

Financial
Management MGT201
VU
Lesson
29
WEIGHTED
AVERAGE COST OF CAPITAL (WACC)
Learning
Objectives:
After
going through this lecture,
you would be able to have an
understanding of the following
topics
·
WACC
(Weighted Average Cost of
Capital)
In
this lecture, we are going
to talk about the very
important component of capital structure
which is
known
as weighted average cost of
capital (WACC).In previous
lecture, we have introduced some of
the
broad
concepts of capital structure. We discuss
about the company's ways to raise
capital. one of two
basic
ways is the equity and the other is
debt .The objective of the company is to
raise capital at the
lowest
possible cost .just as when
you go to the market you try
to buy things at the lowest possible
cost.
Similarly,
companies go looking for
money in financial markets
they try to raise funds at
the lowest
possible
cost. This means that
when the company raises money in the
stock market issues that it
try to
sell
its shares at the price at
which it can earn maximum
profit .Similarly, when a company go to
the
money
market to take loan it tries
to get the loan at the lowest possible rate of
interest .
We
mentioned that weighted
average cost of capital
concept is similar to concept of the
required
rate
of return which we have discussed
earlier lectures. It is also known as
opportunity cost and by
opportunity
cost we mean "the rate of
return that investors sacrifices by
investing in the present
investment".
So, the rate of return that he
can get from the second best
of investment is the opportunity
cost
or ROR. We used the required rate of
return in our present value
formula .WACC is similar to
the
required
rate of return .There is only
slight difference between required rate
of return and
WACC.WACC
only takes into account the
practical aspects such as
impact of taxes and
transaction
costs
or flotation costs. .By
taxes we mean income tax or
corporate tax that the company needs to
pay
to
the govt. at the end of the year
depending upon their net
income and transaction associated with
the
issuing
selling and marketing of the financial
securities like stocks and bonds. When we
talk about
WACC,
we generally include three possible types of
capital.
WACC
= rDxD +
rExE + rPxP
Weighted
% Cost of Bond
(Debt):
rD XD :
Where
rD
is the
Average Rational Investors'
Required ROR for investing in the
Bond, XD
is
the
Weight or Fraction of Total
Capital value raised from
Bonds = Bond Value / Total
Capital
Weighted
% Cost of Common
Equity:
rE XE :
Where
rD
is the
Average Rational Investors'
Required ROR for investing in Common
Share,
XD
is
Weight or Fraction of Total
Capital raised from Common
Equity. Note that rE
is
Not the WACC
and
Not the ROE (=NI / common stock)
Weighted
% Cost of Preferred Equity
rP XP:
Where
rP is the
Average Rational Investors'
Required ROR for investing in Preferred
Share, XP
is
Weight or Fraction of Total
Capital raised from Preferred
Equity
Weighted
Cost of Debt % = rD XD
Required
ROR for Debt
The
first term is the
rD which is the required rate
of return and the cost of
debt can be interpreted
as
the required rate of return.
You
will recall that when we
were talking about bond
pricing that we
also
spoke about the over all
return on a bond and that is
referred to as yield to maturity or
YTM.
YTM=
interest yield +capital gain
yield and it is
representative of over all cost of
debt in the form of
bond.
Cost
of Debt Capital = rD
Practically
speaking, Bonds are Issued (or
sold) in the Market at a Premium (above
Par Value) or
Discount
(below Par Value). And, the
Issuance of Bonds has Transaction
Costs. These transaction
costs
include Legal, Accounting,
and Marketing and Sales
fees. Both these are
factored into the
Market
Price
of the Bond used in PV Formula to
calculate the PreTax Cost of Debt
Capital = rD*.
So,
rather
than
using Market Price of Debt,
use the
Net
proceeds = Market Price Transaction
Costs
Finally,
Debt becomes less Costly
because Additional Interest
creates a new form of Tax
Saving
or
Tax Shield.
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Financial
Management MGT201
VU
After
Tax Cost of Debt = rD =
rD*
(1 
TC)
Where
TC is the Marginal Corporate Tax
Rate on the Net Income of the
Firm
Example:
Company
ABC issues a 2 Year Bond of
Par Value Rs 1000 and a
Coupon Rate of 10% pa
(and
annual
coupon payments). Company ABC pays an
Investment Bank Rs 50 per Bond to
structure and
market
the bond. They decide to sell the
Bond for Rs 950 (i.e. At a
Discount). At the end of the first
year,
Company ABC's Income
Statement shows the Coupon
Interest paid to Bondholders as an
expense.
Interest
represents a Tax Saving or
Shield. Based on the Net
Income and Industry Standard, the
Marginal
Corporate Tax Rate is 30% of
Net Income. Assuming that
the 2 Year Bond represents
the
ONLY
form of Capital, calculate the AfterTax
Weighted Average Cost of
Capital (WACC) %
for
Company
ABC.
Step
1:
Calculate
Required ROR using Bond
Pricing or PV Formula
PV
= 100/
(1+r*) +100/ (1+r*) 2
+1000/
(1+r*) 2
=
100/ (1+r*) + 1100/ (1+r*)
2
=
Net
Proceeds = NP = Market Price
Transaction Costs
=
950  50 = Rs 900
Solve
the Quadratic Equation for
PreTax Required ROR = r*
Using
the Quadratic Formula: r*
= 16% AND r =  5
%
Step
2:
Calculate
After Tax Cost of
Debt
rD =
rD* ( 1  TC ) = 0.16
( 1  0.30) = 0.16 (0.70) =
11
. 2 %
Step
3:
Calculate
Weighted Cost of Capital
(WACC)
WACC
= rD XD.
+ rP XP + rE XE .
=
rD XD + 0 +
0
=
11.2 (1) = 11.2
%
Weighted
Cost of Preferred Equity = rP XP
Required
ROR for Preferred
Equity
The
important thing to remember is
that we calculated the price by using the
Perpetuity Formula
for
Perpetual
Investment & Constant Div
PV
= Present Price = Po= DIV1 / r.
So,
r = DIV1 / Po. If you use the
Actual Observed Market Price
for Po then r = Required
ROR.
Cost
of Preferred Equity Capital =
rP
Practically
speaking, the process of Legally
Structuring, Printing, and Marketing
Preferred Share
Certificates
costs money in the form of
Flotation Costs (including
Brokerage and Underwriting
Fees).
These
Costs are factored directly
into the PV or Observed Market
Price.
PV
= Net Proceeds = Market Price 
Flotation Costs
Preferred
Stock Dividends are paid
out from Net Income
After taxes. So they are
not Tax Deductible
(unlike
Bond Interest
Payments).
Example:
Company
ABC wants to issue a Preferred
Stock of Face Value Rs 10.
The Board of Directors
has
agreed
to fix the Annual Dividend at Rs 2 per
share. The Lawyer's fee
and Stock Brokers'
Commissions
will cost Rs 1 per share.
The Preferred Share is floated at
Face Value. What is the Cost
of
Capital
to Company ABC for raising
money through Preferred
Stocks?
Use
Perpetuity
Formula to Compute the
Required
ROR
r
= DIV1/ Po = Rs 2 / Rs 10 = 20%
Minor
Change in Perpetuity
Formula to Compute the
Cost
of Preferred Equity Capital
Net
Proceeds = NP =PriceFlotation Costs
=101= Rs 9
r
= DIV1/ NP = Rs 2 / Rs 9 = 22%
Flotation
Costs ADD TO COST of Company Issuing
the Preferred Equity
Capital
Weighted
Cost of Common Equity =
rE XE.
Required
ROR for Common Equity
(or Shares): 2 Approaches
Dividend
Growth Model: Gordon Formula
(simplified PV Formula) for Perpetual
Investment &
Constant
Growth in Dividends
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Financial
Management MGT201
VU
r
= DIV1 / Po + g. If you use the Actual
Observed Market Price for Po
then r =
Required
ROR. Now 2 Approaches for proceeding to
calculate Cost of Capital:
CAPM
(SML Equation) Assuming
Efficient Markets
r
= rRF
+ Beta (rM
 rRF).
Advantage: does not rely on
Dividend Forecast
Cost
of Common Equity Capital =
rE
Most
complex cost of capital to
calculate
Required
ROR on Common Equity NEITHER observable
NOR certain unlike Bond
Coupon Interest &
Preferred
Dividends both of which are
fixed
Equity
Capital can be raised in 2
Ways and Required ROR and
Costs are different for
each: (1)
Retained
Earnings and (2) Issue of
New Common Stock. You can
use rE
for
New Stock or Retained
Earnings
(which is lower).
Common
Stock Dividends are paid
out from Net Income
AFTER TAXES. So they are
NOT Tax
Deductible
(unlike Bond Interest
Payments).
Example:
Company
ABC wants to issue more Common
Stock of Face Value Rs 10.
Next Year the
Dividend
is expected to be Rs 2 per share assuming a
Dividend Growth Rate of 10%
pa. The Lawyer's
fee
and Stock Brokers' Commissions
will cost Rs 1 per share.
Investors are confident
about Company
ABC
so the Common Share is floated at a
Market Price of Rs 16 (i.e. Premium of Rs
6).
If
the Capital Structure of Company ABC is
entirely Common Equity, then
what is the
Company's
WACC? Use 2 Approaches and Compare the
Results
Example
 Cost of Common Equity
Capital
Dividend
Growth Model
Step
1: Calculate Required ROR for Common
Stock using Gordon's Formula
(Perpetual Investment
and
Constant Growing Dividend):
Approach
I: Retained Earnings Approach (use
Market Price)
r
= (DIV1/Po) + g = 2/16 + 0.10
=0.125 +0.1 =0.225 =
22.5%
Approach
II: New Stock Issuance
Approach
Net
Proceeds = Flotation Price  Flotation
Costs = 16  1 = 15
r
=(DIV1/NP) + g = 2/15 + 0.10 =
0.133 + 0.1 =0.233 =
23.3%
Cheaper
for Company ABC to Raise
Equity Capital through Retained
Earnings than to incur costs
of
issuing
New Equity
Problem:
Which Cost to Pick?
Example
 Cost of Common Equity
Capital
CAPM
Model (SML) Efficient
Market
Given
some additional data: TBill ROR =
10% pa. Market ROR = 20%.
Beta for ABC Common
Stock
= 1.25
r
= rRF + Beta (rM
 rRF) =
10% + 1.25
(20%10%)
=
10% + 12.5% =
22.5%
Same
answer as Retained Earnings Approach in
Dividends Growth Model.
Advantage: Don't need
to
forecast
dividends in CAPM
Approach.
CAPM
matches Dividends Model if No
Flotation / Transaction Costs and
Market is Efficient
Required
ROR (or Opportunity Cost) %
CAPM
Theory (SML for Efficient
Markets) & NPV
Minimum
ROR required to attract investor into
buying a Security
(i.e.
Stock or Bond ...)
Opportunity
Cost:
Investor Sacrifices the ROR available
from the 2nd best
investment.
Cost
of Capital %
Weighted
Average Cost of Capital
(WACC)
Combined
costs of all sources of
financing used by Firm
(i.e.
Debt and Equity)
Similar
to Required ROR BUT Takes
into account some Practical
Factors:
TAXES:
Interest
Payments are P/L Expenses
and NOT Taxed.
TRANSACTION
COSTS:
Brokerage,
Underwriting, Legal, and Flotation
Costs incurred when a
Firm
issues
Stocks or Bond Securities
126
Financial
Management MGT201
VU
Summary
of Formulas
Total
risk=
market risk
+
company specific risk
σ
2
+
β 2σ
2
+
σ 2
NPV
Bond Pricing
Equation:
Bond
Price = PV = C1/ (1+rD) + C2
(1+rD) 2
+ C3 /
(1+rD) 3
+..... + PAR /
(1+rD) 3
Gordon's
Formula for Share
Pricing:
rCE
= (DIV 1 / Po) + g
= Dividend Yield + Capital
Gains Yield
SML
Equation (CAPM
Theory)
r
= rRF + Beta (rM
 rRF)
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