Exercises in Capital Structure and Cost of Capital

1
Exercises in Capital Structure and Cost of Capital
2
Problem 1

• Dreadnaught Industries has a debt/equity ratio of
  2. Its WACC is 11 percent, and its cost of debt
  is 6 percent. The corporate tax rate is 35
  percent.
• a. What is Dreadnaught's cost of equity capital?
• b. What is Dreadnaught's unlevered cost of equity
  capital?
• c. What would be cost of equity if the
  debt/equity ratio were 1?

3
Problem 2

• Astralite Corp. uses no debt. The cost of equity
  is 13 percent. If the current market value of the
  equity is 25 million, and the corporate tax rate
  is 35 percent, what is the WACC?
• What is the EBIT, if it occurs in perpetuity?
• The company has 10 million shares outstanding. If
  the firm decides to issue 10 million debt at 7
  and retire shares worth 10 million, what will be
  the market value of the firm and the market value
  of the new equity?
• At what price will the firm repurchase the shares
  and how many shares will be repurchased?

4
How do we calculate cost of capital?

• I. The Cost of Equity, RE
• A. Dividend growth model approach
• RE D1 / P0 g
• B. SML (CAPM) approach
• RE Rf b E x (RM - Rf)
• II. The Cost of Debt, RD
• A. For a firm with publicly held debt, the cost
  of debt can be measured as the yield to
  maturity on the outstanding debt.
• B. If the firm has no publicly traded debt, then
  the cost of debt can be measured as the yield
  to maturity on similarly rated bonds.

5
Summary of Capital Cost Calculations

• III. The Weighted Average Cost of Capital
• A. The WACC is the required return on the firm
  as a whole. It is the appropriate discount rate
  for cash flows similar in risk to the firm.
• B. The WACC is calculated as
• WACC (E/V) x RE (D/V) x RD x (1 - Tc)
• where Tc is the corporate tax rate, E is the
  market value of the firms equity, D is the
  market value of the firms debt, and V E D.

6
Question

• How can we calculate the cost of capital of a
  division of a diversified firm?

7
Answer

• We need to estimate the cost of debt and the cost
  of equity. The cost of debt is the YTM on the
  companys bonds, and the cost of equity is
  estimated using CAPM
• Re Rf b (Rm - Rf)

8
The Comparable Company Approach

• Find a pure-play (or free standing, or
  single-segment) company of similar size in the
  same business, and its beta
• b(fs)
• But we just learned that among other things,
  capital structure affects beta. If the two firms
  have the same capital structures, we can
  immediately apply b(fs) to our company.
• But suppose the capital structures are different.
  Then we need to adjust the b(fs) to reflect the
  capital structure of our company.

9
Unlevered vs. Levered Beta

• Let
• b L levered beta
• b U unlevered beta (or the beta of the
  company if it had no debt, the pure asset
  risk coefficient)
• With taxes, the relation between the two betas
  is
• b L b U x 1 (1 - Tc) (D/E)

10
Unlevering Beta

• When we estimate b L fs with linear regression we
  are estimating a levered beta.
• To adjust for the differences in leverage, we
  first unlever b L fs as
• b U fs b L fs / 1 (1 - Tc) (D fs / E fs)
• where D fs and E fs are the value of the debt and
  equity of the free standing firm (in market
  values!)

11
Relevering Beta

• Once we calculate beta b U fs , we have a beta
  coefficient of a company with no debt. We relever
  it to reflect the capital structure of our
  company
• b L c b U fs x 1 (1 - Tc) (D c / E c)
• where D c and E c are the value of the debt and
  equity of our firm (in market values).

12
Estimation Completed

• Then we estimate the cost of equity as
• Re c Rf b L c (Rm - Rf)
• and the WACC as
• WACC Re c E c /(Ec D c) (1-Tc)Rd Dc/(Ec
  D c)

13
Assignment

• You are hired to value the brewing division of a
  publicly traded food company that will be sold to
  another firm. The division uses the same capital
  structure as the overall firm. It has a market
  value of equity of 1,250 million, and book value
  of 550 million. The company has the following
  bond issue outstanding
• Bonds Coupon Rate Book
  Value Yield to Maturity Years to
  Maturity
• 500,000 7
  1,000 6
  4
• The risk-free rate is 4, and the MRP is assumed
  to be 6
• You also can find the observed (levered) betas,
  and capital structure ratios for the firms in the
  same industry.