Growth Options, Beta, and Cost of Capital

Growth Options, Beta, and the Cost of Capital Object) by Antonio Bernardo, Bhagwan Chowdry, and Amit Goyal.

This is a good one! It looks at the betas of firms' assets in place relative to the betas of their growth options and finds that the growth options have significantly higher betas. The authors then show that this difference in betas can lead to significant differences in cost of capital calculations.

Longer version:

In the author's own words, the paper

"...demonstrate[s] empirically that growth opportunities are a very important determinant of a firm's beta, even after controlling for operating and financial leverage, and the failure to account for this can lead to misestimation of the cost of equity capital by as much as 3% depending on the industry.

The paper begins with a discussion of why CAPM is still popular in spite of its many problems and explains the standard procedures for using CAPM to get cost of capitals for untraded projects.

To "disentangle the betas of assets-in-place and of growth opportunities..." the authors assume that Market to Book ratios proxy for growth and that the betas of growth and asstes-in-place are constant for all firms in a given industry (they use Fama & French's industry classifications) at any given point.

Building on Carlson, Fisher, and Giammarion (2004), the authors use the Black-Scholes Option pricing model to demonstrate that the Beta of Growth options must be greater than the beta of assets in place. The explanation:

"the firm's growth opportunity is an option on its assets-in-place and since this option has implicit leverage the beta of its growth opportunity is greater than the beta of its assets-in-place"

Given this, the paper then uses a large sample of firms from 1977 to 2004 and finds " the difference between the beta of growth opportunities and the beta of assets-in-place is positive and statistically significant, at the 95% level, in 34 of 37 industry classifications"

Moreover, this appears to be economically significant as well:

"....consider the Computer industry. For the period 2000-2004, the mean unlevered firm beta in this industry is 1.608; however, a firm at the 25th percentile in market-to-book has an unlevered beta of 1.430 while a firm at the 75th percentile in market-to-book has an unlevered beta of 1.785. This difference in beta of 0.355 represents a roughly 2% higher cost of capital for a project with relatively high growth opportunities relative to a project with relatively low growth opportunities (when using a 6% market equity risk premium)."

Which deseves a wow!

BTW: Table 1 alone is worth the price of admission. Not only does it show this great breakdown along Market to Book ratios for each industry, it also shows that industry betas are NOT constant accross time periods. Check it out!

Cite: Antonio Bernardo, Bhagwan Chowdry, and Amit Goya, March 2005. UCLA Working paper: Growth Options, Beta, and the Cost of Capital. http://www.anderson.ucla.edu/documents/areas/fac/finance/24-05.pdf

(note to my class: the introduction is EXCELLENT!--READ IT ;) Even undergrad studens will have no problems with it!)