FIN 500 Saudi Electronic University Critical Thinking Worksheet

Sep 25, | FIN 500

Description

Module 11: Cost of Capital
Problem 11-1: Preferred Stock Market price
A firm has a preferred stock with SAR 100 par value that pays a dividend of 12%. What is
the market price for the stock if the required rate of return is 7%?
Problem 11-2: Common Stock Market Price
A firm paid a dividend payment of SAR 650 last year and is expected to grow indefinitely
at a rate of 7%. If you can achieve a 10% return on equity, what is the value of the stock?
Problem 11-3- Preferred Stock Value
A corporation preferred stock is selling for SAR 1750 per share and pays an annual
dividend of SAR 152 per share. If the investor requires a return of 7%, what is the
appropriate market value for the shares?
Problem 11-4: Growth Rate
If a firm’s return on equity is 20% and management plans to retain 75% of earnings for
investment purposes, what will be the firm’s growth rate?
Problem 11-5: Dividend Constant Model-Stock Expected Rate of Return
A corporation paid a dividend of SAR 625 last year and the shares are selling for SAR
6250 per share. The dividend is expected to grow at 7% indefinitely. What is the stock’s
expected rate of return?
Problem 11-6: Required Rate of Return (CAPM)
A corporation’s stock has a beta of 1.2. The risk-free rate is 8.5% and the expected
return on the market is 11.5%. What is the required rate of return on the stock using the
Capital Asset Pricing Model (CAPM)?
Problem 11-7: Cost of Debt
A firm’s bond with a SAR 1000 par value currently selling at SAR825. The coupon rate is
10% with 12.5 years to the maturity date and the corporate tax is 25%. What is the cost
of debt after tax?
11-8: WACC Calculation
A corporation’s balance sheet shows SAR 400 million in debt, SAR 50 million in preferred
stock, and SAR 550 million in total common equity.
DATA
The firm’s tax rate is:
15,00%
Rate on Debt (Rd) Before Tax
7,00%
Rate on Preferred Stock (Rps)
6,00%
Rate on Common Stock (Rcs)
11,00%
What is its Weighed Average Cost of Capital (WACC)?
Weight-Common Stock
550
Weight-debt
400
Weight-Preferred Stock
50
1000
WACC
Dividend rate
Par value
Discount rate
12
100
0,07
Dividend rate/Discount rate
Present Value
Discount rate
Growth rate
Dividend payment (D1)
0,1
0,07
Dividend *1+Growth rate
Dividend payment (D1)/(Discount rateGrowth rate)
Price
Dividend rate
Par value
Discount rate
Present Value
152
1750
0,07
Retention Rate
Return on Equity
Growth Rate
0,75 1-0.25
0,20
Retention Rate*Return on Equity
Dividend rate/Discount rate
Price
Dividend Payment (D1)
Growth Rate
6250
668,75
0,07
(Dividend Payment/Price)+Growth
Rate
Expected Return
Beta
Risk free return
Market return
1,200
0,085
0,115
Risk free return+Beta*(Market returnRisk free return)
Required rate of return
par value
net price
coupon rate
years
tax rate
Dividend*Growth Rate
1000
-825
100
12,5
0,25
After Tax Cost
Rate(years,coupon rate, net price, par
value)
Cost*(1-tax rate)
Rate on Debt (Rd) After Tax
Rate before Tax*(1-Tax rate)
Cost
Solution
Weight-Common Stock/1000
Weight-debt/1000
Weight-Preferred Stock/1000
(Weight-Common Stock/1000*Rate on Common
Stock (Rcs)+(Weight-Preferred Stock*Rate on
Preferred Stock (Rps))+(Weight-debt*Rate on
Debt (Rd) Before Tax)
Foundations of Finance
Ninth Edition
Chapter 9
The Cost of
Capital
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The Cost of Capital: Key Definitions
and Concepts
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Capital
Capital
• Capital represents the funds used to finance a firm’s
assets and operations. Capital constitutes all items on
the right hand side of balance sheet, i.e., liabilities and
common equity.
• Main sources: Debt, Preferred stock, Retained earnings
and Common Stock
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Opportunity Cost of Capital
• Cost of Capital
– The firm’s cost of capital is also referred to as the firm’s
opportunity cost of capital.
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Investor’s Required Rate of
Return (1 of 2)
• Investor’s Required Rate of Return – the minimum rate
of return necessary to attract an investor to purchase or
hold a security.
• Investor’s required rate of return is not the same as cost of
capital due to taxes and transaction costs.
– Impact of taxes: For example, a firm may pay 8%
interest on debt but due to tax benefit on interest
expense, the net cost to the firm will be lower than 8%.
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Investor’s Required Rate of
Return (2 of 2)
• Impact of transaction costs on cost of capital: For
example, If a firm sells new stock for $50.00 a share and
incurs $5 in flotation costs, and the investors have a
required rate of return of 15%, what is the cost of capital?
• The firm has only $45.00 to invest after transaction cost.
0.15 × $50.00 = $7.5
$7.5
k=
= 0.1667or16.67% (rather than 15% )
( $45.00 )
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Financial Policy
• A firm’s financial policy indicates the desired sources of
financing and the particular mix in which it will be used.
• For example, a firm may choose to raise capital by issuing
stocks and bonds in the ratio of 6:4 (60% stocks and 40%
bonds). The choice of mix will impact the cost of capital.
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Determining the Costs of the
Individual Sources of Capital
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The Cost of Debt (1 of 3)
• The bondholder’s required rate of return on debt is the
return that bondholders demand. As seen in Chapter 7,
this can be estimated using the bond price equation:
Bond market price =
interest paid in year 1
interest paid in year 2
+
1
(1+ bondholder’s required rate of return ( r ) ) (1+ bondholder’s required rate of return ( r ) )
b
+
b
interest paid in year 3
(1+ bondholder’s required rate of return ( rb ) )
2
3
+
principal
(1+ bondholder’s required rate of return ( rb ) )
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3
The Cost of Debt (2 of 3)
• Since firms must pay flotation costs when they sell bonds,
the net proceeds per bond received by firm is less than the
market price of the bond. Hence, the cost of debt capital (K d )
will be higher than the bondholder’s required rate of
return. It can be calculated using the following equation:
Net proceeds per bond =
=
interest paid in year 1
+
1
(1+ cost of debt capital or kb )
interest paid in year 3
(1+ cost of debt capital or kb )
3
interest paid in year 2
(1+ cost of debt capital or kb )
+
2
principal
(1+ cost of debt capital or kb )
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3
The Cost of Debt (3 of 3)
See Example 9.1
• Investor’s required rate of return on a 8% 20-year bond
trading for $908.32 = 9%
• After-tax cost of debt = Cost of debt  (1 − tax rate )
• At 34% tax bracket = 9  (1 − 0.34 ) = 5.94%
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The Cost of Preferred Stock (1 of 2)
• If flotation costs are incurred, preferred stockholder’s
required rate of return will be less than the cost of
preferred capital to the firm.
• Thus, in order to determine the cost of preferred stock, we
adjust the price of preferred stock for flotation cost to give
us the net proceeds.
• Net proceeds = issue price − flotation cost
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The Cost of Preferred Stock (2 of 2)
• Cost of Preferred Stock: rps =
Pn =
Dp
Pn
net proceeds (i.e., Issue price − flotation costs)
Dp = preferred stock dividend per share
• Example: Determine the cost for a preferred stock that
pays annual dividend of $4.25, has current stock price
$58.50, and incurs flotation costs of $1.375 per share.
$4.25
Cost =
= 0.074 or 7.44%
( 58.50 − 1.375 )
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The Cost of Common Equity (1 of 2)
• Cost of equity is more challenging to estimate than the
cost of debt or the cost of preferred stock because
common stockholder’s rate of return is not fixed as there
is no stated coupon rate or dividend.
• Furthermore, the costs will vary for two sources of equity
(i.e., retained earnings and new issue).
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The Cost of Common Equity (2 of 2)
• There are no flotation costs on retained earnings but the
firm incurs costs when it sells new common stock.
• Note that retained earnings are not a free source of capital.
There is an opportunity cost.
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Cost Estimation Techniques
• Two commonly used methods for estimating common
stockholder’s required rate of return are:
– The Dividend Growth Model
– The Capital Asset Pricing Model
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The Dividend Growth Model (1 of 4)
• Investors’ required rate of return (For Retained Earnings):
D1
kcs =
+g
Pcs
• D1 = Dividends expected one year hence
• Pcs = Price of common stock
• g = growth rate
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The Dividend Growth Model (2 of 4)
• Investors’ required rate of return (For new issues)
k ncs
D1
=
+g
NPcs
• D1 = Dividends expected one year hence
• Pcs = Net proceeds per share
• g = growth rate
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The Dividend Growth Model (3 of 4)
• Example: A company expects dividends this year to be $1.10,
based upon the fact that $1 were paid last year. The firm
expects dividends to grow 10% next year and into the
foreseeable future. Stock is trading at $35 a share.
• Cost of retained earnings:
D 
K cs =  1  + g
 Pcs 
1.1
+ 0.10 = 0.1314 or 13.14%
35
• Cost of new stock (with a $3 flotation cost):
 D 
K ncs =  1  + g
 NPcs 
 1.10 

 + 0.10 = 0.1343 or 13.43%
35
3
(
)


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The Dividend Growth Model (4 of 4)
• Dividend growth model is simple to use but suffers from
the following drawbacks:
– It assumes a constant growth rate
– It is not easy to forecast the growth rate
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The Capital Asset Pricing Model (1 of 2)
kc = rf +  ( rm − rf )
rf =
Risk-free rate
β = Beta
rm − rf =
Market Risk Premium or expected rate of return
for “average security” minus the risk-free rate
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The Capital Asset Pricing Model (2 of 2)
Example: If beta is 1.25, risk-free rate is 1.5% and expected
return on market is 10%
kc = rrf +  ( rm − rf )
= 0.015 + 1.25 ( 0.10 − 0.015 )
= 12.125%
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Capital Asset Pricing Model Variable
Estimates
• CAPM is easy to apply. Also, the estimates for model
variables are generally available from public sources.
• Risk-Free Rate: Wide range of U.S. government securities
on which to base risk-free rate
• Beta: Estimates of beta are available from a wide range of
services, or can be estimated using regression analysis of
historical data.
• Market Risk Premium: It can be estimated by looking at
history of stock returns and premium earned over risk-free
rate.
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The Weighted Average Cost of
Capital
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The Weighted Average Cost of
Capital
Bringing it all together: WACC
• To estimate WACC, we need to know the capital structure
mix and the cost of each of the sources of capital.
• For a firm with only two sources: debt and common equity,
Weighted average cost of capital
= ( after – tax cost of debt × proportion of debt financing)
+ ( cost of equity × proportion of equity financing)
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WACC Example
• A firm borrows money at 7% interest after taxes and pays
12% for equity. The company raises capital in equal
proportions, i.e., 50% debt and 50% equity.
• WACC = (0.07 × 0.5) + (0.12 × 0.5)
= 0.095 or 9.5%
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Business World Cost of Capital
• In practice, the calculation of cost of capital may be more
complex:
– If firms have multiple debt issues with different required
rates of return.
– If firms also use preferred stock in addition to common
stock financing.
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Table 9-1 Calculating the Weighted
Average Cost of Capital (1 of 2)
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Table 9-1 Calculating the Weighted
Average Cost of Capital (2 of 2)
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Table 9-2 Capital Structure and
Capital Costs for Ash Inc.
Source of Capital
Bonds
Amount of Funds
Raised ($)
Percentage
of Total
After-Tax
Cost of
Capital
1,750,000
35%
7%
250,000
5%
13%
Retained earnings
3,000,000
60%
16%
Total
5,000,000
100%
Blank
Preferred stock
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Table 9-3 The Weighted Average Cost
of Capital for Ash Inc. (1 of 2)
Panel A: Cost of
Capital for $0 To
$5,000,000 in New
Capital
Panel A: Cost of
Capital for $0 To
$5,000,000 in New
Capital
Panel A: Cost of
Capital for $0 To
$5,000,000 in New
Capital
Panel A: Cost of
Capital for $0 To
$5,000,000 in
New Capital
Capital Structure
Capital Structure
Capital Structure
Capital Structure
Source of Capital
Bonds
Preferred stock
Retained earnings
Total
Weights
Cost of capital
Product
35%
7%
2.45%
5%
13%
0.65%
60%
16%
9.60%
100%
Kwacc =
12.70%
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Table 9-3 The Weighted Average Cost
of Capital for Ash Inc. (2 of 2)
Panel B: Cost of
Capital for More
Than $5,000,000
Panel B: Cost of
Capital for More
Than $5,000,000
Panel B: Cost of
Capital for More
Than $5,000,000
Panel B: Cost of
Capital for More
Than $5,000,000
Capital Structure
Capital Structure
Capital Structure
Capital Structure
Source of Capital
Bonds
Preferred stock
New Common Stock
Total
Weights
Cost of capital
Product
35%
7%
2.45%
5%
13%
0.65%
60%
18%
10.80%
100%
Kwacc =

13.90%
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Calculating Divisional Costs of
Capital
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Divisional Costs of Capital
• Firms with multiple operating divisions often have unique
risks and different costs of capital for each division.
• Consequently, the WACC used in each division is
potentially unique for each division.
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Advantages of Divisional WACC
• Different discount rates reflect differences in the systematic
risk of the projects evaluated by different divisions.
• It entails calculating one cost of capital for each division
(rather than each project).
• Divisional cost of capital limits managerial latitude and the
attendant influence costs.
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Using Pure Play Firms to Estimate
Divisional WACCs
• Divisional cost of capital can be estimated by identifying
“pure play” comparison firms that operate in only one of
the individual business areas.
• For example, Valero Energy Corp. may use the WACC
estimate of firms that operate in the refinery industry to
estimate the WACC of its division engaged in refining
crude oil.
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Divisional WACC Example
• Table 9-4 contains hypothetical estimates of the divisional
WACC for the refining and retail (convenience store)
industries.
• Panel A: Cost of debt (tax = 38%)
• Panel B: Cost of equity (betas differ)
• Panels D & E: Divisional WACCs
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Table 9-4 Divisional WACC
Computations (1 of 5)
Panel A: After-Tax Cost of Debt
Pre-Tax Cost
of Debt
×
(1 − Tax Rate)
After-Tax
Cost of Debt
Refining
9.00%
×
0.62
0.0558
Retailing—Convenience
Stores
7.50%
×
0.62
0.0465
Company Division
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Table 9-4 Divisional WACC
Computations (2 of 5)
Panel B: After-Tax Cost of Equity
×
MarketRisk
Premium
=
Cost of
Equity
1.1
×
0.07
=
0.097
0.8
×
0.07
=
0.076
Risk-Free
Rate
+
Beta
Refining
0.02
+
Retailing—Convenience
Stores
0.02
+
Blank
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Table 9-4 Divisional WACC
Computations (3 of 5)
Panel C: Target Debt Ratios
Blank
Target Debt Ratio
Refining
10%
Retailing—Convenience
Stores
50%
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Table 9-4 Divisional WACC
Computations (4 of 5)
Panel D: Divisional WACC for Refining
Capital Structure
Weight
×
After-Tax Cost
of Capital
=
Product
Debt
0.10
×
0.0558
=
0.0056
Equity
0.90
×
0.0970
=
0.0873
Blank
Blank
×
WACC
=
0.0929 or 9.29%
Blank
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Table 9-4 Divisional WACC
Computations (5 of 5)
Panel E: Divisional WACC for Retail (Convenience Stores)
Capital Structure
Weight
×
After-Tax Cost
of Capital
=
Product
Debt
0.50
×
0.0465
=
0.0233
Equity
0.50
×
0.0760
=
0.03580
Blank
Blank
×
WACC
=
0.0613 or 6.13%
Blank
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Divisional WACC-Estimation Issues
and Limitations
• Sample chosen may not be a good match for the firm or
one of its divisions due to differences in capital structure,
and/or project risk.
• Good comparison firms for a particular division may be
difficult to find.
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Table 9-5 Choosing the Right WACCDiscount Rates and Project Risk (1 of 2)
There are good reasons for using a single, company-wide WACC to evaluate the firm’s investments even
where there are differences in the risks of the projects the firm undertakes. However, the most common
tool used by firms that use a variety of discount rates to evaluate new investments in an effort to
accommodate risk differences is the divisional WACC. The divisional WACC represents something of a
compromise that minimizes some of the problems encountered when attempting to estimate both the
project-specific costs of capital and the costs that arise when a single discount rate is used that is equal
to the firm’s WACC.
Method
WACC
Description
Estimated
WACC for the
firm as an
entity; used as
the discount
rate on all
projects.
Advantages
•
Familiar concept to
most business
executives.
•
Minimizes estimation
costs, as there is only
one cost of capital
calculation for the firm.
•
Reduces the problem
of influence cost
issues.
Disadvantages
When to Use
•
Does not adjust
discount rates for
differences in
project risk.
•
Projects are
similar in risk
to the firm as
a whole.
•
Does not provide
for flexibility in
adjusting for
differences in
project debt in the
capital structure.
•
Using multiple
discount rates
creates
significant
problems with
influence
costs.
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Table 9-5 Choosing the Right WACCDiscount Rates and Project Risk (2 of 2)
Method
Divisional
WACC
Description
Estimated
WACC for
individual
business units
or divisions
within the firm;
used as the
only discount
rates within
each division.
Advantages
Disadvantages
•
Uses division-level
risk to adjust
discount rates for
individual projects.
•
Does not capture
intradivision risk
differences in
projects.
•
Reduces influence
costs to the
competition among
division managers
to lower their
division’s cost of
capital.
•
Does not account for
differences in project
debt capacities within
divisions.
•
Potential influence
costs associated with
the choice of discount
rates across divisions.
•
Difficult to find singledivision firms to proxy
for divisions.
When to Use
•
Individual
projects within
each division
have similar
risks and debt
capacities.
•
Discount rate
discretion
creates
significant
influence costs
within divisions
but not
between
divisions.
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Cost of Capital to Evaluate New
Capital Investments
• Cost of capital can serve as the discount rate in evaluating
new investment when the projects offer the same risk as
the firm as a whole.
• If risk differs, it is better to calculate a different cost of
capital for each division. Figure 9-1 illustrates the danger
of not doing so.
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Figure 9-1 Global Energy Divisional
Costs of Capital
Using a company-wide cost of capital for a multidivisional firm results in
systematic overinvestment in high-risk projects and underinvestment in low-risk
projects.
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Key Terms
• Capital structure
• Cost of debt
• Cost of common equity
• Cost of preferred equity
• Divisional WACC
• Financial policy
• Flotation costs
• Opportunity cost
• Weighted average cost of capital (WACC)
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Copyright
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