Corporate Cash Holding Policy: A Multistage Approach with an Application in the Agribusiness Sector

1
Corporate Cash Holding Policy A Multistage
Approach with an Application in the Agribusiness
Sector

• Astrid Prajogo, Davi Valladao, John M.
  Mulvey
• QWAFAFEW Meeting
• February 22, 2011
• Operations Research and Financial Engineering
  Department, Princeton University.
• Electrical Engineering Department, Pontifical
  Catholic University of Rio de Jainero.

2
Outline

• Introduction Motivation
• The Model
• Notation
• Model Assumptions
• Mathematical Formulation
• An Application in the Agribusiness Sector
• Regime Analysis in the Agribusiness Sector
• Numerical Results
• A Fixed Policy Approximation
• Conclusion and Future Work

3
Introduction
We observe a significant increase in the
cash-to-asset ratio of SP 500 companies between
1993 to 2010.
4
Introduction

• A recent study by Standard Poors shows that
  theres an all-around increase in corporate cash
  holding.
• Global, and
• across all industries

Top Global Companies (excl. Financials) by Cash Holding1 Top Global Companies (excl. Financials) by Cash Holding1 Top Global Companies (excl. Financials) by Cash Holding1 Top Global Companies (excl. Financials) by Cash Holding1
Company Name Total cash2 Industry classification Head-quarters
General Electric Co. 78,392.0 Industrial conglomerates U.S.
Toyota Motor Corp. 48,304.8 Automobile manufacturers Japan
China Mobile Ltd. 46,786.0 Wireless telecom Hong Kong
Microsoft Corp. 43,253.0 Systems software U.S.
Cisco Systems Inc. 38,925.0 Communications equipment U.S.
Petroleo Brasileiro S.A. - Petrobras 34,658.9 Intgrtd oil gas Brazil
Volkswagen AG 34,632.2 Automobile manufacturers Germany
General Motors Co. 33,476.0 Automobile manufacturers U.S.
Google Inc. 33,380.0 Internet software svc U.S.
Total S.A. 27,081.0 Intgrtd oil gas France
1 Source SP Cross-Market Commentary The
Largest Corporate Cash Holdings Are All Over The
Map. Data taken as of Jan. 7, 2011. 2 Total cash
in the latest quarter (Mil. ).
5
Introduction
Cash holding can be bad for a firm because

• Cash may be better invested elsewhere, earning
  above risk-free rate returns.
• Cash provides managers more freedom in choosing
  projects, even the ones with negative NPV.
• High excess cash levels may be a signal of
  managerial concerns regarding the uncertainty of
  future operating cash flows and lack of
  investment opportunities, hinting at a negative
  link between cash holdings and returns.
• High cash reserves may induce the company to be
  seen as a prime target for hostile takeovers.
• Jensen Meckling (1976), Harford (1999), Lie
  (2002)

6
Introduction
Cash holding can be good for a firm because

• Internal cash allows for immediate investments
  and eliminates the costs incurred from external
  financing.
• Buffer stock during economic crisis.
• Cash helps reduce borrowing cost.
• Fazzari et al. (1988), Froot et al.(1993)

7
Introduction
A Brief Walk through the Literature

• Opler et al. (1999)
• Investigates the risk determinants of corporate
  cash holdings
• Finds a positive link between growth
  opportunities and excess cash.
• Harford (1999)
• High-cash firms are more likely to make
  value-decreasing investments.
• Mikkelson Partch (2003)
• Investigates that relationship between cash
  holding and operating performance.
• Concludes that cash holding does not hinder
  operating performance.
• Bates (2009)
• Documents a dramatic increase in cash holdings of
  U.S. manufacturing companies from 10 in 1980 to
  24 in 2004
• Increase in cash holding among corporations is
  caused by an increase in cash flow risk and RD
  expenditures.
• Palazzo (2008) and Simutin (2010)
• Independently found that firms with a high excess
  cash level exhibit higher future stock returns
  compared to its peers with low excess cash.

8
Introduction
Source Simutin (2010). Sample average of
regression factors in each cash decile.

• A few observations
• High betas for firms with high excess cash
• High market-to-book value of assets for firms
  with high excess cash.
• Smaller sized firms tend to belong in the lowest
  or highest decile based on excess cash.
• High-cash firms tend to have lower debt.

9
Introduction
Period Low High High-Low
1960-2006 0.852 1.253 0.401
1960-1982 0.913 1.242 0.220
1982-2006 0.794 1.262 0.469
Source Simutin (2010). Value-weighted monthly
returns are significant at the 1-level

• Firms with high excess cash exhibit higher stock
  returns than firms with low excess cash.
• The Fama-Macbeth regression factors are unable to
  explain the stock returns generated by this
  High-Low portfolio.
• No causality argument here.

10
Introduction
We propose a model of a firm facing stochastic
investment opportunities and stochastic cost of
external financing that are dependent on the
business cycle (regime-switching framework).

• Two sources of funding for investment and
  production
• cash (internal financing) and
• a single period debt (external financing)
• The model endogenously determines the best
• production,
• investment,
• financing,
• dividend payout, and
• cash holding policies
• to maximize shareholders value over the planning
  horizon.

11
An Application The Agribusiness
Sector

• The agribusiness sector is intended to include
  those firms whose operations involve the use of
  agriculture commodities.
• We define the companies in this sector as those
  U.S. companies that are classified within the
  Global Industry Classification Standards (GICS)
  subsectors
• Agricultural Chemicals (15101030),
• Agricultural Products (30202010), and
• Packaged Foods and Meats (30202030).
• Data compiled using CRSP and Compustat.
• 70 unique agribusiness companies to be included
  in the sample from January 1990 to March 2010.
• The agribusiness sector index return at the end
  of month t is calculated as the
  market-cap-weighted average of the stock returns
  of the companies that are identified to be in the
  agribusiness sector during month t.

12
An Application Descriptive
Statistics

We observe a similar increase in the
cash-to-asset ratio of the agribusiness companies
between 1990 to 2010, although the increase is
not as dramatic as in the SP 500.
13
An Application The Agribusiness
Sector

The relationship between the agribusiness index
and the SP 500 can help us determine business
cycles in the agribusiness sector.
14
An Application Hidden Markov
Model

• The uncertainty of the risk factors is assumed to
  be dependent on the business cycle of the
  agribusiness sector ? Use a Hidden Markov Model
  (HMM)

pt,r
pe,t
pe,e
pr,r
pt,t
Recession
Transition
Expansion
pr,t
pr,e
15
An Application Hidden Markov
Model

• Let the SP 500 and Agribusiness sector returns,
  rt,A and rt,M , be our observed variables and the
  regimes as the latent variable, Rt.

Rt-1
Rt
Rt1
rt-1,A , rt-1,M
rt,A , rt,M
rt1,A , rt1,M

• The regimes follow the discrete probability
  transition matrix P, where
• Pi, j ProbRt j Rt-1 i.
• Consider K regimes in the agribusiness sector.
  Then, we write the joint distribution of the
  monthly returns, rt,A and rt,M as

16
An Application HMM Calibration
Results
Transition Probability Matrix

• HMM calibration results using SP 500 and
  cap-weighted Agribusiness Index monthly total
  returns.
• Sample data from January 1, 1990 to March 31,
  2010.

Expansionary Period
Transition Period
Recessionary Period
17
An Application HMM Calibration
Results

• Red denotes market recession, Blue denotes
  market transition, and Green denotes market
  expansion in the agribusiness sector.
• The regimes persistence is gives us comfort that
  the chosen variables may indeed hold some
  information on the business cycles of the
  agribusiness sector.

18
An Application Descriptive
Statistics

19
An Application Descriptive
Statistics

20
The Model Notation
t0
t1
t2
s 1
s 2
s 3
s 4
s 5
s 6
21
The Model Notation
22
The Model Assumptions

• Production, Qt
• Quantity of production during period t is decided
  at time t-1 and sold at time t.
• Production quantity is constrained by the
  capacity function, which depends on the capital
  level.

• Financing/Borrowing, Dt
• Single-period debt.
• Non-negative debt.

• Investments, It
• Investing increases the production constraint
  during period t by increasing the amount of
  capital
• But the cost of investment is stochastic
• Investments are cheaper during recessions and
  more expensive during expansions.

• Dividends, Et
• Non-negative dividends, i.e. no equity issuance.

23
The Model Cash Flow at t

• The cash flow of the firm at time t after all
  decisions can be written as follows

Accrued interest on cash savings

Revenue from production during period t
-
Payment for debt outstanding

New borrowing
-
Cost of production during period t1
-
Investments for production during period t1
-
Dividend Payout

Cash at time t.
24
The Model
Cash flow constraint
Production constraint
25
Modeling the End-Effect

• Stochastic programming requires a finite planning
  horizon T.
• Theres a need to address the effect of
  production, dividends, etc. after T on the
  objective value. We call this the end-effect.

Solution Aggregate the constraints for t gt T.

• Production Constraint
• Cash Constraint
• Investment Constraint

26
An Application
Base Case Parameters
Base case parameter values
27
An Application
Base Case Parameters
Problem Size

• 2,560 scenarios
• 1,518,957 constraints
• 143,360 variables, and
• 3,186,392 non-zeros
• Solving time 358.9 seconds (using 8GB memory
  266GHz Intel Core i7 MacBook Pro)

28
Numerical Results Solution Ratios
29
Numerical Results Solution Ratios
t0
t1
t2
s 1
?1,1 ?1,2
Take the average, conditioned on regime 1
?1(1) (?1(1) ?1(2) ?1(3) ?1(4)) /
4 and ?1(2) ?1(3) ?1(4) ?1(1)
R1,1 R1,2 1
s 2
s 3
?1,3 ?1,4
R0 1
R1,3 R1,4 1
s 4
Take the average, conditioned on regime 2
?1(5) (?1(5) ?1(6) ) / 2 and ?1(6) ?1(5)
s 5
?1,5 ?1,6
R1,5 R1,6 2
s 6
30
Numerical Results Solution Ratios
31
Numerical Results Solution Ratios
Cash-to-Asset Ratio Cash-to-Asset Ratio Cash-to-Asset Ratio Cash-to-Asset Ratio
Time Regime 1 (Expansion) Regime 2 (Transition) Regime 3 (Recession)
0 NaN 0.1098 NaN
1 NaN 0.2335 0.0077
2 0.0000 0.3206 0.0346
3 0.0029 0.3398 0.0579
4 0.0129 0.3335 0.0586
5 0.0318 0.2717 0.0606
6 0.0453 0.1254 0.0006
Investment-to-Asset Ratio Investment-to-Asset Ratio Investment-to-Asset Ratio Investment-to-Asset Ratio
Time Regime 1 (Expansion) Regime 2 (Transition) Regime 3 (Recession)
0 NaN 0.0000 NaN
1 NaN 0.0000 0.2395
2 0.1386 0.0000 0.1956
3 0.0725 0.0000 0.1731
4 0.0152 0.0000 0.1772
5 0.0098 0.0000 0.1683
6 0.0031 0.0000 0.6880
32
A Fixed Policy Approximation

Motivation

• Drawback of the Original Problem
• Curse of Dimensionality
• Difficult to interpret the solution provided by a
  stochastic program
• Difficult to test the robustness of a stochastic
  program solution

• An Alternative using Fixed Policy (FP) Rules
• Use policy rules on a set of Monte Carlo
  simulated independent paths.
• Fixed policy rule using Monte Carlo simulation by
  setting a target
• cash ratio, and
• investment ratio
• at each stage for each regime.
• Use the average cash and investment ratios under
  each regime given by the SP.
• Sub-optimal solution

33
A Fixed Policy Approximation

Model Overview
At each time t, the fixed policy requires the
firm to maximize dividends while satisfying the
target cash-to-asset and investment-to-asset
ratios.
Target cash ratio
Target Investment ratio
34
A Fixed Policy Approximation

Motivation

• Fixed Policy vs Original Problem
• The policy rule provides us with a sub-optimal
  solution.
• We measure the Objective Gap between the two
  approaches
• (Objective(xorig) Objective(xFP)) /
  Objective(xorig)
• Objective(xorig) 520.46
• Objective(xFP) 473.72
• Objective Gap 8.9

35
Introduction
Companies may not be acting optimally based on
our model. Could cash savings be motivated by
fear? Could cash savings be a leading indicator
of market returns?
36
Conclusion Future Work

• Conclusion
• Our model shows that there is a benefit to
  corporate cash holding.
• In particular, firms save cash in order to
  facilitate investments during recession, when
  external financing is costly.
• The fixed policy rule might be a good
  approximation of the optimal solution.

• Future Work
• Extensions incorporating equity issuance,
  hedging policy, etc.
• Investigate a firms true objective function by
  calibrating the model to real (cash) data?
• The stochastic programming approach presents to
  us some difficulties in computing error bounds.
  Policy rules will address this problem. How can
  we combine the two approaches?

37
Bibliography
Bates, T.W., Kahle, K.M., Stulz, R.M. (2009).
Why Do US Firms Hold So Much More Cash than They
Used To? The Journal of Finance, (64)5,
1985-2021. Fazzari, S. M., Hubbard, R. G.,
Petersen, B. C., Blinder, A. S. Poterba, J. M.
(1988). Financing Constraints and Corporate
Investment. Brookings Papers on Economic Activity
1988(1), 141-206. Froot, K.A., Schartstein, D.S.,
Stein, J.C. (1993). Risk Management
Coordinating Corporate Investment and Financing
Policies. The Journal of Finance, 48(5),
1629-1658. Harford, J. (1999). Corporate Cash
Reserves and Acquisitions. The Journal of
Finance, 54(6), 1969-1997. Jensen, M. Meckling,
W. (1976). Theory of the Firm Managerial
Behavior, Agency Costs and Ownership Structure.
The Journal of Financial Economics, 3,
305-360. Lie, E. (2002). Excess Funds and Agency
Problems An Empirical Study of Incremental Cash
Disbursements. Review of Financial Studies, 13,
219-247. Mikkelson, W. H. Partch, M. M.
(2003). Do Persistent Large Cash Reserves Hinder
Performance? The Journal of Financial and
Quantitative Analysis, 38(2), 275-294. Opler,
T., Pinkowitz, L., Stulz, R. Williamson, R.
(1999). The Determinants and Implications of
Corporate Cash Holdings, The Journal of Financial
Economics, 52, 3-46. Palazzo, D. (2009,
January). Firms Cash Holding and the
Cross-Section of Equity Returns. Retrieved
November 1, 2010, from http//ssrn.com/abstract13
739618. Simutin, M. (2010). Excess Cash and Stock
Returns. Financial Management, 39(3) 1197-1222.
38
THANK YOU
39
The Model Notation
40
Appendix Cost
Per Unit

• Assume that the agriculture commodity index is a
  good proxy for the unit cost of raw materials
  used in production.
• Volatility clustering behavior motivates the use
  of the GARCH(1,1) model.

• Calibration results using sample data from
  1/1/1990 to 2/28/2010

41
Appendix
Profit Margin

• Unit sales price follows the formula
  , where
  is the gross profit margin.
• The quarterly data of Gross profit margin
  (Revenue COGS) / Revenue is available from each
  companys income statement compiled in the
  Compustat database.
• Due to the small number of data points, we choose
  to simulate the profit margin from the sample
  data.

42
Aappendix
Scenario Trees
43
Numerical Results Solution Ratios