Download CHAPTER 9 The Cost of Capital

CHAPTER 10
The Cost of Capital




Sources of capital
Component costs
WACC
Adjusting for flotation costs
10-1
What sources of long-term
capital do firms use?
Long-Term Capital
Long-Term Debt
Preferred Stock
Common Stock
Retained Earnings
New Common Stock
10-2
Calculating the weighted
average cost of capital
WACC = wdrd(1-T) + wprp + wcrs


The w’s refer to the firm’s capital
structure weights.
The r’s refer to the cost of each
component.
10-3
The Weighted Average Cost of
Capital
WACC = wdrd(1-T) + wprp + wcrs

Capital Structure Weights
The weights in the above equation are intended to
represent a specific financing mix (where wi = % of
debt, wp = % of preferred, and ws= % of common).
Specifically, these weights are the target percentages
of debt and equity that will minimize the firm’s overall
cost of Using or raising new funds.
10-4
Firm Capital Structure Weight


Assume the capital structure weight of
the firm is 30% debt, 10% preferred
stock and 60% equity
WACC = 0.3rdd(1-T) + 0.1rp + 0.6rs
10-5
Component cost of debt
WACC = wdrd(1-T) + wprp + wcrs


rd is the cost of debt capital.
The yield to maturity on outstanding
L-T debt is often used as a measure
of rd.
10-6
Borrowing firm
Cost of debt (rd)
Coupon interest
=
Yield to maturity
Par value
“Tax deductible”
- Partially subsidized
rd (1-T)
10-7
A 15-year, 12% semiannual coupon
bond sells for $1,153.72. What is
the cost of debt (rd)?
INPUTS
OUTPUT

30
N
I/YR
-1153.72
60
1000
5
PV
PMT
FV
The bond pays a semiannual coupon, so
rd = 5.0% x 2 = 10%.
10-8
Component cost of debt




Why tax-adjust, i.e. why rd(1-T)?
WACC = wdrd(1-T) + wprp + wcrs
Interest is tax deductible
Assume Corp tax is 40%
Interest is tax deductible, so
A-T rd = B-T rd (1-T)
= 10% (1 - 0.40) = 6%
10-9
Borrowing firm
Cost of debt (rd)=6%
Coupon interest
=
Yield to maturity = 10%
Par value
“Tax deductible”
- Partially subsidized
rd (1-T)
= 10% (1 - 0.40) = 6%
10-10
Component cost of preferred stock
WACC = wdrd(1-T) + wprp + wcrs


rp is the cost of preferred stock, which
is the return investors require on a
firm’s preferred stock.
Preferred dividends are not taxdeductible, so no tax adjustments
necessary. Just use nominal rp.
10-11
What is the cost of preferred stock?

The cost of preferred stock can be
solved by using this formula:
rp = Dp / Pp
= $10 / $111.10
= 9%
10-12
Is preferred stock more or less risky
to borrowing firm?


More risky; although the firm has the option
not to pay preferred dividend under certain
circumstances.
However, under company law, if preferred
dividend is not paid (1) firm cannot pay
common dividend, & (2) difficult to raise
additional external funds.
10-13
Component cost of equity
WACC = wdrd(1-T) + wprp + wcrs

rs is the cost of common equity using
retained earnings.
10-14
Why is there a cost for
retained earnings?



Earnings can be reinvested or paid out as
dividends.
Investors could buy other securities, earn a
higher return.
If earnings are retained, there is an
opportunity cost (the return that
stockholders could earn on alternative
investments).
10-15
To determine the cost of
common equity, rs

CAPM: rs = rRF + (rM – rRF) b
10-16
If the rRF = 7%, rM = 13%, and the firm’s
beta is 1.2, what’s the cost of common
equity based upon the CAPM?
rs = rRF + (rM – rRF) b
= 7.0% + (6.0%)1.2
= 14.2% ~14%
10-17
Cost of issuing new common
stock?

When a company issues new common
stock they also have to pay flotation
costs to the underwriter.
10-18
Cost of issuing new common
stock
WACC = wdrd(1-T) + wprp + wcre

re is the cost of common equity of
issuing new common stock
10-19
If issuing new common stock incurs a
flotation cost of 15% of the proceeds,
what is re?
D 0 (1  g)
re 
g
P0 (1 - F)
Flotation
cost
factor
≈
D 0 (1  g)
g
P0
$4.19(1.05 )

 5.0%
$50(1 - 0.15)
$4.3995

 5.0%
$42.50
 15.4%
10-20
Flotation costs


Flotation costs are highest for common
equity. However, since most firms
issue equity infrequently,
We will frequently ignore flotation costs
when calculating the WACC.
10-21
Ignoring flotation costs,
what is the firm’s WACC?
WACC =
=
=
=
wdrd(1-T) + wprp + wcrs
0.3(10%)(0.6) + 0.1(9%) + 0.6(14%)
1.8% + 0.9% + 8.4%
11.1%
10-22
The Marginal Cost
& Investment Decisions

The Weighted Marginal Cost of Capital
(WMCC)
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
The WACC typically increases as the volume of
new capital raised within a given period increases.
This is true because companies need to raise the
return to investors in order to entice them to
invest more in the company ( ie. to compensate
them for the increased risk introduced by larger
volumes of capital raised.
10-23
The Marginal Cost
& Investment Decisions
WMCC
11.76%
11.75%
11.66%
11.50%
11.25%
11.13%
$2.5
$4.0
Total Financing
(millions)
10-24
The Marginal Cost
& Investment Decisions

The Weighted Marginal Cost of Capital
(WMCC)

In addition, the cost will eventually increase when
the firm runs out of cheaper retained equity and is
forced to raise new, more expensive equity
capital.
10-25
The Weighted Average Cost of
Capital
WACC = ka = wiki + wpkp + wskr or n

Capital Structure Weights
For example, assume the market value of the firm’s debt is $40
million, the market value of the firm’s preferred stock is $10
million, and the market value of the firm’s equity is $50 million.
Dividing each component by the total of $100 million gives us
market value weights of 40% debt, 10% preferred, and 50%
common.
10-26
The Marginal Cost
& Investment Decisions (cont.)

The Weighted Marginal Cost of Capital (WMCC)
 Finding Break Points
Finding the break points in the WMCC schedule will allow us
to determine at what level of new financing the WACC will
increase due to the factors listed above.
BPj = AFj/wj
where:
BPj = breaking point form financing source j
AFj = amount of funds available at a given cost
wj
= target capital structure weight for source j
10-27
The Marginal Cost
& Investment Decisions (cont.)

The Weighted Marginal Cost of Capital
(WMCC)
Finding
Break
Assume that
the firm
has $2Points
million of retained earnings
available. When it is exhausted, the firm must issue new (more
expensive) equity. Furthermore, the company believes it can
raise $1 million of cheap debt after which it will cost 7% (after-tax)
to raise additional debt.
Given this information, the firm can determine its break points as
follows:
10-28
The Marginal Cost
& Investment Decisions (cont.)

The Weighted Marginal Cost of Capital
(WMCC)
 Finding Break Points
BPequity
= $2,000,000/.50 = $4,000,000
BPdebt
= $1,000,000/.40 = $2,500,000
This implies that the firm can fund up to $4 million of new
investment before it is forced to issue new equity and $2.5 million
of new investment before it is forced to raise more expensive debt.
Given this information, we may calculate the WMCC as follows:
10-29
The Marginal Cost
& Investment Decisions (cont.)
WACC for Ranges of Total New Financing
Range of total
Source of
New Financing
Capital
$0 to $2.5 million
$2.5 to $4.0 million
over $4.0 million
Weighted
Weight
Cost
Cost
Debt
40%
5.67%
2.268%
Preferred
10%
9.62%
0.962%
Common
50%
15.80%
7.900%
WACC
11.130%
Debt
40%
7.00%
2.800%
Preferred
10%
9.62%
0.962%
Common
50%
15.80%
7.900%
WACC
11.662%
Debt
40%
7.00%
2.800%
Preferred
10%
9.62%
0.962%
Common
50%
16.00%
8.000%
WACC
11.762%
10-30
The Marginal Cost
& Investment Decisions (cont.)
WMCC
11.76%
11.75%
11.66%
New Equity was
issued
11.50%
New Debt was
issued
11.25%
11.13%
$2.5
$4.0
Total Financing
(millions)
10-31