# The CFO of Sterling Chemical is interested in evaluating the cost of equity capital for his firm....

## Question:

The CFO of Sterling Chemical is interested in evaluating the cost of equity capital for his firm. However, Sterling uses very little debt in its capital structure (the firm's debt-to-equity capitalization ratio is only 20%), while larger chemical firms use substantially higher amounts of debt. The following table shows the levered equity betas, debt-to-equity ratios, and debt betas for three of the largest chemical firms

Company Name Levered Equity Betas Debt/Equity Capitalization Assumed Debt Betas
Eastman Chemical Co. (EMN) 1.79 30.77% 0.30
Celanese Corp. (CE) 1.98 23.55% 0.30
Dow Chemical Company (DOW) 1.71 21.60% 0.30

a. Use the information given above to estimate the unlevered equity betas for each of the companies.

b. If Sterling's debt-to-equity capitalization ratio is 0.20 and its debt beta is 0.30, what is your estimate of the firm's levered equity beta?

## Unlevered Firm:

Unlevered firm is a firm that does not use debt in the capital. Debt expense is a tax-deductible item which is deducted from the income before tax calculation. So debt provides a tax shield to the company.

Beta is a measure of risk in the stock. If the volatility in the stock is high, then the stock is very risky and vice versa.

Unlevered beta is the beta of the venture without the effect of the obligation. On the off chance that the influence is more means, the undertaking has more income or earnings to pay its debts.

Unlevered beta is determined utilizing the recipe underneath:

{eq}\beta _{unlevered} \ = \ \frac{\beta _{Equity} \ + \ \beta _{Debt}\left ( \frac{Debt}{Equity} \right )}{1 \ + \ \left ( \frac{Debt}{Equity} \right )} {/eq}

The financial information of the three companies is as below:

Company Name Levered Equity Betas Debt/Equity Capitalization Assumed Debt Betas
EMN 1.79 30.77% 0.3
CE 1.98 23.55% 0.3
DOW 1.71 21.60% 0.3

a.

Compute the Unlevered equity beta of EMN.

{eq}\beta _{unlevered}\left ( EMN \right ) \ = \ \frac{\beta _{Equity} \ + \ \beta _{Debt}\left ( \frac{Debt}{Equity} \right )}{1 \ + \ \left ( \frac{Debt}{Equity} \right )} \\ \beta _{unlevered}\left ( EMN \right ) \ = \ \frac{1.79 \ + \ 0.3\left ( 0.3077 \right )}{1 \ + \ \left ( 0.3077 \right )} \\ \beta _{unlevered}\left ( EMN \right ) \ = \ \frac{1.88231}{1.3077} \\ \beta _{unlevered}\left ( EMN \right ) \ = \ 1.4394 {/eq}

Hence, the unlevered beta of EMN is 1.4394.

Compute the Unlevered equity beta of CE.

{eq}\beta _{unlevered}\left ( CE \right ) \ = \ \frac{\beta _{Equity} \ + \ \beta _{Debt}\left ( \frac{Debt}{Equity} \right )}{1 \ + \ \left ( \frac{Debt}{Equity} \right )} \\ \beta _{unlevered}\left ( CE \right ) \ = \ \frac{1.98 \ + \ 0.30\left ( 0.2355 \right )}{1 \ + \ \left ( 0.2355 \right )} \\ \beta _{unlevered}\left ( CE \right ) \ = \ \frac{2.05065}{1.2355} \\ \beta _{unlevered}\left ( CE \right ) \ = \ 1.6598 {/eq}

Hence, the unlevered beta of CE is 1.6598.

Compute the Unlevered equity beta of DOW.

{eq}\beta _{unlevered}\left ( DOW \right ) \ = \ \frac{\beta _{Equity} \ + \ \beta _{Debt}\left ( \frac{Debt}{Equity} \right )}{1 \ + \ \left ( \frac{Debt}{Equity} \right )} \\ \beta _{unlevered}\left ( DOW \right ) \ = \ \frac{1.71 \ + \ 0.30\left ( 0.2160 \right )}{1 \ + \ \left ( 0.2160 \right )} \\ \beta _{unlevered}\left ( DOW \right ) \ = \ \frac{1.7748}{1.2160} \\ \beta _{unlevered}\left ( DOW \right ) \ = \ 1.4595 {/eq}

Hence, the unlevered beta of DOW is 1.4595.

b.

Analysis of Sterling & Computation of levered equity beta:

For computation of firm's levered equity betas, first the average of unlevered equity betas of the three companies should be obtained.

{eq}Average \ = \ \frac{1.4394 \ + \ 1.6598 \ + \ 1.4595}{3} \\ Average \ = \ \frac{4.5587}{3} \\ Average \ = \ 1.5195 {/eq}

Therefore, the levered equity beta is 1.5195.

Compute the levered equity beta.

{eq}\beta _{Equity} \ = \ \beta _{unlevered}\left ( 1 \ + \ \frac{Debt}{Equity} \right ) \ - \ \beta _{Debt}\left ( \frac{Debt}{Equity} \right ) \\ \beta _{Equity} \ = \ 1.5195\left ( 1 \ + \ 0.20 \right ) \ - \ 0.2\left ( 0.3 \right ) \\ \beta _{Equity} \ = \ 1.8234 \ - \ 0.06 \\ \beta _{Equity} \ = \ 1.7634 {/eq}

Hence, the levered equity beta is 1.7634. 