Chapter 6

Box 6.2, pg. 151Estimating Carborundum's Cost of Capital

Kennecot Copper Corp is considering

purchasing Carborundum Company. What

discount rate should Kennecott have used to

evaluate this potential acquisition?

Info given:

Corborundum's Equity beta 1.16

LT Treasury bond rate 7.6%Historical spread between returns on S&P500

index & LT Treas. Bonds 7.5%

Corcor. Market value of equity 271.0$

Corbor. Market value of debt 86.2$ If proceed with acquisition, it will be financed

with: debt 100.0$ payment of dividend to Kennecott 140.0$ Cash Flows being discounted by Kennecott

were those it would receive from

Carborundum, net of financing costs.

Calculation of Carborundum's pre-acquisition

cost of equity capital

1.160

0.075

0.0870

0.076

0.1630

16.30%

1). Unlever Carbor's equity beta under

current capital structure, then relevering to

reflect new capital structure.

assume tax rate = 50%

Ba =

1.16

[ 1 + (1 - 0.5)86.2/271]

1.15904059

Ba = 1.00

Under the new financial restructuring:

Carbor's debt to equity ratio would rise

currently:

Corcor. Market value of equity 271

Corbor. Market value of debt 86.2

D/E 0.32

After acquisition:

Corcor. Market value of equity 271

Pay dividend (140)

Equity 131

Corbor. Market value of debt 86

100

186

D/E 1.42

Increase in leverage

Be =

The new equity beta would be: 1.71

Now, substitute a beta of 1.71 into equation

6.1, so that can get the cost of equity capital

under its postacquistion capital structure

1.71

0.075

0.1283

0.076

0.2043

Kennecot Copper Corp is considering

purchasing Carborundum Company. What

discount rate should Kennecott have used to

evaluate this potential acquisition? 20.4%

million

million

million

million

Page 146, equ 6.1

Corborundum's Equity beta BetaHistorical spread between returns on S&P500 index & LT

Treas. Bonds x Project risk premium

equity beta x spread between S&P500 & LT Treasury bonds +LT Treasury bond rate Risk-free rate

cost of equity capital

Good for analyzing CF's under current capital structure

Due to CF's being discounted are CF's to Kennecot, then

should use discount rate from Carborundum's cost of equity

under new capital structure

Equ 6.5, page 150

Be

1 + (1-t)D/ECorborundum's Equity beta

[ 1 + (1 - 0.5)86.2/271]

Carbor's asset beta

E

D

E

D

Equ 6.6, page 150

Ba [ 1 + (1-t)D/E]

1.00(1 + .5 x 1.42)

Page 146, equ 6.1

new equity beta BetaHistorical spread between returns on S&P500 index & LT

Treas. Bonds x Project risk premium

equity beta x spread between S&P500 & LT Treasury bonds +LT Treasury bond rate Risk-free rate

cost of equity capital

x Project risk premium

Risk-free rate

x Project risk premium

Risk-free rate

Estimating Vulcan Materials'

Divisional Costs of Capital

Info given:

LT Treasury bond rate 6.3%Risk premium (relative to LT T-bond

rate) 5.0%Average asset betas:

Contruction 0.64 Chemicals 0.84 Metals 0.79 Oil & Gas 1.10 Use equ 6.1, page 146 Beta

x Project risk premium

+

Risk-free rate

Contruction Chemicals MetalsLT Treasury bond rate 0.063 0.063 0.063 + avg asset beta 0.64 0.84 0.79 x risk premium 0.05 0.05 0.05

0.03 0.04 0.04

0.095 0.105 0.103

Cost of capital by business segment 9.50% 10.50% 10.25%

Oil & Gas

0.063

1.10

0.05

0.06

0.118

11.80%

Chapter 6, page 165

Comparing WACC, APV, LE Methods

for calculating the cost of capital

Info given:

Giant Mfg.

Invest $30 million in a new solar power source

annual FCF's in perpetuity 4,888,000

k = 16%

(30,000,000)

30,550,000

NPV = 550,000

New info:

addition to debt 6.50$

Interest rate on the debt 10%

Tax rate 30%

Calculate the value of the project using 3 different methods:

APV Method (equ 6.10) Adjusted Present Value Method

APV =

NPV of project if all

equity financed

The only financing side effect is the tax savings provided by the tax deductibility of interest payments

Annual tax savings = the tax x the annual interest expense

Tax rate 0.30

Interest Rate 0.10

Addition to debt 6,500,000

Annual tax savings 195,000$

550,000

195,000$

0.10

APV = 2,500,000$

Using market values, the debt ratio for this project =

Addition to debt 6,500,000

New equity portion 26,000,000

Equity:

Investment 30,000,000

APV (adjusted PV) 2,500,000

Total 32,500,000

WACC Method

Equ 6.11 page 164 use equ 6.11 to estimate the project's levered cost of equity capital

ke = k* + D/E (1-t)(k* - kd) using debt ratio of

k* 0.16

D 6.5$

E 26.0$

t 0.30

kd 0.10

0.1705

17.05%

WACC Equ 6.9 pg 155

ko = weke + wdkd (1-t) + wpkp

weight of the equity 0.80

cost of equity 0.1705

wt x cost 0.1364

+

weight of the debt 0.20

cost of the debt 0.10

wt x cost 0.014

0.1504

15.04%

At this discount rate of 15.04%, calculate the NPV

(30,000,000)

4,888,000

15.04%

(30,000,000)

32,500,000

NPV = 2,500,000$

LE Method

LE discount rate: ke = k* + D/E (1-t)(k* - kd)

LE cash flows: LCFi = CF1 - debt service charges

LE investment: Io - amt borrowed to finance projectCombine the levered cost of equity (17.05%), with the CF's to equity

Debt amount 6.50

annual after tax interest expense 0.70

interest rate on the debt 0.10 multiply debt amt x after tax int x int

rate on debt 455,000$

FCF's (from above-given) 4,888,000

Less: (455,000)

annual CF to equity 4,433,000$

Investment 30,000,000$

Debt portion 6,500,000$

Equity investment in the project 23,500,000$

At this discount rate of 17.05%, calculate the NPV

(23,500,000)

4,433,000

0.1705

(23,500,000)

26,000,000

NPV = 2,500,000$

Investment

Perpetuity/interest rate

add both together

profitable, postive NPV

million

Adjusted Present Value Method

+

NPV of financing side

effects caused by project

acceptance

The only financing side effect is the tax savings provided by the tax deductibility of interest payments

NPV

+

Annual tax savings

Interest Rate

The tax benefits of debt financing have turned project to be more profitable

20%

80%

debt is set to 20% of the

project's present value of 32.5

mil

use equ 6.11 to estimate the project's levered cost of equity capital

20%

given

mil

mil

tax rate

interest rate on the debt

cost of equity capital

(1- .30) 0.0700

cost of debt

Investment

FCF's (from above-given)

discount rate

same result as when we used the APV method

ke = k* + D/E (1-t)(k* - kd)

LCFi = CF1 - debt service charges

Io - amt borrowed to finance projectCombine the levered cost of equity (17.05%), with the CF's to equity

million

( 1 - .30)

Investment

FCF's calculated above

discount rate

same result as when we used the APV & WACC methods

Chapter 6 Estimating the Project Cost of Capital

sample problem 1

page 168

Info given:

A company is deciding whether to issue stock to raise money for

an investment project

Project Beta 1.0

Project Expected return 20%

Risk free rate 10%

Company's stock price beta 2.5

Expected return on market 15%

Should the company go ahead with the project?

With a project beta of 1.0, the project's required return = the

expected return on the market, or 15%

Since the project's expected return of 20% exceeds the project's

cost of capital, the company should make the investment

Calculate the cost of equity capital for the company:

Company's stock price beta 2.5

market risk premium 5%

Company's cost of equity capital:

Company's stock price beta 2.50

market risk premium 0.05

0.13

Risk free rate 0.10

0.225

Company's cost of equity capital: 22.5%

proj expected return - expected return on mkt

Beta

x Project risk premium

+

Risk-free rate

Chapter 6 Estimating the Project Cost of Capital

sample problem 2

page 168

Multi Foods has 4 divisions:

Contribution to

Firm's Value Company

10% Pet Products

25% Candlelight

50% Freezies

15% RedyEeet

100%

a).

Estimate the asset betas for MultiFoods 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)Pet Products

Candlelight

Freezies

RedyEeet

Equ 6.3, page 149

Ba = Be

1 + D/EPet Products

Candlelight

Freezies

RedyEeet

b). Info given:

Risk free rate

avg market rate of return

What is cost of capital for each of the divisions?

using CAPM

kpp = rf + Ba(rm - rf) .08 + .33(0.16 - .08)

c). With a D/TA of 0.50, what is MultiFoods' equity beta?

Pet Products

Candlelight

Freezies

RedyEeet

with D/TA

D/E =

equity beta =

equity beta =

d).

If the debt of each division also had a beta = 0.50, what would

be the cost of capital for each division? For Multi Foods?

Ba = (D/TA)Bd + (E/TA)Be

Company

Pet Products

Candlelight

Freezies

RedyEeet

D/TA

Bd

E/TA

Be

Risk free rate

avg market rate of return

What is cost of capital for each of the divisions?

CAPM kpp = rf + Ba(rm - rf) .08 + .50(0.16 - .08)

Weights Company

10% Pet Products

25% Candlelight

50% Freezies

15% RedyEeet

weighted avg. asset beta

CAPM cost of capital for Multi Foods =

Risk free rate

weighted avg. asset beta

avg market rate of return

Be

Equity Beta

D/TA (debt to

total assets

0.5 0.33 1 3

1.5 0.50 1 2

1.75 0.20 1 5

2.25 0.25 1 4

0.50 D/E

1.00 D/E

0.25 D/E

0.33 D/E

0.33 Asset beta

0.75 Asset beta

1.40 Asset beta

1.69 Asset beta

8% rf 0.08

16% rm 0.16

cost of capital

0.1067 Pet Products 10.67%

0.1400 Candlelight 14.00%

0.1920 Freezies 19.20%

0.2150 RedyEeet 21.50%

cont Asset Beta

cont x

asset

beta

10% 0.33 0.0333

25% 0.75 0.1875

50% 1.40 0.7000

15% 1.69 0.2531

weighted avg 1.1740

0.50

1.00

1.174 x (1 + D/E)

2.348

0.5

Asset Beta Cost of Capital %

D/TA (debt to

total assets

0.50 12.00% 0.33

1.00 16.00% 0.50

1.50 20.00% 0.20

1.81 22.50% 0.25

Pet Products Candlelight Freezies RedyEeet

0.33 0.50 0.20 0.25

0.5 0.5 0.5 0.5

0.67 0.50 0.80 0.75

0.50 1.5 1.75 2.25

8% rf 0.08

16% rm 0.16

Cost of Capital

Pet Products 0.12

Candlelight 0.16

Freezies 0.2

RedyEeet 0.225

Asset Beta

0.50 0.05

1.00 0.25

1.50 0.75

1.81 0.27

weighted avg. asset beta 1.32

18.58%

0.08

1.32

0.16

D/E Asset Beta

Cost of

Capital (%)

Pet Products 0.50 0.33 10.67%

Candlelight 1.00 0.75 14.00%

Freezies 0.25 1.40 19.20%

RedyEeet 0.33 1.69 21.50%

E/TA

0.67

0.50

0.80

0.75

Chapter 6

page 186

Appendix B

Dividend Growth Model

Equity Cost of

Capital =

Dividend

Yield +

Expected dividend

growth rate

ke = DIV1 + g

Po

ke Equity Cost of Capital

DIV1 expected dividend in year 1

Po current stock price

g average expected annual dividend growth rate

See page 187, Box 6.5 for comparison to CAPM

The dividend discount model (DDM) is a way of valuing a

company based on the theory that a stock is worth the

discounted sum of all of its future dividend payments. In other

words, it is used to value stocks based on the net present value

of the future dividends.

average expected annual dividend growth rate

See page 187, Box 6.5 for comparison to CAPM