chapter 6 hw prob 4, 5, & 1 add'l post-answers
TRANSCRIPT
Chapter 6 HW prob
Page 172
Problem 4
Info:
Corporation's Data
Beta Market Value $ % of total
Debt 0.1 100,000 25%
Preferred 0.4 200,000 50%
Common 1.5 100,000 25%
Total 400,000 100%
Riskless interest rate 10%
Market Risk Premium 5%
Calculate:
a). Discount rates for each security
kd = rf + Bd(rm-rf)Debt discount rate 10.50%
Preferred discount rate 12.00%
Common discount rate 17.50%
b). The asset beta for the corporation
Ba = beta x the weight
Debt 0.1 25% 0.025
Preferred 0.4 50% 0.2
Common 1.5 25% 0.375
Ba = 0.6
c). The weighted average cost of capital (WACC)
ko = weke + wdkd (1-t) + wpkp
Debt 0.1050 Debt discount rate
0.2500 % of total
0.0263
Preferred 0.1200
0.5000
0.0600
Common 0.1750
0.2500
0.0438
WACC 13.0%
d). The discount rate for the unlevered assets
The business risk is the same for the unlevered assets as it is for the firm,
so the discount rate for the unlevered assets is the same as the cost of
capital for the company 13.0%
Chapter 6 HW prob similar to sample problem 2 in the text
Page 172
Problem 5
Info:
Shebert Theater wants to purchase a
movie theater chain, Consolidated
Cinemas, which is owned by Tryon
Info on movie house chains Be 1). 2).
Equity
Betas
debt to total
assets
Equity portion
of total D/E Asset Beta
Movie House Beta D/TA
NCO Theater, Inc. 1.70 0.40 1 2.5 0.60 1.00 0.67 1.02
Worldwide/Global 0.50 0.10 1 10 0.90 1.00 0.11 0.45
Screen Rocks 2.50 0.50 1 2 0.50 1.00 1.00 1.25
Ultimate Theater (0.10) 0.75 1 1.33 0.25 1.00 3.00 -0.025
total 2.695
Risk free rate 7.5% average asset beta 0.67375 3).
Market risk premium 8.5%
a). What is the cost of equity capital for Consolidated?
1). transfer the debt to asset ratio to the debt to equity ratio
D/E = D/(TA - D)
Equ 6.3, page 149
2). Ba = Be
1 + D/E
3). Total asset betas & find average
Use equ 6.1,
page 146 Beta
x Project risk premium
4). average asset beta 0.67375 +
Market risk premium 0.085 Risk-free rate
0.05727
Risk free rate 0.075 +
0.13227
Cost of capital 13.23%
b). What qualifications would you include with your estimate?
Can the companies chosen in this study serve as a good substituition or proxy?
Chapter 6 Estimating the Project Cost of Capital
HW Problem
Soda has 4 divisions:
Be as a fraction
Contribution to
Firm's Value Company Equity Beta
D/TA (debt to
total assets D/E
Asset
Beta
Cost of
Capital (%)
35% Coke 2.00 0.20 1 5 Coke 0.25 1.60 15.60%
10% Pepsi 1.50 0.33 1 3 Pepsi 0.50 1.00 12.00%
30% Gatorade 1.25 0.50 1 2 Gatorade 1.00 0.625 9.75%
25% Rootbeer 0.50 0.25 1 4 Rootbeer 0.33 0.38 8.25%
100%
a).
Estimate the asset betas for Soda
divisions, assume the debt betas are -0-,
ignore taxes
transfer the debt to asset ratio to the debt to equity ratio
D/E = D/(TA - D)Coke 0.25 D/E
Pepsi 0.50 D/E
Gatorade 1.00 D/E
Rootbeer 0.33 D/E
Equ 6.3, page 149
Ba = Be
1 + D/ECoke 1.60 Asset beta
Pepsi 1.00 Asset beta
Gatorade 0.63 Asset beta
Rootbeer 0.38 Asset beta
b). Info given:
Risk free rate 6% rf 0.06
avg market rate of return 12% rm 0.12
What is cost of capital for each of the divisions?
using CAPM
kpp = rf + Ba(rm - rf) cost of capital
0.1560 Coke 15.60%
0.1200 Pepsi 12.00%
0.0975 Gatorade 9.75%
0.0825 Rootbeer 8.25%
0.5
c).
With a D/TA of 0.50, what is Soda
Company's equity beta? cont Asset Beta
cont x
asset
beta
Coke 35% 1.600 0.5600
Pepsi 10% 1.000 0.1000
Gatorade 30% 0.625 0.1875
Rootbeer 25% 0.375 0.0938
weighted avg 0.9413
with D/TA 0.50
D/E = 1.00
equity beta =
equity beta = 1.883
d).
If the debt of each division also had a beta
= 0.50, what would be the cost of capital
for each division? For Soda Company? 0.5
Ba = (D/TA)Bd + (E/TA)Be
Company Asset Beta Cost of Capital %
D/TA (debt to
total assets E/TA
Coke 1.70 16.20% 0.20 0.80
Pepsi 1.17 13.02% 0.33 0.67
Gatorade 0.88 11.25% 0.50 0.50
Rootbeer 0.50 9.00% 0.25 0.75
Coke Pepsi Gatorade Rootbeer
D/TA 0.20 0.33 0.50 0.25
Bd 0.5 0.5 0.5 0.5
E/TA 0.80 0.67 0.50 0.75
Be 2.00 1.5 1.25 0.5
Risk free rate 6% rf 0.060 0.06 rm - rf
avg market rate of return 12% rm 0.120
What is cost of capital for each of the divisions?
CAPM kpp = rf + Ba(rm - rf) Cost of Capital
Coke 0.162
Pepsi 0.1302
Gatorade 0.1125
Rootbeer 0.09
Weights Company Asset Beta
35% Coke 1.70 0.595
10% Pepsi 1.17 0.117
30% Gatorade 0.88 0.263
25% Rootbeer 0.50 0.125
weighted avg. asset beta 1.100
CAPM cost of capital for Soda Company = 12.60%
Risk free rate 0.06
weighted avg. asset beta 1.10
Definition of 'Unlevered Beta'
A type of metric that compares the risk of an unlevered company to the risk of the market. The unlevered beta is the beta of a company without any debt. Unlevering a beta removes the financial effects from leverage.