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Expected Return
Free Risk Return Rf Market Return Rm High Risk
3% 7% Expected return> 7%
Definitions
Return
• Rf is the return expected from the absolutely risk-free investment
• Rm is the return expected from the market
variance
• Covariance measure of the degree to which returns on two risky assets move in tandem
• Variance how far each number in the set is from the mean
The weighted average cost of capital (WACC)
• For any firm the capital structure consists of equity and debt
• Weighted value of each portion is• Equity / Value E/V
• Debt / Value D/V
• The WACC formula is
WACC = Ke (E/V) + Kd (D/V) (1-Tc)
where Ke is cost of equity
Kd is cost of debt
Tc is Tax rate
Equity
Debt
Value = E + D
Common Question Sample
• ABC company is aiming to expand their business by establishing a new production plant XYZ. This project will cost the company £xx million.
With given information; Calculate the weighted average cost of capital (WACC).
Given information
Equity
Debt
New Company
Equity
Debt
Existing Company
Common Given Information • Rf• Rm• Covariance• Variance• Tax rate
• Existing Company • Cost of equity (Ke)• Capital Structure
• New Company• Cost of dept (Kd)• Capital Structure
Calculation Formulas
For Existing Company - Step 1: Beta = Covariance / Variance- Step 2: Ke = Rf + Beta ( Rm - Rf)- Step 3: WACC = Ke (E/V) + Kd (D/V) (1-Tc)
To avoid the effect of debt (leveraged), we need to calculate the value of Unleveraged Beta
- Step 4: Beta (unleverage) = Beta (leverage) / 1 + (D/E) (1-Tc)
Equity
Debt
Equity
Debt
Existing Company New Company For New Company
-Step 5: calculate new company Beta using formula # 4 -Step 6: Ke = Rf + Beta ( Rm - Rf)- Step 7: WACC = Ke (E/V) + Kd (D/V) (1-Tc)
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Sample # 1
Common Given Information
• Rf = 7%• Rm = 16%• Covariance = 1.5%• Variance = 1%• Tax rate = 40 %
Companies information
• Company EAM (Existing)• Cost of equity (Ke) ??• Capital Structure D/E = 1.2
• Company DA (New)• Cost of dept (Kd) = 10%• Capital Structure
60 % Equity & 40 % Debt
Sample Requirements
For Existing Company - Step 1: Beta = Covariance / Variance- Step 2: Ke = Rf + Beta ( Rm - Rf)- Step 3: WACC = Ke (E/V) + Kd (D/V) (1-Tc)
To avoid the effect of debt (leveraged), we need to calculate the value of Unleveraged Beta
- Step 4: Beta (unleverage) = Beta (leverage) / 1 + (D/E) (1-Tc) Equity
Debt
Equity
Debt
EAM DA
For New Company-Step 5: calculate new company Beta using formula # 4 -Step 6: Ke = Rf + Beta ( Rm - Rf)- Step 7: WACC = Ke (E/V) + Kd (D/V) (1-Tc)
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Sample Solution
(a) Calculate beta & Ke of EAM
- Step 1: Beta = Covariance / Variance= 1.5 / 1 = 1.5
-Step 2: Ke = Rf + Beta ( Rm - Rf)= 0.07 + (1.5) (.09)= 0.07 + .135= 0.205= 20.5%
Equity
Debt
D/E = 60 /40 = 1.5Cost of dept (Kd) = 10%
Equity
Debt
D/E = 1.2
EAM DA
Sample Solution
(b) unleverage Beta of EAM
Beta (unleverage) = Beta (leverage) / 1 + (D/E) (1-Tc) = 1.5 / [1 + (1.2) (.6)= 1.5 / [1 + .72]= 1.5 / 1.72= 0.8721 Equity
Debt
D/E = 60 /40 = 1.5Cost of dept (Kd) = 10%
Equity
Debt
D/E = 1.2
EAM DA
Sample Solution
(c) Leverage Beta & Ke of DA
Step 1: Beta (unleverage) = Beta (leverage) / 1 + (D/E) (1-Tc) Hence, Beta (leverage, Da) = Beta (unleverage, EAM) x [1 + (D/E) (1-Tc)]
= 0.8721 x [ 1 + (1.5) (.6) ]= 0.8721 x [ 1+ .9)= 0.8721 x 1.9= 1.6569
Note that, the D/E here for DA
-Step 2: Ke = Rf + Beta ( Rm - Rf)= 0.07 + (1.6569) (.09)= 0.07 + .1491= 0.2191= 21.91%
Equity
Debt
D/E = 60 /40 = 1.5Cost of dept (Kd) = 10%
Equity
Debt
D/E = 1.2
EAM DA
Sample Solution
(d) WACC of DA
Step 1: WACC = Ke (E/V) + Kd (D/V) (1-Tc)= (0.2191) (.6) + (0.1) (.4) (.6)= .1314 + 0.024= .1554= 15.54% Equity
Debt
D/E = 60 /40 = 1.5Cost of dept (Kd) = 10%
Equity
Debt
D/E = 1.2
EAM DA
Summary
4 Formulas
Beta = Covariance / Variance
Ke = Rf + Beta ( Rm - Rf)
WACC = Ke (E/V) + Kd (D/V) (1-Tc)
Beta (unleverage) = Beta (leverage) / 1 + (D/E) (1-Tc)
5 Common Given Information
• Rf• Rm• Covariance• Variance• Tax rate
3 of 4 Companies Given Information
• Company (Existing)• Cost of equity (Ke) • Capital Structure
• Company (New)• Cost of dept (Kd)• Capital Structure
Exam Tips
(1) The cost of debt and D/E may be given as information inside the credit rating agency table as below,
Based on the company rate, get the D/E and cost of debt directly from table. Say, the company rated as BBB, that means D/E = .75 and Kd = 9.5%
Exam Tips
(2) The existing company has no debts
That means, Beta (unleverage) = Beta (leverage), and
WACC = Ke
(3) XYZ company will issue a 5 year bond with an annual coupon of 12%of the nominal-value of the bond.
Even thought they will issue bond for 5 years, the cost of debt still 12% (annually)
