Download - Chapter 6 Review in Class
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