Valuation and Return Dynamics of New Ventures

Author(s)

·  Jonathan Berk

·  Richard Green

·  Vasant Naik

 

Reference

Review of Financial Studies, 17 (2004), 1-35.

Abstract

We develop and analyze a model of a multi-stage investment project

that captures many features of R&D ventures and start-up

companies. An important feature these problems share is that the

firm learns about the potential profitability of the project

throughout its life, but that technical uncertainty about the

research and development effort is only resolved through

additional investment by the firm.  Consequently, the risks

associated with the ultimate cash flows the firm realizes on

completion of the project have a systematic component even while the

purely technical risks are idiosyncratic.  Our model captures

these different sources of risk, and allows us to study their

interaction in determining the risk premia earned by the venture

during development.  We show that the systematic risk,

and the required risk premium, of the venture are highest early in

its life, and decrease as it approaches completion.
 

Retrieve the Paper (as an Adobe Acrobat PDF file)  

If you have trouble with this download, try right clicking and choose save to file.
 

Closed form solution in the case when p(t) is a non-constant deterministic function of the state

To download a PDF file with the closed form solution in this case, click here

 

 

Obtaining the computer code used to generate the tables and figures

Caveat Emptor --- The code used in the paper is available below although we make no promises about readability. 

Case with No Learning (closed form solution)

The tables and figures in the case without learning were generated in a two step process. First a c program with source file genconst.c generates the constants for each stage in the closed form solution. You will need a number of Numerical Recipes in C routines.  For obvious reasons I have not included them.  If you do not already have them, you will need to purchase them.  This program takes input.tex as an input file (yes, this file is TeXable).  The constants are then read out into files that the mathematic spreadsheet constants.nb reads in and generates the figures and tables. Click here to download a self extracting archive, or here for a zip file that contains all these files.

Case with Learning (numerical solution)

Things are much harder for the case with learning because we do not have a closed form solution. First a c program with source files nfppde.c and win.c (this second file may or may not be required depending on your compiler) generates an output file that contains the value and risk premium over a range of values specified interactively at the outset.  The input file that specifies the parameters and accuracy is called input.tex (and is TeXable).   Once this program has run (and it can take a while), the output files are read by the mathematica spreadsheet out.nb.  All graphs and tables in the learning section of the paper are generated by this spreadsheet.  Click here to download a self extracting archive, or here for a zip file that contains all these files.

 

 IMPORTANT NOTE:    The program is written so that alpha and beta in the program relate in the following way to a1 and  a2 in the paper:a=a1 and b= M a2- a,where M is defined in Appendix C.    So, for example, if M=4, a1=1 and a2=0.5 (as it is in the paper) then a=1  and  b = 4 0.5 -1 =1.