The Cost of Equity

1
The Cost of Equity
Chapter 12
Case Part 2 - Q1

• The Cost of Equity (CAPM)
• E(rS) rf bs E(rm) - rf
• Equity Beta
• bS sSm / sm2
• Example
• The following are U-Air stocks and TSE300 index
  returns for
• the 1994-1997 period
• Year U-Air TSE300
• 1994 4.00 -0.18
• 1995 30.00 14.53
• 1996 42.00 28.35
• 1997 34.00 14.98

2
Calculating the Equity Beta

• Calculating average returns
• Calculating the covariance
• Calculating the market variance
• Calculating beta

3
Case Part 2 Q2
Calculating the Cost of Equity

• U-Airs Cost of Equity (CAPM)
• Given a 5.09 average T-bill rate, the average
  historical market risk-premium for the 1994-1997
  period is
• By the CAPM, if the current T-bill rate is 4,
  then the cost of U-Airs equity is given by
• E(rs) rf bs E(rm) - rf

4
An alternative Method for Calculating the Cost of
Equity

• For U-Air it is given that
• Year Dividend
• 0 0.39 (1g)4 D-4 D0
• -1 0.37 (1g)4 0.33 0.39
• -2 0.36 gt g
• -3 0.34
• -4 0.33 Also D1 Do(1g) 0.391.0427
  0.41
• Since P0 3.65, by the dividend growth model
• rs (D1/P0) g
• For the remainder of the case, we will assume
  that the Cost of Equity is that obtained by the
  CAPM, i.e. 16.6

5
Case Part 2 Q2
The Investment Decision

• Suppose that U-Air is an all equity firm. Recall
  that the new Bahamas project generates the
  following CFs (Ks)
• Year CF
• 0 (41,600)
• 1 4,740 IRR 10.95
• 2 11,180
• 3 15,185
• 4 25,954.375
• Assume
• U-Air is an all equity firm
• The Bahamas project beta is the same as U-Airs
  beta (1.35)
• Decision
• NPV -5,690.98 lt 0 gt reject the project. Or
• Since by the CAPM (SML) the required return for
  beta of 1.35 is 16.6, and IRR10.95lt16.6 gt
  reject the Bahamas project

6
The SML and the Investment Decision
Expected Return ()
SML
U-Air
16.6
Bahamas Project
IRR 10.95
4
Beta
1.35
7
Determinants of Beta

• Factors affecting Equity Beta
• Business Risk
• Cyclicity of Revenues
• Operating Leverage
• Financial Risk
• Financial Leverage

8
Financial Leverage

• When the firm is not All Equity
• Recall the beta of a portfolio (p) with N assets
  is given by
• The Firms Assets are financed by Equity and Debt
• Firms Assets Portfolio with Equity and Debt
• bASSETS bEQUITY S/(SB) bDEBT B/(SB)

Assets Equity (S) Debt (B)
9
The Cost of Capital of a Levered Firm

• Recall the return of a portfolio (p) with N
  assets is given by
• The Weighted Average Cost of Capital(WACC)
• WACC rASSETS rS S/(SB) rB (1 Tc)
  B/(SB)

after-tax cost of debt
10
Case Part 2 Q3

• Assuming that a project has the same beta and
  financial leverage as the whole firm
• calculate the NPV of the project based on the
  firms WACC
• compare the IRR of the project to its WACC
• It is given that Equity/Assets 0.53, and
• Debt/Assets 0.47
• Recall by the CAPM rS 16.6
• U-Airs Long-Term bonds are traded with YTM
  6.04
• Recall that Tc 0.4
• Then, U-Airs Weighted Average Cost of
  Capital(WACC) is
• WACC rS S/(SB) rB (1 Tc) B/(SB)

11
Case Part 2 Q4
WACC of the Bahamas Project

• If the Bahamas project has the same beta and
  financial leverage, then
• Also IRR10.95gt10.5 gt accept the Bahamas
  project

12
Case Part 2 Q5 Q6
When the Firms beta Differs from the Projects
Beta

• The project and the firm may have different betas
• when the project and the firm are not from the
  same line of business
• - use industry beta (not always available, e.g.
  Amazon.com)
• when the projects risk is inherently different
  (even if same industry)
• Suppose that the beta of the Bahamas line is 1.8
  (higher than U-Air). By the CAPM
• rBAHAMAS rf bs E(rm) - rf
• Then, the WACC of the Bahamas project is
• WACCBAHAMAS rBAHAMAS S/(SB) rB (1 Tc)
  B/(SB)
• Or IRR10.95lt12.72 gt reject the Bahamas
  project