CP

Estimating the Optimal Capital Structure 495

both theoretically and empirically, that beta increases with financial leverage. Indeed,

Robert Hamada developed the following equation to specify the effect of financial

leverage on beta:^17

b bU[1 
(1 T)(D/S)]. (13-8)

The Hamada equation shows how increases in the market value debt/equity ratio in-

crease beta. Here bUis the firm’s unlevered beta coefficient, that is, the beta it would

have if it has no debt. In that case, beta would depend entirely upon business risk and

thus be a measure of the firm’s “basic business risk.”

TABLE 13-2 The Cost of Debt for Strasburg Electronics

with Different Capital Structures

Percent Financed with Debt (wd) Cost of Debt (rd)

0% 8.0%

10 8.0

20 8.1

30 8.5

40 9.0

50 11.0

60 14.0

Note: The capital structure weights are based on market values.

Taking a Look at Global Capital Structures

To what extent does capital structure vary across different
countries? The following table, which is taken from a recent
study by Raghuram Rajan and Luigi Zingales, both of the
University of Chicago, shows the median debt ratios of firms
in the largest industrial countries.
Rajan and Zingales also show that there is considerable
variation in capital structure among firms within each of the
seven countries. However, they also show that capital struc-
tures for the firms in each country are generally determined
by a similar set of factors: firm size, profitability, market-to-
book ratio, and the ratio of fixed assets to total assets. All in
all, the Rajan-Zingales study suggests that the points devel-
oped in this chapter apply to firms all around the world.

Source:Raghuram G. Rajan and Luigi Zingales, “What Do We Know about
Capital Structure? Some Evidence from International Data,” The Journal of
Finance,Vol. 50, no. 5, December 1995, 1421-1460. Used with permission.

Median Percentage of Debt to Total Assets

in Different Countries

Country Book Value Debt Ratio

Canada 32%

France 18

Germany 11

Italy 21

Japan 21

United Kingdom 10

United States 25

(^17) See Robert S. Hamada, “Portfolio Analysis, Market Equilibrium, and Corporation Finance,” Journal of
Finance,March 1969, 13–31. Note that Thomas Conine and Maurry Tamarkin extended Hamada’s work to
include risky debt. See “Divisional Cost of Capital Estimation: Adjusting for Leverage,” Financial Manage-
ment,Spring 1985, 54 –58.

Capital Structure Decisions 491