Chapter 6 Review in Class

(1)

Chapter 6 Chapter 6

Box 6.2, pg. 151 Box 6.2, pg. 151

Estimating Carborundum's Cost of Capital Estimating Carborundum's Cost of Capital

Kennecot Copper Corp is considering

purchasing

purchasing Carborundum Carborundum Company. Company. WhatWhat

discount rate should Kennecott have used to

evaluate this potential acquisition?

Info given: Info given: C

Coorrbboorruunndduumm''s s EqEquuiitty y bbeettaa 11..1166 LLT T TTrreeaassuurry y bboonnd d rraattee 77..66%% Historical spread between returns on S&P500

Historical spread between returns on S&P500 index & LT Treas. Bonds

index & LT Treas. Bonds 7.5%7.5%

C

Coorrccoorr. . MMaarrkkeet t vvaalluue e oof f eeqquuiittyy $$ 227711..00 C

Coorrbboorr. . MMaarrkkeet t vvaalluue e oof f ddeebbtt $$ 8866..22 If proceed with acquisition, it will be

If proceed with acquisition, it will be financedfinanced

with: debt

with: debt $$ 100.0100.0

payment of dividend to Kennecott

payment of dividend to Kennecott $$ 140.0140.0 Cash Flows being discounted by Kennecott

Cash Flows being discounted by Kennecott were those it would receive from

were those it would receive from Carborundum, net of financing costs. Carborundum, net of financing costs.

Calculation of Carborundum's pre-acquisition Calculation of Carborundum's pre-acquisition cost of equity capital

cost of equity capital

1.160 1.160 0.075 0.075 0.0870 0.0870 0.076 0.076 0.1630 0.1630

(2)

16.30% 16.30%

1).

1). Unlever Unlever Carbor's eqCarbor's equity beta uity beta underunder

current capital structure, then relevering to current capital structure, then relevering to reflect new capital structure.

reflect new capital structure. a

assssuummee ttaaxx rraattee == 5500%%

B

_a_a

=

1.16 1.16 [ 1 + (1 - 0.5)86.2/27 [ 1 + (1 - 0.5)86.2/27 1.15904059 1.15904059

B

_a_a

=

1.001.00 Under the new financial restructuring:

Under the new financial restructuring: Carbor's debt to equity ratio would rise Carbor's debt to equity ratio would rise currently:

currently: C

Coorrccoorr. . MMaarrkkeet t vvaalluue e oof f eeqquuiittyy 227711 C

Coorrbboorr. . MMaarrkkeet t vvaalluue e oof f ddeebbtt 8866..22 D

D//EE 00..3322

After acquisition:

C

Coorrccoorr. . MMaarrkkeet t vvaalluue e oof f eeqquuiittyy 227711 Pay dividend

Pay dividend (140)(140)

E

Eqquuiittyy 113311

C

(3)

100 100 186 186 D D//EE 11..4422 Increase in leverage Increase in leverage

B

_e_e

=

The new equity beta would be:

The new equity beta would be: 1.711.71

Now, substitute a beta of 1.71 into equation Now, substitute a beta of 1.71 into equation 6.1, so that can get the cost of equity

6.1, so that can get the cost of equity capitalcapital under its postacquistion capital structure under its postacquistion capital structure

1.71 1.71 0.075 0.075 0.1283 0.1283 0.076 0.076 0.2043 0.2043 Kennecot Copper Corp is considering

Kennecot Copper Corp is considering

purchasing

purchasing Carborundum Carborundum Company. Company. WhatWhat

discount rate should Kennecott have used to

evaluate this potential acquisition?

(4)

million million million million million million million million Page 146, equ 6.1 Page 146, equ 6.1 C

Coorrbboorruunndduumm''s s EqEquuiitty y bbeettaa BBeettaa Historical spread between returns on S&P500 index

Historical spread between returns on S&P500 index & LT& LT Treas. Bonds

Treas. Bonds _{x Project}_{x Project}

equity beta x

equity beta x spread between S&P500 & LT Treasury bondsspread between S&P500 & LT Treasury bonds ++ LT Treasury bond rate

(5)

cost of equity capital cost of equity capital

Good for analyzing CF's under current capital structure Good for analyzing CF's under current capital structure Due to CF's being discounted are CF's to Kennecot, then Due to CF's being discounted are CF's to Kennecot, then

should use discount rate from Carborundum's cost of equity should use discount rate from Carborundum's cost of equity under new capital structure

under new capital structure

Equ 6.5, page 150 Equ 6.5, page 150

B

_e_e

1 + (1-t)D/E

Corborundum's Equity beta Corborundum's Equity beta ]]

Carbor's asset beta Carbor's asset beta

E E D D E E

(6)

D D Equ 6.6, page 150 Equ 6.6, page 150

B

_a_a

[ 1 +

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

(1-t)D/E]

1.00(1 + .5 x 1.00(1 + .5 x 1.42)1.42) Page 146, equ 6.1 Page 146, equ 6.1 n

neeww eeqquuiittyy bbeettaa BBeettaa Historical spread between returns on S&P500 index

Historical spread between returns on S&P500 index & LT& LT Treas. Bonds

Treas. Bonds _{x Project}_{x Project}

equity beta x

equity beta x spread between S&P500 & LT Treasury bondsspread between S&P500 & LT Treasury bonds ++ LT Treasury bond rate

LT Treasury bond rate Risk-freeRisk-free

(7)

risk premium risk premium

ate ate

(8)

(9)

risk premium risk premium

ate ate

(10)

Estimating Vulcan Materials' Estimating Vulcan Materials' Divisional Costs of Capital Divisional Costs of Capital Info given:

Info given:

LT Treasury bond rate

LT Treasury bond rate 6.3%6.3%

Risk premium (relative to LT T-bond Risk premium (relative to LT T-bond rate)

rate) 5.0%5.0%

Average asset betas: Average asset betas: Contruction Contruction 0.640.64 Chemicals Chemicals 0.840.84 Metals Metals 0.790.79

Oil & Gas

Oil & Gas 1.101.10

Use equ 6.1, page 146

Use equ 6.1, page 146 BetaBeta x

x Project Project risk risk premiumpremium +

+

Risk-free rate Risk-free rate

C

Coonnttrruuccttiioonn CChheemmiiccaallss MMeettaallss LT Treasury bond rate

LT Treasury bond rate 0.0630.063 0.0630.063 0.0630.063 + avg asset beta

+ avg asset beta 0.640.64 0.840.84 0.790.79 x risk premium x risk premium 0.050.05 0.050.05 0.050.05 0.03 0.03 0.04 0.04 0.040.04 0.095 0.095 0.105 0.105 0.1030.103 Cost of capital by business segment

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Oil & Gas Oil & Gas 0.063 0.063 1.10 1.10 0.05 0.05 0.06 0.06 0.118 0.118 11.80% 11.80%

(12)

Chapter 6, page 165 Chapter 6, page 165

Comparing WACC, APV, LE Methods Comparing WACC, APV, LE Methods for calculating the cost of capital for calculating the cost of capital Info given:

Info given: Giant Mfg. Giant Mfg.

Invest $30 million in a new solar

Invest $30 million in a new solar power sourcepower source a

annnnuuaal l FFCCFF''s s iin n ppeerrppeettuuiittyy 44,,888888,,000000 k k == 1166%% (30,000,000) (30,000,000) 30,550,000 30,550,000 N NPPVV == 555500,,000000 New info: New info: a addddiittiioonn ttoo dedebbtt $$ 66..5500 IInntteerreesst t rraatte e oon n tthhe e ddeebbtt 1100%% T

Taaxx rraattee 3300%%

Calculate the value of the project using 3 different methods: Calculate the value of the project using 3 different methods:

A

AP

PV

V M

Me

etth

ho

od

d ((e

eq

qu

u 6

6..1

10 0))

A

Ad

djju

usstte

ed

d P

Prre

esse

en

nt

t V

Va

a

APV =

NPV of project if all

equity financed

The only financing side effect is the

The only financing side effect is the tax savings provided by thetax savings provided by the Annual tax savings = the tax x

Annual tax savings = the tax x the annual interest expensethe annual interest expense T

Taaxx rraattee 00..3300

IInntteerreesstt RRaattee 00..1100 A

Addddiittiioon n tto o ddeebbtt 66,,550000,,000000 Annual

Annual tax tax savings savings $$ 195,000195,000 550,000 550,000

(13)

195,000 195,000 $ $ 0.10 0.10 A APPV V == $$ 22,,550000,,000000 Using market values, the debt ratio for this project =

Using market values, the debt ratio for this project = A Addddiittiioon n tto o ddeebbtt 66,,550000,,000000 N Neew w eeqquuiitty y ppoorrttiioonn 2266,,000000,,000000 Equity: Equity:

IInnvveessttmmeenntt 3300,,000000,,000000 A

APPV V ((aaddjjuusstteed d PVPV)) 22,,550000,,000000

T

Toottaall 3322,,550000,,000000

WACC Method

Equ

Equ 6.11

6.11 page

page 164

164

ususe eqe equ 6u 6.1.11 to 1 to esestitimamatt

k

_e_e

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

_d_d

))

using debt ratio of using debt ratio of kk** 00..1166 D D $$ 66..55 E E $$ 2266..00 tt 00..3300 kk_d_d 0.100.10 0.1705 0.1705 17.05% 17.05%

WACC

WACC Equ 6

Equ 6.9

.9 pg

pg 155

155 k

k

_o_o

= w

_e_e

kk

_e_e

+ w

_d_d

kk

_d_d

(1-t) + w

_p_p

kk

_p_p

w

weeiigghht t oof f tthhe e eeqquuiittyy 00..8800 ccoosst t oof f eeqquuiittyy 00..11770055

(14)

w wt t x x ccoosstt 00..11336644 + + w weeiigghht t oof f tthhe e ddeebbtt 00..2200 ccoosst t oof f tthhe e ddeebbtt 00..1100 w wt t x x ccoosstt 00..001144 0.1504 0.1504 15.04% 15.04% At this discount rate of 15.04%, calculate the NPV

At this discount rate of 15.04%, calculate the NPV

(30,000,000) (30,000,000) 4,888,000 4,888,000 15.04% 15.04% (30,000,000) (30,000,000) 32,500,000 32,500,000 N NPPVV == $$ 22,,550000,,000000

LE Method

LE d

LE dis

isco

count r

unt rat

ate:

e: k

k

_e_e

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

LE c

LE cas

ash fl

h flow

ows:

s: LC

LCFF

_ii

= CF

₁₁

-

- d

de

eb

bt

t sse

errv

v

LE

LE in

inve

vest

stme

ment:

nt: II

_o_o

- amt borrowed to

Combine the levered cost of equity (17.05%), with the CF's to e Combine the levered cost of equity (17.05%), with the CF's to e

D

Deebbt t aammoouunntt 66..5500 a

annnnuuaal l aafftteer r ttaax x iinntteerreesst t eexxppeennssee 00..7700 iinntteerreesst t rraatte e oon n tthhe e ddeebbtt 00..1100 multiply debt amt x after tax int x int

multiply debt amt x after tax int x int rate on debt

rate on debt $$ 455,000455,000 FFCCFF''s s ((ffrroom m aabboovvee--ggiivveenn)) 44,,888888,,000000

Less:

(15)

a

annnnuuaal l CCF F tto o eeqquuiittyy $$ 44,,443333,,000000

IInnvveessttmmeenntt $$ 3030,,000000,,000000 D

Deebbt t ppoorrttiioonn $$ 66,,550000,,000000 E

Eqquuiitty y iinnvveessttmmeennt t iin n tthhe e pprroojjeecctt $$ 2233,,550000,,000000 At this discount rate of 17.05%, calculate the NPV

At this discount rate of 17.05%, calculate the NPV

(23,500,000) (23,500,000) 4,433,000 4,433,000 0.1705 0.1705 (23,500,000) (23,500,000) 26,000,000 26,000,000 N NPPVV == $$ 22,,550000,,000000

(16)

Investment Investment

Perpetuity/interest rate Perpetuity/interest rate add both together

add both together

profitable, postive NPV profitable, postive NPV million million

ue

ue Method

Method

+

NPV of financing side

effects caused by project

acceptance

ax

ax deductibility deductibility of of interest interest paymentspayments

NPV NPV + +

(17)

Annual tax savings Annual tax savings Interest Rate

Interest Rate

The tax benefits of debt financing have turned project to be

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

20% 20% 80% 80%

debt is set to 20% of the debt is set to 20% of the

project's present value of 32.5 project's present value of 32.5 mil

mil

the project's levered cost of equity capital the project's levered cost of equity capital

20% 20% given given mil mil mil mil tax rate tax rate

interest rate on the debt interest rate on the debt

(18)

((11-- ..3300)) 00..00770000 cost of debt cost of debt Investment Investment FCF's (from above-given) FCF's (from above-given) discount rate discount rate

same result as when we used the APV method same result as when we used the APV method

- k

_d_d

))

ce charges

finance

finance project

project

uity uity million million ( 1 - .30) ( 1 - .30)

(19)

Investment Investment FCF's calculated above FCF's calculated above discount rate discount rate

same result as when we used the APV & WACC methods same result as when we used the APV & WACC methods

(20)

Chapter 6 Estimating the Project Cost of Capital Chapter 6 Estimating the Project Cost of Capital sample problem 1 sample problem 1 page 168 page 168 Info given: Info given:

A company is deciding whether to issue stock

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

an investment project an investment project P Prroojjeecctt BBeettaa 11..00 P Prroojjeecct t EExxppeecctteed d rreettuurrnn 2200%% R Riisskk ffrreeeerraattee 1100%% C Coommppaannyy''s s ssttoocck k pprriicce e bbeettaa 22..55 E Exxppeecctteed d rreettuurrn n oon n mmaarrkkeett 1155%%

Should the company go ahead with the project?

With a project beta of

With a project beta of 1.0, the project's required return = the1.0, the project's required return = the expected return on the market, or 15%

expected return on the market, or 15%

Since the project's expected return of 20% exceeds the project's Since the project's expected return of 20% exceeds the project's cost of capital, the company should make the investment

cost of capital, the company should make the investment Calculate the cost of equity capital for the company:

Calculate the cost of equity capital for the company: C

Coommppaannyy''s s ssttoocck k pprriicce e bbeettaa 22..55 m

maarrkkeettrriisskk pprreemmiiuumm 55%% Company's cost of equity capital:

Company's cost of equity capital:

C

Coommppaannyy''s s ssttoocck k pprriicce e bbeettaa 22..5500 m

maarrkkeet rt riissk pk prreemmiiuumm 00..0055 0.13 0.13 R

Riissk k ffrreee e rraattee 00..1100 0.225 0.225 C

(21)

proj expected return - expected return on mkt proj expected return - expected return on mkt

Beta Beta x

x Project Project risk risk premiumpremium +

+

Risk-free rate Risk-free rate

(22)

Chapter 6 Estimating the Project Cost of Capital Chapter 6 Estimating the Project Cost of Capital sample problem 2

sample problem 2 page 168

page 168

Multi Foods has 4 divisions: Multi Foods has 4 divisions:

Contribution to Contribution to F Fiirrmm''s s VVaalluuee CCoommppaannyy 1 100%% PPeet t PPrroodduuccttss 2 255%% CCaannddlleelliigghhtt 5

500%% FFrreeeezziieess 1 155%% RReeddyyEEeeeett 100% 100% a). a).

Estimate the asset betas for

Estimate the asset betas for MultiFoods divisionsMultiFoods divisions, assume the, assume the debt betas are -0-, ignore taxes

debt betas are -0-, ignore taxes transfer the debt to asset ratio to

transfer the debt to asset ratio to the debt to equity ratiothe debt to equity ratio

D/E = D/(TA - D)

Pet Products Pet Products Candlelight Candlelight Freezies Freezies RedyEeet RedyEeet Equ 6.3, page 149 Equ 6.3, page 149

B

_a_a₌₌

B

_e_e

1

1 +

+

D/E

Pet Products Pet Products Candlelight Candlelight Freezies Freezies RedyEeet RedyEeet b).

b). Info given:Info given:

Risk free rate Risk free rate

(23)

avg market rate of return avg market rate of return What is cost of

What is cost of capital for each of the capital for each of the divisions?divisions? using CAPM using CAPM

k

_pp_pp

= r

_f_f

+ B

_a_a

(r

_m_m

- r

_f_f

)

.08 .08 + + .33(0.16 .33(0.16 - - .08).08) c).

c). With a D/TA of 0.50, what is MultiFoods' equity beta?With a D/TA of 0.50, what is MultiFoods' equity beta? Pet Products Pet Products Candlelight Candlelight Freezies Freezies RedyEeet RedyEeet with D/TA with D/TA D/E = D/E = equity beta = equity beta = equity beta = equity beta = d). d).

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

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

B

_a_a

= (D/TA)B

_d_d

+ (E/TA)B

_e_e

Company Company Pet Products Pet Products Candlelight Candlelight

(24)

Freezies Freezies RedyEeet RedyEeet D/TA D/TA Bd Bd E/TA E/TA Be Be

Risk free rate Risk free rate avg market rate of return avg market rate of return What is cost of

What is cost of capital for each of the capital for each of the divisions?divisions? CAPM CAPM

k

_pp_pp

= r

_f_f

+ B

_a_a

(r

_m_m

- r

_f_f

)

.08 .08 + + .50(0.16 .50(0.16 - - .08).08) W Weeiigghhttss CCoommppaannyy 1 100%% PPeet t PPrroodduuccttss 2 255%% CCaannddlleelliigghhtt 5

500%% FFrreeeezziieess 1

155%% RReeddyyEEeeeett

w

weeiigghhtteed d aa CAPM cost of capital for Multi Foods =

CAPM cost of capital for Multi Foods =

Risk free rate Risk free rate weighted avg. asset beta weighted avg. asset beta avg market rate of return avg market rate of return

(25)

B B_e_e Equity Beta Equity Beta D/TA (debt to D/TA (debt to total assets total assets 0 0..55 00..3333 11 33 1 1..55 00..5500 11 22 1 1..7755 00..2200 11 55 2 2..2255 00..2255 11 44 0.50 0.50 D/ED/E 1.00 1.00 D/ED/E 0.25 0.25 D/ED/E 0.33 0.33 D/ED/E 0.33

0.33 Asset betaAsset beta 0.75

1.69 Asset betaAsset beta

8%

(26)

16% 16%

rm

0.160.16 cost of capital cost of capital 0 0..11006677 PPeet t PPrroodduuccttss 1100..6677%% 0 0..11440000 CCaannddlleelliigghhtt 1144..0000%% 0

0..1199220 F0 Frreeeezziieess 1199..2200%% 0

0..22115500 RReeddyyEEeeeett 2211..5500%%

ccoonntt AAsssseet t BBeettaa

cont x cont x asset asset beta beta 1 100%% 00..3333 00..00333333 2 255%% 00..7755 00..11887755 5 500%% 11..4400 00..77000000 1 155%% 11..6699 00..22553311 weighted avg weighted avg 1.17401.1740 0.50 0.50 1.00 1.00 1.174 x (1 + D/E) 1.174 x (1 + D/E) 2.348 2.348 0.5 0.5 A

Asssseet Bt Betetaa CCoost st oof Cf Capapiitatal l %%

D/TA (debt to D/TA (debt to total assets total assets 0.50 0.50 1 122..0000%% 0..30 333 1.00 1.00 1 166..0000%% 0..50 500

(27)

1.50 1.50 2 200..0000%% 0..20 200 1.81 1.81 2 222..5500%% 0..20 255 P

Peet t PPrroodduuccttss CCaannddlleelliigghhtt FFrreeeezziieess RReeddyyEEeeeett 0 0..3333 00..5500 00..2200 00..2255 0 0..55 00..55 00..55 00..55 0 0..6677 00..5500 00..8800 00..7755 0 0..5500 11..55 11..7755 22..2255 8% 8%

rr

_f_f 0.080.08 16% 16%

rm

0.160.16 Cost of Capital Cost of Capital P Peet t PPrroodduuccttss 00..1122 C Caannddlleelliigghhtt 00..1166 FFrreeeezziieess 00..22 R ReeddyyEEeeeett 00..222255 Asset Beta Asset Beta 0.50 0.50 0.05 0.05 1.00 1.00 0.25 0.25 1.50 1.50 0.75 0.75 1.81 1.81 0.27 0.27 g g. . aasssseet t bbeettaa 11..3322 18.58% 18.58% 0.08 0.08 1.32 1.32 0.16 0.16

(28)

D D//EE AAsssseet t BBeettaa Cost of Cost of Capital (%) Capital (%) P Peet t PPrroodduuccttss 00..5500 00..3333 1100..6677%% C Caannddlleelliigghhtt 11..0000 00..7755 1144..0000%% FFrreeeezziieess 00..2255 1..41 400 1199..2200%% R

(29)

E/TA E/TA 0.67 0.67 0.50 0.50

(30)

0.80 0.80 0.75 0.75

(31)

Chapter 6 Chapter 6 page 186 page 186 Appendix B Appendix B

Dividend Growth Model Dividend Growth Model

Equity Cost of Equity Cost of C Caappiittaall == Dividend Dividend Y Yiieelldd ++ Expected dividend Expected dividend growth rate growth rate k k_e_e = DIV = DIV₁₁ ++ gg P P_o_o k

k_e_e Equity Cost of CapitalEquity Cost of Capital DIV

DIV₁₁ expected dividend in year 1expected dividend in year 1 P

P_o_o current stock pricecurrent stock price

gg averaaverage expege expected acted annual divnnual dividend gidend growtrowth rh r See page 187, Box 6.5 for comparison See page 187, Box 6.5 for comparison

(32)

The dividend discount model (DDM) is a way of

The dividend discount model (DDM) is a way of valuing avaluing a company based on the theory that a stock is worth the company based on the theory that a stock is worth the discounted sum of

discounted sum of all of its future all of its future dividend payments. dividend payments. In otherIn other words, it is used to value

words, it is used to value stocks based on the net present valuestocks based on the net present value of the future dividends.

of the future dividends.

te te

to CAPM to CAPM