3. Definitions
Return
โข Rf is the return expected from the absolutely risk-free investment
โข Rm is the return expected from the market
variance
โข Covariance measure of the degree to which returns on two risky
assets move in tandem
โข Variance how far each number in the set is from the mean
4. The weighted average cost of capital (WACC)
โข For any firm the capital structure consists of equity and debt
โข Weighted value of each portion is
โข Equity / Value ๏ E/V
โข Debt / Value ๏ D/V
โข 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
5. Common Question Sample
โข ABC company is aiming to expand their business by establishing a new
production plant XYZ. This project will cost the company ยฃxx million.
With given information; Calculate the weighted average cost of capital (WACC).
6. Given information
Equity
Debt
New Company
Equity
Debt
Existing Company
Common Given Information
โข Rf
โข Rm
โข Covariance
โข Variance
โข Tax rate
โข Existing Company
โข Cost of equity (Ke)
โข Capital Structure
โข New Company
โข Cost of dept (Kd)
โข Capital Structure
7. 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)
1
2
3
4
2
3
8. Sample # 1
Common Given Information
โข Rf = 7%
โข Rm = 16%
โข Covariance = 1.5%
โข Variance = 1%
โข Tax rate = 40 %
Companies information
โข Company EAM (Existing)
โข Cost of equity (Ke) ??
โข Capital Structure ๏ D/E = 1.2
โข Company DA (New)
โข Cost of dept (Kd) = 10%
โข Capital Structure
60 % Equity & 40 % Debt
9. 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)
1
2
3
4
2
3
10. 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 = 1.5
Cost of dept (Kd) = 10%
Equity
Debt
D/E = 1.2
EAM DA
12. 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 = 1.5
Cost of dept (Kd) = 10%
Equity
Debt
D/E = 1.2
EAM DA
13. 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 = 1.5
Cost of dept (Kd) = 10%
Equity
Debt
D/E = 1.2
EAM DA
14. 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
โข Rf
โข Rm
โข Covariance
โข Variance
โข Tax rate
3 of 4 Companies Given Information
โข Company (Existing)
โข Cost of equity (Ke)
โข Capital Structure
โข Company (New)
โข Cost of dept (Kd)
โข Capital Structure
15. 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%
16. 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)