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.