# Chapter 12_ The Cost of Capital by hcj

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```									The Cost
of Capital

Oct 17, 2012

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Learning Goals

n   Determining the value of K, the required
rate of return for an investor
n   Sources of capital funding (Debt, Equity)
n   Cost of each type of funding
n   Calculation of the weighted average cost of
capital funding (WACC) = K
n   Construction and use of the marginal cost of
capital schedule (MCC) for decision making

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Cost of Capital
n   Capital is the term used by firms for
funds needed for investment
purposes, i.e., capital equipment
(not for day to day operating needs)
n   This capital carries a cost because
each source of capital funding costs
money to raise (i.e., issuing stock
costs a lot of money)
Cost of Capital

n   To properly evaluate investment
decisions, the firm must know how
much it will cost them to raise capital
funds from all sources
n   WACC = K = hurdle rate
n   If it costs more to raise the capital (K)
than you make on your investment,
then you don’t make the investment!
Sources of Capital
n   Borrowing: issue Bonds, bank loans,
n   Issuing Preferred stock
n   Issuing Common stock
n   Net Income (earnings)
n   Each of these sources carries a different
cost based on the required rate of return
of each provider (source) of these funds
Optimal Capital
Structure
n   The capital structure of a firm is how the
firm has elected to finance its assets
n   It is the level or percentage of total
assets financed by debt, preferred stock
and common equity (common stock and
retained earnings)
n   Each firm has an optimal level of debt
and equity at which it can operate most
efficiently and profitability (Draw curve)
Weighted Cost of Capital Model
n   Compute the cost of each source of
capital, i.e., debt, preferred stock,
common stock, retained earnings
n   Determine percentage (weights) of each
source of capital in the firm’s optimal
capital structure
n   Calculate Weighted Average Cost of
Capital (WACC)
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1. Compute Cost of Debt

n   Required rate of return for creditors
n   e.g. Suppose that a company issues bonds with
a before tax cost of 10%.
n   Since interest payments are tax deductible, the
true cost of the debt is the After Tax cost (ATkd
= Int Rate (1 – T), where T is tax rate)
n   If the company’s tax rate (state and federal
combined) is 40%, the after tax cost of debt AT
kd = 10%(1-.4) = 6% (show example)

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Flotation Costs –           cost of issuing
securities to the general public

n   Accounting
n   Legal
n   Prospectus – (pass out examples)
n   Underwriting (investment banker)
n   Filing Fees (SEC)
2. Compute Cost Preferred Stock
n   Cost to raise a dollar of preferred stock.
Dividend (Dp)
Required rate kp =
Market Price (PP) - F

v Dp = preferred stock dividend
v Pp = Market price per share
v F = flotation costs per share
v Flotation costs reduce the amount of money you
get when you sell preferred stock
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Cost of Preferred Stock

v Example:  You can issue preferred
stock with a market price of \$45, and
flotation costs of \$3 per share, for a
net price of \$42 and if the preferred
stock pays a \$5 dividend,
vThe cost of preferred stock:
kp =    \$5.00 = 11.9%   (vs 11.1%)
\$42.00
3. Compute Cost of Common Equity

n   Two Types of Common Equity Financing
– Retained Earnings (internal common equity)
– Issuing new shares of common stock
(external common equity)

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3. Compute Cost of Common Equity

n   Cost of Common Equity (Retained Earnings)
– Management should retain earnings only
if they earn as much as stockholder’s
next best investment opportunity of the
same risk.
– Cost of Common Equity = opportunity
cost of common stockholders’ funds.
– Two methods to determine
n Dividend Growth Model

n Capital Asset Pricing Model
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3. Compute        Cost of Common Equity
n   Cost of Common Equity (Retained Earnings)
– Dividend Growth Model
D1
kS =   P0
+ g

Ks = cost of internal common equity
D1 = the next dividend to be paid
Po = the current market price of the stock
g = the projected rate of growth of the company
3. Compute Cost of Common Equity
n   Cost of Internal Common Equity
– Dividend Growth Model

kS = D1 + g
P0
Example:
The market price (Po) of a share of common
stock is \$60. The prior dividend paid (D0) was
\$3, and the expected growth rate (g) is 10%.

If you are given D0, you must calculate D1
D1 = D0 (1 + g)
D1 = 3.00 (1.10) = 3.30
3. Compute Cost of Common Equity
n   Cost of Internal Common Equity
– Dividend Growth Model

D1
kS =         + g
P0
Example:
The market price of a share of common stock
is \$60. The prior dividend (D0) is \$3, and the
expected growth rate is 10%.
(D1 = 3.00 x 1.10 = 3.30)

3.30        + .10   =.055 + .10 = 15.5%
kS =
60
3. Compute Cost of Common Equity

n   Cost of New Common Stock
– Must adjust the Dividend Growth Model
equation for flotation (F) costs of the new
common shares.
D1
kn = P - F + g
0

Kn = cost of sale of new common stock
D1 is the next dividend to be paid
Po is the current market price of shares outstanding
F is the flotation cost
G is the rate of growth
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3. Compute Cost of Common Equity

Example:
If additional shares are issued, floatation
costs will be 12% of price per share. D0 =
\$3.00 and estimated growth is 10%, Price is
\$60 as before. Flotation cost = \$60 x .12 =
\$7.20.
(Po – F = \$60.00 – 7.20 = \$52.80)
(D1 = 3.00 x 1.10 = 3.30)

3.30
kn =             + .10      = .0625 + .10 = 16.25%
52.80                              18
Weighted Average Cost of Capital
Gallagher Corporation estimates the following
costs for each component in its capital structure:

Source of Capital          Cost

Bonds (after tax)       kd = 6.0%
Preferred Stock         kp = 11.9%
Common Stock
Retained Earnings ks = 15.5%
New Shares        kn = 16.25%

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Gallagher’s tax rate is 40%
Weighted Average Cost of Capital
vIf using retained earnings (Internal Equity) to
finance the equity portion:

WACC = (WTd x AT kd ) + (WTp x kp ) + (WTs x ks)

WACC = weighted average cost of capital
WT = the weight, or percentage of each element of capital
(% of debt, preferred and common stock to total assets)
ATkd = after tax cost of debt
Kp = Cost of preferred stock
Ks = Cost of equity (Internal – retained earnings)
Weighted Average Cost of Capital

vIf using retained earnings (internal equity) to
finance the common equity portion :

WACC= ka= (WTd x AT kd ) + (WTp x kp ) + (WTs x
k s)

v Assume that Gallagher’s desired capital
structure is 40% debt, 10% preferred and
50% common equity.

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Weighted Average Cost of Capital
vIf using retained earnings (Internal Equity) to
finance the equity portion:

WACC = (WTd x AT kd ) + (WTp x kp ) + (WTs x ks)

v Assume that Gallagher’s desired capital
structure is 40% debt, 10% preferred and
50% common equity.
WACC =
Cost of Debt           .40 x 6.0% = 2.40%
+ Cost of Preferred .10 x 11.9% = 1.19%
+ Cost of Int. Equity .50 x 15.5% = 7.75%
1.00          = 11.34%
Weighted Average Cost of Capital
vIf using new common stock (External Equity) to
finance the common stock portion:

WACC = (WTd x AT kd ) + (WTp x kp ) + (WTs x ks)

Then we must use the cost of stock
WACC =
Cost of Debt       .40 x 6.0%   = 2.40%
+ Cost of Pref     .10 x 11.9% = 1.19%
+ Cost of Ext. Eq. .50 x 16.25% = 8.13%
= 11.72%
Marginal Cost of Capital
n   Gallagher’s weighted average cost will
change if one component cost of capital
changes.
n   This may occur when a firm raises a
particularly large amount of capital such
that investors think that the firm is riskier.
n   The WACC of the next dollar of capital
raised is called the marginal cost of capital.

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Spending Capital Money
n   The assumption is that the capital
money is spent in direct proportion to
the optimal capital structure.
n   So, if we spend \$100,000, it would be in
the following proportions:
Capital Structure             Spend
Debt          40%             40,000
Preferred     10%             10,000
Common        50%             50,000
(Buckets)     Total          100,000
Calculating the Breakpoint
n   Assume now that Gallagher Corporation has
\$100,000 in retained earnings with which to
finance its capital budget.
n   We can calculate the point at which they will
need to issue new equity since we know that
Gallagher’s desired capital structure calls for
50% common equity.

Breakpoint = Available Retained Earnings
Equity Percentage of Total
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Calculating the Breakpoint
Breakpoint = (\$100,000)/.5 = \$200,000
n   What this means is that once we spend
\$200,000 in total on capital projects, we
will have used up our retained earnings
of \$100,000 (internal equity).
n   Therefore, if we spend over \$200,000, we
will need additional financing from the
issue of new shares of stock since 50% of
our spending must come from Equity.
n   The cost of issuing new shares is greater
than internal equity due to flotation costs
Making Decisions Using
MCC
Marginal weighted cost of capital curve:
Weighted Cost of Capital

13%

11.72%
12%
11.34%
11%
Using new
Using new
10%
Using internal
Using internal         common equity
common equity
common equity
common equity
0         100,000     200,000     300,000    400,000
Total Financing

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Making Decisions Using
MCC
n          Graph IRRs of potential projects

Marginal weighted cost of capital curve:
Weighted Cost of Capital

12%

11%       Project 1
IRR =        Project 2        Project 3
10%       12.4%        IRR =            IRR =
12.1%            11.5%
9%

0          100,000     200,000     300,000    400,000
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Total Financing
Making Decisions Using
MCC
n                       Graph IRRs of potential projects
Graph MCC Curve
Marginal weighted cost of capital curve:
11.72%
Weighted Cost of Capital

12%
11.34%
11%       Project 1
IRR =        Project 2        Project 3
10%       12.4%        IRR =            IRR =
12.1%            11.5%
9%

0          100,000     200,000     300,000    400,000
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Total Financing
Making Decisions Using MCC
n      Graph IRRs of potential projects
n      Graph MCC Curve
v           Choose projects whose IRR is above the weighted
marginal cost of capital
Marginal weighted cost of capital curve:
11.72%
Weighted Cost of Capital

12%
11.34%
11%       Project 1
IRR =        Project 2        Project 3
10%       12.4%        IRR =            IRR =
12.1%            11.5%
9%        Accept Projects #1 & #2
0          100,000     200,000     300,000    400,000
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Total Financing
MCC and Capital Budgeting
Decisons
n   See pages 250 – 256
n   Calculate the breakpoints
Calculate the new MCC’s
Plot MCC’s and Investment Projects
n   See Figures 9-5 and 9-6 for results
n   Do all the Self-test problems before
doing the homework

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