Problem

$1$ Firms $1,2,$ and $3$ are all in the same industry. Their levered betas, capital structure $($Debt$/$Equity ratio$)$ and debt detas are as given in the adjacent table.

$2$ Find their unleverd betas

$3$ Average unleverd betas of these three firms is a good approximation of the unleverd beta of your firm, Firm$4$

$4$ Your firm $($Firm$4)$ has a debt$/$equity ratio of $0\mathrm{.}2.$

$5$ Find the levered beta of your firm $($Firm$4)$

Given a$.$ Solution:

Analysis of unlevered equity beta with risky debt beta $=\mathrm{.}30$ Tax Rate $38\%$

Levered Debt$/$Equity Assumed Unlevered

Company Name Equity Betas Capitalization Debt Betas Equity Betas

Firm$1($F$1)1\mathrm{.}790\mathrm{.}310\mathrm{.}30$

Firm$2($F$2)1\mathrm{.}980\mathrm{.}240\mathrm{.}30$

Firm$3($F$3)1\mathrm{.}710\mathrm{.}220\mathrm{.}30$

Average

b$.$ Solution

Analysis of Sterling

Analysis based on simple average of unlevered equity betas

beta unlevered D$/$E beta debt D$/$E beta levered

$0\mathrm{.}200\mathrm{.}300\mathrm{.}20$