing their skills. Second, because
human capital cannot be purchased, HINT firms have lower investment and external financ-
ing needs. Empirically, HINT firms indeed tend to have higher free cashflows. Some cash is
likely held for precautionary reasons, but similar patterns emerge from data on firms that seem
financially unconstrained (such as those paying dividends).
Our analysis suggests a second motive for prudent financial policy next to the classic pre-
cautionary motive. As intangible investment requires cooperation of skilled labor, firms need
23Unobserved investment by innovative employees includes training, coding software, developing firm capabilitiesby accumulating organizational capital, gathering and analysing data or designing a marketing campaign.
36
to reward human capital using deferred compensation (in the form of career prospects, bonuses
and share grants). Firms can reduce average compensation cost by offering some insurance
to risk-averse employees, as in Berk et al. (2010). This implies that firms with more intangi-
ble assets may choose lower leverage, higher cash holdings and a payout policy favoring share
repurchases over dividends.
Several empirical facts are consistent with a retention motive for prudent corporate poli-
cies. An appropriate empirical analysis clearly requires better measures on human capital value
and forms of deferred compensation to assess more precisely how intangible investment affects
human and financial capital policies by firms.
A changing nature of investment has broad implications. Delayed compensation of human
capital implies lower capital spending, and intangible investment should be added to traditional
CAPEX measures. As rising human capital investment is not tradeable, the amount of investable
assets in the economy may fall. In general equilibrium, a structural decline in demand for
external funding and a rising innovator share may explain the gradual fall in interest rates
since the 1980s, and the re-allocation of excess savings into real estate values in all developed
countries (Dottling and Perotti, 2019).
37
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40
Appendix A Explanation of Motivating Facts Calculations
This appendix contains definitions of the empirical measures used in Section 2, as well as someaccompanying notes to the figures and table. Unless otherwise noted, the source of each dataitem is Compustat.
A.1 Variable definitions
Variable Definition
Intangibles Ratio A firm’s stock of intangible assets (data item K INT from the Peters and Taylor Total Q dataset) dividedby total assets. The stock of intangible assets is measured as capitalized annual spending on R&D pluscapitalized annual spending on organizational capital plus intangible assets reported on the balancesheet (including goodwill). Throughout the paper, total assets are defined as the sum of intangibleassets and PP&E (Compustat data item PPENT).
Net Leverage Long-term debt (data item DLTT) plus short-term debt (DLC) minus cash and marketable securities(CHE), divided by total assets. This variable is winsorized at the 1-99 level.
Cash Holdings Cash and marketable securities (data item CHE) divided by total assets. This variable is winsorized atthe 1-99 level.
Tangible Investment The annual net change in tangible assets, measured as PP&E in the current year (data item PPENT)plus depreciation of tangible assets (DP minus AM) minus PP&E in the previous year, divided by op-erating cashflows. Throughout the paper, operating cashflows are operating income before depreciation(OIBDP) plus Intangible Investment minus taxes (TXT) minus interest payments (XINT). This variableis set to missing for firms with negative operating cashflows, and is winsorized at the 1-99 level.
Intangible Investment Annual R&D spending (data item XRD) plus 0.3×SG&A spending (XSGA) plus the annual net changein intangible assets reported on the balance sheet, divided by operating cashflows. The annual netchange in reported intangibles is intangible assets reported on the balance sheet in the current year(INTAN) plus amortization (AM) minus intangible assets reported on the balance sheet in the previousyear. Missing values of XRD and XSGA are interpolated following Peters and Taylor (2017). Startingin 2006, the fair-value expense of annual stock option grants to employees (OPTFVGR) is deductedfrom SG&A, as this expense is not a cash outlay. This variable is set to missing for firms with negativeoperating cashflows, and is winsorized at the 1-99 level.
Free Cashflows Operating cashflows minus Tangible Investment minus Intangible Investment, divided by operatingcashflows. This variable is set to missing for firms with negative operating cashflows, and is winsorizedat the 1-99 level.
Debt Issued Cash received from issuing long-term debt (data item DLTIS). When DLTIS is missing, the variableequals the long-term debt (DLTT) in the current year minus the difference between the previous year’svalues of long-term debt and debt scheduled to mature in two years (DD2). This variable is winsorizedat the 1-99 level.
Retained Earnings Free Cashflows minus Dividends minus Repurchases. This variable is set equal to 0 if negative, and iswinsorized at the 1-99 level.
Deferred Equity The annual grant-date fair value of restricted stock (data item STKCO, set to 0 if missing before 2005)plus stock option grants paid to non-executive employees, divided by Debt Issued plus Retained Earningsplus Deferred Equity. Employee option grant values are measured following ? as the Black-Scholes valueof total stock options granted minus the Black-Scholes value of stock options granted to top executiveslisted in Compustat ExecuComp.
Dividends Annual payouts of common dividends (data item DVC) divided by Free Cashflows. This variable iswinsorized at the 1-99 level.
Repurchases Annual spending on share repurchases divided by Free Cashflows. Spending on repurchases is measuredfollowing Fama and French (2001) to exclude shares bought back to fulfill employee option exercises. Itequals the annual change in number of shares in the corporate treasury (data item TSTKC). For firms withzero or missing values of TSTKC in the two previous years, it equals open-market purchases of commonstock (PRSTKC) minus sales of common stock (SSTK). This variable is winsorized at the 1-99 level.
Retained Cashflows Free Cashflows minus Dividends minus Repurchases, divided by Free Cashflows. This variable is win-sorized at the 1-99 level.
41
A.2 Figure and table notes
Figure 1. Net Leverage or Cash Holdings are plotted for the median HINT firm, LINT firm,and HINT firm that does not operate in an IT sector. IT sectors are the Fama-French 48 in-dustries Computers, Electronic Equipment, Measuring and Control Equipment, and BusinessServices (SIC codes 7370 to 7379 only).
Figure 2. Plots show Tangible Investment, Intangible Investment, and Free Cashflows for themedian HINT and LINT firm. Each variable’s median value is calculated over five-year intervalsthat end in the year shown on the figure.
Figure 3. For each firm, Debt Issued, Retained Earnings, and Deferred Equity are averagedover five-year intervals that end in the year shown on the figure, and then divided by the sumof the averaged values of the three variables. The resulting values are averaged across all HINTor LINT firms in each five-year interval, and then plotted in the figure.
Figure 4. Plots show Dividends, Repurchases, and Retained Cashflows for the median HINTand LINT firm. Plots show the median annual value, averaged over five-year intervals that endin the year shown on the figure.
Table 1. Columns (1) through (3) report variables for the median HINT and LINT firm, aswell as the difference in medians. Columns (4) through (6) report values for HINT and LINTfirms with positive values of Dividends in the year, while columns (7) through (9) report valuesfor HINT and LINT firms in the S&P 500 index during the year.
42
Appendix B General Solution to Problem 7
The main text in Section 3 focuses on specific solution regions to Problem 7. This appendix
presents the general solution to the problem, covering all possible cases. The insider’s maxi-
mization problem at t = 0 can be expressed using the Lagrangian function (7), re-posted here
for convenience:24
maxA0,w,b
L = (1− b){A0 + q(Ah1 + Ah2) + (1− q)(Al1 + Al2)− w
}−A0 (17)
+ µh
{w + b[A0 + θh1 + θh2 − w]− ρb2σ2 − (1− α)ηsh
}+ µl
{w + b[A0 + θl1 + θl2 − w]− ρb2σ2 − (1− α)ηsl
}+ φh
{(1− b)[θh2 − w]− b[A0 + θh1 ]
}+ φl
{(1− b)[θl2 − w]− b[A0 + θl1]
}+ λ{C0 − CPREC
}
Maximizing Eq. (17) with respect to each choice variable yields:
∂L∂A0
= b(−1 + µh + µl − φh − φl) + λ = 0 (18)
∂L∂w
= (1− b)(−1 + µh + µl − φh − φl) = 0 (19)
∂L∂b
= −{q(θh1 + θh2 ) + (1− q)(θl1 + θl2) +A0 − w
}(20)
+ µh
{A0 + θh1 + θh2 − w − 2ρbσ2
}+ µl
{A0 + θl1 + θl2 − w − 2ρbσ2
}− φh
{A0 − w + θh1 + θh2
}− φl
{A0 − w + θl1 + θl2
}= 0
24Formally, the Lagrangian should also consist of non-negativity constraints for A0, w, b. We omit these con-straints for ease of readibility.
43
The complementary slackness conditions are:
µh
{w + b[A0 + θh1 + θh2 − w]− ρb2σ2 − (1− α)ηsh
}= 0 (21)
µl
{w + b[A0 + θl1 + θl2 − w]− ρb2σ2 − (1− α)ηsl
}= 0 (22)
φh
{(1− b)[θh2 − w]− b[A0 + θh1 ]
}= 0 (23)
φl
{(1− b)[θl2 − w]− b[A0 + θl1]
}= 0 (24)
λ{A0 − If0 − I
f1 − θ
l1
}= 0 (25)
Together, conditions (18)–(25) define the optimal choices (A∗0, w∗, b∗, µh, µl, φh, φlλ).
As in the main text, we split the analysis into the RET Region, defined by a slack (PREC)
and λ = 0, and the PREC Region, defined by a binding (PREC) and λ > 0. By Lemmas 1 and
2, (PCh) always binds and (ICh) is always slack, so µh > 0 and φh = 0. Table 2 summarizes
all remaining cases, categorized into RET and PREC region.
B.1 RET Region
In the RET Region, λ = 0, and hence the FOCs w.r.t. C0 and w (Eqs. (18) and (19)) collapse
to one single condition:
µh + µl = 1 + φl. (26)
Hence, in the RET region there is indeterminacy between w ≥ 0 and A0 ≥ APREC (as discussed
in the main text). Instead, the solution determines the optimal level of insurance provided to
the employee, defined as
INS(w,A0; b) = bA0 + (1− b)w.
Given the optimal b∗RET , INS(w,A0, b) follows as the residual from (PCh):
INS(w,A0; b∗RET ) = ρb∗2RETσ2 + (1− α)ηsh − b∗RET [θh1 + θh2 ]
44
Table 2: Possible cases for the solution to Problem 17. “=” indicates a bindingconstraint, “>” indicates that a constraint is slack.
RET Region PREC RegionRET interior RET-PCL RET-IC PREC PREC-IC
(PCh) = = = = =(PCl) > = > > >(ICl) > > = > =(PREC) > > > = =
To determine b∗RET , plug (26) into the firm’s FOC w.r.t. b (20):
b∗RET =(1− q + φl − µl)∆θ
2(1 + φl)ρσ2(27)
The optimal share grant depends on parameters, as well as the Lagrangian multipliers µl and
φl, associated with the constraints (PCl) and (ICl). Within the RET region, there are three
cases to consider, as indicated in Table 2.
Case 1: RET interior. In this case, (PCl) and (ICl) are both slack, and hence µl = φl = 0,
and b∗RET directly follows from (27):
b∗RET =(1− q)∆θ
2ρσ2
The cost of providing stock compensation is that it exposes the employee to risk. The benefit is
that a share grant is worth less in the low state than a fixed deferred salary, reducing the rents
paid in the low state. At this interior solution, the insider optimally trades off these two forces.
Case 2: RET-PCL. In this case, (PCl) binds and (ICl) is slack, so that µl > 0 and φl = 0.
Note that b∗RET decreases in µl, hence the insider offers a lower level of stock compensation than
he would if (PCl) were slack. In this case, the insider would optimally like to offer so much
stock compensation that the employee leaves in the low state. To prevent the employee from
leaving, the insider reduces b to the point where (PCl) is just satisfied. The optimal b follows
45
from combining (PCh) and (PCl):
b∗RET =(1− α)η∆s
∆θ(28)
The optimal level µ∗l follows from plugging (28) and φl = 0 into (27).
Case 3: RET-IC. In this case, (PCl) is slack and (ICl) binds, so that µl = 0 and φl > 0. Note
that b∗RET increases in φl, hence the insider offers a higher level of stock compensation than
he would if (ICl) were slack. In this case, the insider would optimally like to leave so much
rents to the employee in the low state that she cannot commit not to divert resources in the
low state. To overcome this moral hazard problem, the insider offers a higher level of b, so as to
reduce the rents received by the employee in the low state, up to the point where (ICl) is just
satisfied (at the cost of higher INS, to still satisfy (PCh)). In this case, the optimal b follows
from combining (PCh) and (ICl):
θl2 + b∆θ = ρb2σ2 + (1− α)ηsh. (29)
The optimal b∗RET is defined as the smaller root to this quadratic equation, and φ∗l follow from
plugging b∗RET into (27).
B.2 PREC Region
In the PREC Region, λ > 0 and (PREC) binds, such that optimal cash holdings immediately
follow as C0 = CPREC , so that A0 = APREC . From (18), it is clear that with λ > 0, it must be
that −1 + µh + µl − θh − θl < 0. But this implies that ∂L∂w < 0, by Eq. (19), and hence the firm
is at the corner where w = 0.
The optimal equity grant can be derived by plugging APREC into (PCh) and solving for b∗.
This yields a quadratic equation that implicitly defines the optimal equity grant:
b[(1− η)(I0 + I1) + αηI1 + θh1 − θl1 + θh2 ]− ρb2σ2 − (1− α)ηsh = 0. (30)
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The smaller root to this equation, which we denote denote b∗PREC , is optimal as it minimizes
compensation cost.
Is it feasible for the firm to offer b∗PREC while holding CPREC? This depends on whether
the insider’s incentive compatibility constraint (ICl) is satisfied. Re-arranging (ICl), it puts an
upper bound on the share grant the insider can grant without
b ≤ θl2θl1 + θl2 +APREC
=θl2
If0 + If1 + θl2≡ b
Case 4: PREC If b∗PREC ≤ b, (PCh) and (PREC) bind, while all other constraints remain
slack. The insider offers b∗PREC and w∗ = 0, while holding CPREC to ensure re-investment.
Relative to the RET region, the insider offers less stock compensation, because the cash holdings
that are needed to ensure re-investment in the low state already provide more than enough
insurance to the employee in the high state.
Case 5: PREC-IC If b∗PREC > b, the insider’s moral hazard problem cannot be overcome in
the low state, and diversion will occur. The problem is that the high cash savings are simply
too attractive for the insider not to divert. Interestingly, it may still be possible to prevent
diversion by setting b = 0 and w = (1− α)ηsh. With b = 0, the insider does not need to share
any cash with the employee, and instead pays a high fixed salary in both states. Plugging these
into (ICl), it is clear that this contract can prevent diversion if
θl2 ≥ (1− α)ηsh.
If b∗PREC > b and θl2 < (1−α)ηsh, there is no contract that prevents the moral hazard problem
and at the same time allows to retain the employee. Hence, in this case the project cannot be
undertaken.
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Appendix C Proofs
This appendix contains proofs of lemmas and propositions.
C.1 Lemma 1 (Section 3)
Proof. Impose that (PCi) binds and re-arrange:
(1− b)w + bA0 = ρb2σ2 + (1− α)ηsi − b[θi1 + θi2].
Similarly, re-arranging (ICi) can be written as
(1− b)θi2 − bθi1 ≥ (1− b)w + bA0.
Combining the two equations yields the condition θi2 ≥ (1−α)ηsi + ρb2σ2, which is satisfied for
i = h, l by Assumption 2.
C.2 Lemma 2 (Section 3)
Proof. To establish that (PCh) optimally binds, we first suppose that the constraint is slack
and then show that the insider can do better by lowering b to the point where (PCh) binds.
Formally, if (PCh) was slack, then µh = 0, and hence µl = 1 + φh + φl − λb by Eq. (18).
Plugging this into the first order condition w.r.t. b (20), it is clear that with µh = 0:
∂L∂b
= −q∆θ − 2µlρbσ2 − λ
b
[A0 − w + θl1 + θl2
]< 0.
The first two terms are clearly negative. To see that the third term is also negative, note that
there are two cases to consider. First, if (PREC) is slack, then λ = 0 and the term drops out.
If (PREC) is slack, λ > 0 but the firm sets the wage optimally at w = 0, such that the bracket
is positive. Therefore, the first order condition is negative if µh > 0, and the insider strictly
prefers lowering the share grant until µh = 0 and (PCh) binds.
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C.3 Lemma 3 (Section 3)
Proof. It is easy to see that the employee’s compensation must be deferred until t = 2. If
compensation vested at t = 1, in every state the employee would strictly prefer to accept the
outside offer and depart the firm.
We next suppose that b∗ = 0, and then show that it is not possible for conditions (18)–(25)
of Problem (17) to all hold.
If b∗ = 0, then w = (1 − α)ηsh to satisfy the participation constraint in state H, so that
(PCl) is slack and µh > 0, µl = 0. Similarly, (ICh) is satisfied given that θh2 > (1 − α)ηsh by
Assumption 2.
Now there are two cases to consider. First, if (1 − α)ηsh > θl2, then the insider is unable to
satisfy (ICl) at b = 0, and hence in this case b = 0 cannot be optimal.
Second, if (1−α)ηsh ≤ θl2, then (ICl) is slack and hence φl = 0. It then follows from (19) that
µh = 1. Plugging µh = 1 and µl = φl = φh = 0 into the FOC w.r.t. b in Eq. (20) shows that
∂L∂b
= (1− q)[(Ah1 + Ah2)− (Al1 + Al2)] > 0.
Hence, in this case insiders prefer to increase b, inconsistent with b = 0 at the optimum.
C.4 Lemma 5 (Section 3)
Proof. In the PREC Region, λ > 0 and (PREC) binds, such that optimal cash holdings
immediately follow as C0 = CPREC . From (18), it is clear that with λ > 0, it must be
that −1 + µh + µl − θh − θl < 0. But this implies that ∂L∂w < 0, by Eq. (19), so the in-
sider’s problem decreases in w. Hence the firm optimally sets the wage at the corner w =
0.
Note that we omit the non-negativity constraint for w in the Lagrangian (17) for readability.
If it was added to the problem, and the Lagrangian multiplier was denoted κ, the FOC w.r.t.
b (19) would show that:
κ = (1− b)(1− µh − µl + θh + θl) > 0,
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implying that the non-negativity constraint is binding and hence w = 0.
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