Cash Flow Multipliers and Optimal Investment Decisions

• Date: 01 June 2015
• DOI: http://doi.org/10.1111/eufm.12047
• Author: Eduardo Schwartz,Holger Kraft
• Published date: 01 June 2015

Cash Flow Multipliers and Optimal

Investment Decisions

Holger Kraft

Goethe University, Department of Finance, Frankfurt am Main, Germany

E-mail: holgerkraft@finance.uni-frankfurt.de

Eduardo Schwartz

UCLA Anderson School of Management, Los Angeles, USA

E-mail: eduardo.schwartz@anderson.ucla.edu

Abstract

Valuation multipliers are frequently used in practice. By postulating a simple

stochastic process for the firm’s cash flows in which the drift and the variance of

the process depend on the investment policy, we develop a stylised model that

links the cash flow multiplier to the optimal investment policy. Our model implies

that the multiplier increases with investment at a decreasing rate. On the other

hand, the multiplier is inversely related to discount rates. Using an extensive data

set we examine the implications of our model. We find strong support for the

variables postulated by the model.

Keywords: firm valuation, valuation multiples, real options

JEL classification: C61, G12, G13, M40

Valuation multiples are frequently used in practice since they offer a quick way to value a

firm without estimating the whole series of future cash flows. This paper offers

a parsimonious model that relates the value of a firm to its current cash flow. Postulating a

simple stochastic process for the firm’s cash flows (before investment) in which the drift

We thank David Aboody, Saurabh Ahluwalia, Geert Bekaert, Michael Brennan, Judson

Caskey, Peter Ove Christensen, John A. Doukas (the editor), Mark Garmaise, Daniel

Hoechle, Jack Hughes, Ralph Koijen, Christian Laux, Volker Laux, Hanno Lustig, Kristian

Miltersen, Claus Munk, Naim Bugra Ozel, Richard Roll, Geoff Tate, and an anonymous

referee for very helpful discussions, comments, and suggestions. We also thank seminar

participants at Aarhus University, Georgia State University, Hebrew University Jerusalem,

Koc University Istanbul, Universidad Carlos III in Madrid, Universidad de Valladolid

(Simposio de Opciones Reales), the 1st World Finance Conference in Viana do Castelo

(Portugal), the Copenhagen Business School, and the Financial Economics Conference at

Graduate School of Economics of the Fundacao Getulio Vargas in Rio de Janeiro for many

helpful comments and suggestions. All remaining errors are of course our own. Holger Kraft

gratefully acknowledges financial support by Deutsche Forschungsgemeinschaft (DFG).

European Financial Management, Vol. 21, No. 3, 2015, 399–429

doi: 10.1111/eufm.12047

© 2014 John Wiley & Sons Ltd

and the variance of the process depend on the investment policy of the firm, we derive a

closed‐form solution of the cash flow multiplier that takes into account optimal

investment and how this investment affects future cash flows. We show how the cash flow

multiplier is (negatively) related to the discount rate and (positively related) to optimal

investment. Furthermore, it is shown that the multiplier depends on optimal investment in

a nonlinear way. Then this multiplier is decomposed into two parts: the first part reflects

the firm value without investment, whereas the second part captures the option to invest

optimally in the future.

Using a data set comprised of more than 15,800 firms over 38 years we examine the

different predictions of our model using macro and firm‐specific explanatory variables.

Both types of variables can be subdivided into variables that are part of our model and

variables that are used as controls. For instance, we include macro variables that affect the

discount rate such as the real short‐term interest rate, the slope of the term structure of

interest rates, and a credit spread (spread of Baa bonds over Treasuries). Increases in all of

these variables have a positive effect on the discount rate, and therefore should have a

negative effect on the cash flow multiplier. Besides, we add inflation and the volatility of

the S&P500 index to control for the state of the economy. As firm specific variables we

include the proportion of cash flows invested that comes directly from our theoretical

model and should, if investment is optimal, be positively related to the cash flow

multiplier. We also run regressions where we include a squared term to check the model

prediction that the multiplier increases with investment at a decreasing rate. In most of the

regressions we include size, leverage, and a dividend dummy as control variables as well

as firm and/or industry fixed effects. Besides, we study the effect of R&D expenses that

are part of a firm’s investment policy, but that are missing in about 50% of the

observations. We find that all the explanatory variables related to the discount rate ‐the

real short term interest rate, the slope of the term structure, and the spread of Baa bonds

over Treasuries ‐have the correct sign and most of them are significantly negative. The

proportion of cash flow invested is always highly significant and positive as predicted by

the model. We also provide empirical evidence that the relationship is nonlinear and relate

the cash flow multiplier to the average size of an industries’investment policy.

Furthermore, firms in certain industrial sectors require more investment because

obsolescence in the sector is faster, because the sector is more competitive, or because the

sector is more heavily regulated. In our theoretical model the drift of the cash flow process

(without investments) can proxy for this phenomenon. The smaller (or more negative) is

this drift without investments, the more investment will be required to keep or increase the

level of future cash flows. This would imply that, even though the cash flow multiplier for

a given firm is positively related to the proportion of its cash flow invested, the multiplier

should be negatively related to the average investment proportion of the industry to which

it belongs since it would be a more intensive investment industry. We find evidence of this

in the data as well.

While some of our empirical results are consistent with simpler models, i.e. that the

multiplier is positively related to the reinvestment rate and negatively related to the

interest rate, in our model the reinvestment rate is endogenous and the relation between

the multiplier and the reinvestment rate is non‐linear. In addition, as mentioned above, our

model can address issues that simpler models cannot, such as the relation of the firm

multiplier to the average investment proportion of the industry to which it belongs.

Our paper is related to severalstrands of the literature. First it contributes to an extensive

literature on multiples. Boatsman and Baskin (1981) and Alford (1992) analyse the

© 2014 John Wiley & Sons Ltd

400 Holger Kraft and Eduardo Schwartz