Chapter 6 Box 6.2, pg. 151 Estimating 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 LT Treasury bond rate Historical spread between returns on S&P500 index & LT Treas. Bonds Corcor. Market value of equity Corbor. Market value of debt If proceed with acquisition, it will be financed with: debt payment of dividend to Kennecott Cash Flows being discounted by Kennecott were those it would receive from Carborundum, net of financing costs.
1.16 7.6%
$ $
7.5% 271.0 86.2
$ $
100.0 140.0
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 equity beta under current capital structure, then relevering to reflect new capital structure. assume tax rate =
50%
Ba = 1.16 [ 1 + (1 - 0.5)86.2/27 1.15904059
Ba =
1.00
Under the new financial restructuring: Carbor's debt to equity ratio would rise currently: Corcor. Market value of equity Corbor. Market value of debt D/E
271 86.2 0.32
After acquisition: Corcor. Market value of equity Pay dividend Equity
271 (140) 131
Corbor. Market value of debt
86
D/E
100 186 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 Historical spread between returns on S&P500 index & LT Treas. Bonds
x Project
equity beta x spread between S&P500 & LT Treasury bonds LT Treasury bond rate
+ Risk-free
Beta
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/E Corborundum's Equity beta ] 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 Historical spread between returns on S&P500 index & LT Treas. Bonds equity beta x spread between S&P500 & LT Treasury bonds LT Treasury bond rate
cost of equity capital
Beta x Project + Risk-free
risk premium
ate
risk premium
ate
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
LT Treasury bond rate + avg asset beta x risk premium
Cost of capital by business segment
Contruction Chemicals Metals 0.063 0.063 0.063 0.64 0.84 0.79 0.05 0.05 0.05 0.03 0.04 0.04 0.095 0.105 0.103 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 k=
(30,000,000) 30,550,000 550,000
NPV =
New info: addition to debt Interest rate on the debt Tax rate
4,888,000 16%
$
6.50 10% 30%
Calculate the value of the project using 3 different methods:
APV Method (equ 6.10)
Adjusted Present Va NPV of project if all APV = equity financed
The only financing side effect is the tax savings provided by the 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
APV = $
0.10 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 ke = k* + D/E (1-t)(k* - k d)
use use eq equ u 6.1 6.11 1 to esti estima matt k* D E t kd
using debt ratio of 0.16 $ 6.5 $ 26.0 0.30 0.10
0.1705 17.05%
WACC Equ 6.9 6.9 pg 155 ko = weke + wdkd (1-t) + wpkp weight of the equity cost of equity
0.80 0.1705
wt x cost + weight of the debt cost of the debt wt x cost
0.1364 0.20 0.10 0.014 0.1504 15.04%
At this discount rate of 15.04%, calculate the NPV (30,000,000) 4,888,000 15.04%
NPV =
$
(30,000,000) 32,500,000 2,500,000
LE Method LE d dis isco count unt rat rate: e: ke = k* + D/E (1-t)(k* LE ccas ash h flow flows: s: LC LCFFi = CF1 - debt serv LE inve invest stme ment: nt: Io - amt borrowed to Combine the levered cost of equity (17.05%), with the CF's to e Debt amount annual after tax interest expense interest rate on the debt multiply debt amt x after tax int x int rate on debt $ FCF's (from above-given) Less:
6.50 0.70 0.10 455,000 4,888,000 (455,000)
annual CF to equity $
4,433,000
Investment $ Debt portion $ Equity investment in the project $
30,000,000 6,500,000 23,500,000
At this discount rate of 17.05%, calculate the NPV (23,500,000) 4,433,000 0.1705
NPV =
$
(23,500,000) 26,000,000 2,500,000
Investment Perpetuity/interest rate add both together profitable, postive NPV
million
ue Method
+
NPV of financing side effects caused by project acceptance
ax 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
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
- kd) ce charges finance project
uity 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 Project Expected return Risk free rate Company's stock price beta Expected return on market Should the company go ahead with the project?
1.0 20% 10% 2.5 15%
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 market risk premium Company's cost of equity capital:
2.5 5%
Company's stock price beta
2.50
market ri risk pr premium
0.05 0.13
Risk free rate Company's cost of equity capital:
0.10 0.225 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 10% 25% 50% 15% 100%
a).
Company Pet Products Candlelight Freezies RedyEeet
Estimate the asset betas for MultiFoods divisions, 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/E Pet 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 cost of capital for each 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 10% 25% 50% 15%
Company Pet Products Candlelight Freezies RedyEeet weighted a CAPM cost of capital for Multi Foods = Risk free rate weighted avg. asset beta avg market rate of return
Be
Equity Beta 0 .5 1 .5 1.75 2.25
8%
D/TA (debt to total assets 0.33 0.50 0.20 0.25
1 1 1 1
0.50 1.00 0.25 0.33
D/E D/E D/E D/E
0.33 0.75 1.40 1.69
Asset beta Asset beta Asset beta Asset beta
rf
0.08
3 2 5 4
rm
16%
0.16
cost of capital 0.1067 0.1400 0.1920 0.2150
cont 10% 25% 50% 15%
Pet Products Candlelight Fr F reezies RedyEeet
10.67% 14.00% 19.20% 21.50%
Asset Beta 0.33 0.75 1.40 1.69 weighted avg
cont x asset beta 0.0333 0.1875 0.7000 0.2531 1.1740
0.50 1.00 1.174 x (1 + D/E) 2.348
0.5
Asse sset Bet Beta a Cost of Cap Capiital tal % 0.50 12.00% 12 1.00 16.00% 16
D/TA (debt to total assets 0.33 0.50
1.50 1.81
Pet Products 0.33 0 .5 0.67 0.50 8% 16%
20 2 0.00% 22.50% 22 Candlelight Freezies 0.50 0.20 0 .5 0.5 0.50 0.80 1 .5 1.75
rf rm Cost of Capital
Pet Products Candlelight Freezies RedyEeet
Asset Beta 0.50 1.00 1.50 1.81 g. asset beta 18.58% 0.08 1.32 0.16
0.20 0.25
0.12 0.16 0 .2 0.225
0.05 0.25 0.75 0.27 1.32
0.08 0.16
RedyEeet 0.25 0 .5 0.75 2.25
Pet Products Candlelight Freezies RedyEeet
D/E Asset Beta 0.50 0.33 1.00 0.75 0.25 1.40 0.33 1.69
Cost of Capital (%) 10.67% 14.00% 19.20% 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 = ke = DIV1
Dividend Yield + + g
Expected dividend growth rate
Po ke Equity Cost of Capital DIV1 expected dividend in year 1 Po current stock price g average average expected expected annual annual dividend dividend growt growth hr See page 187, Box 6.5 for comparison
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.
te to CAPM
