Blank L., Tarquin A. Engineering Economy (McGraw-Hill Series in Industrial Engineering and Management)
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SECTlON
10.3
Debt-Equity Mix and Weighted Average Cost
of
Capital
Mo
st projects are funded with a combination
of
debt and equity capital made
available specifically for the project or taken from a corporate
pool
of
capital.
The weight
ed
average cost
of
capital (WACC)
of
the pool is estimated by the rel-
ative fractions from debt and equity sources.
If
known exactly, these fractions are
used to estimate WACC; otherwise the historical fractions for each source are
used
in
the relation
WACC = (equity fraction)(cost
of
equity capital)
+ (debt fraction)(cost
of
debt capital)
[10.1]
The two cost terms are expressed as percentage interest rates.
Since virtually all corporations have a mixture
of
capital sources, the WACC
is a value between the debt and equity costs
of
capital. If the fraction
of
each type
of
equity
fin
ancing
-common
stock, preferred stock, and retained earnings-
is
known, Equation [10.
1]
is expanded.
WACC
= (common stock fraction) (cost
of
common stock capital)
+ (preferred stock fraction) (cost
of
preferred stock capital)
+ (retained earnings fraction) (cost
of
retained earnings capital)
+ (debt fraction)(cost
of
debt capital) [10.2]
Figure 10
-2
indicates the usual shape
of
cost
of
capital curve
s.
If
100%
of
the
capital
is
derived from equity or 100% is from debt sources, the WACC equals
the cost
of
capital
of
that source
of
funds. There is virtually always a mixture
of
capital sources involved for any capitalization program. As an illustration only,
Figure
10
-2
indicates a minimum WACC at about 45% debt capital. Most firms
operate over a range
of
D-E mixe
s.
For example, a range
of
30% to 50% debt
"-
o
'"
o
U
o
I
ormal I
opera
ting_:
ran
ge :
I
I
I
45%
I
I
I
I
~
I
I
I
Minimum
WACC
Percent debt cap
it
al (D-E
mi
x)
100
%
Figure
10-2
General shape
of
dif
fe
rent
cost
of
capital curves.
355
356
CHAPTER
10
Making Choices: The Method, MARR, and Multiple Attributes
financing for some companies may be very acceptable to lenders, with no increases
in risk or MARR. However, another company may be considered
"risky" with
only
20% debt capital. It takes knowledge about management ability, current pro-
ject
s,
a
nd
the economic health
of
the specific industry to determine a reasonable
operating range
of
the D-E mix for a particular company.
A new program
in
genetics engineering at Gentex will require $10 milljon
in
capital.
The chief financial officer (CFO) has estimated the following amounts
of
financing at
the indicated interest rates:
Common stock sales
Use
of
reta
in
ed earnings
Debt financing through bonds
$5
million at 13.7%
$2 million at 8.9%
$3 million at 7.5%
Historically, Gentex has financed projects using a D-E mix
of
40% from debt sources
costing 7.5%, and
60% from equity sources costing 10.0%. Compare the historical
WACC value with that for
trus current genetics program.
Solution
Equation [10.1]
is
used to estimate the historical WACC.
WACC = 0.6(10) + 0.4(7.5) = 9.0%
For the current program, the equity financing
is
comprised
of
50% common stock
($5
million out
of
$10 million) and 20% retained earnings, with the remaining 30%
from debt sources. The program WACC by Equation [10.
2]
is
rugher than the historical
average
of
9
%.
WACC = stock portion + retruned earnings portion + debt portion
= 0.5(13.7) + 0.2(8.9) + 0.3(7.5) = 10.88%
The WACC value can be computed using before-tax or after-tax values for
cost
of
capital. The after-tax method is the correct one since debt financing has a
distinct tax advantage, as discussed in the next section. Approximations
of
after-
tax or before-tax cost
of
capital are made using the effective tax rate Te
in
the
relation
After-tax cost
of
debt = (before-tax cost)
(1
-
TJ
[10.3]
The effective tax rate
is
a combination
of
federal, state, and local tax rates. They
are reduced to a single number
Te to simplify computations. Equation [10.3]
may be used to approximate the cost
of
debt capital separately
or
in
serted into
Equation
[J
0.1] for
an
after-tax WACC rate. Chapter 17 treats taxes and after-tax
economic analysis
in
detail.
SECTION lOA Determination
of
the Cost
of
Debt Capital
10.4
DETERMINATION OF THE COST OF DEBT CAPITAL
Debt financing includes borrowing, primarily via bonds and loans. In the
United States, bond interest and loan interest payments are tax-deductible
as
a
corporate expense. This reduces the taxable income base upon which taxes are
calculated, with the end result
of
less taxes paid. The cost
of
debt capital is,
therefore, reduced because there is an annual
tax savings
of
the expense cash
flow times the effective tax rate
Te'
This tax savings is subtracted from the debt-
capital expense cash flow in order
to
calculate the cost
of
debt capital. In for-
mula form,
Tax savings
= (expenses)(effective
tax
rate)
= expenses
(T
e) [10.4]
Net
cash flow = expenses -
tax
savings = expenses
(1
- Te) [10.5]
To
find the cost
of
debt capital, develop a
PW
or AW-based relation
of
the net
cash flow (NCF) series with
i*
as the unknown. Find
i*
by hand through trial
and error, or
by
the RATE or IRR functions on a computer spreadsheet. This
is the cost
of
debt capital percentage used in the WACC computation in Equa-
tion [10.1].
EXAMPLE
10.4
t"
AT&T will generate $5 million in debt capital by issuing five thousand $1000 8% per year
10-year bonds.
If
the effective tax rate
of
the company is 50% and the bonds are discounted
2% for quick sale, compute the cost
of
debt capital (a) before taxes and (b) after taxes from
the company perspective. Obtain the answers by hand and by computer.
Solution by Hand
(a) The annual bond dividend
is
$1000(0.08) = $80, and the 2% discounted sales price
is
$980 now. Using the company perspective, find the
i*
in the PW relation
0 = 980 - 80(P/A,i*.10) - 1000(P/F,i*,10)
i*
= 8.3%
The before-tax cost of debt capital is
i*
= 8.3%, which is slightly higher than the
8% bond interest rate, because
of
the 2% sales discount.
(b) With the allowance to reduce taxes by deducting the bond interest, Equation [lOA]
shows a tax savings
of
$80(0.5) = $40 per year. The bond dividend amount for the
PW relation is now $80 - $40 = $40. Solving for
i*
after taxes reduces the cost
of
debt capital by nearly one-half, to 4.25%.
Solution
by
Computer
Figure 10- 3
is
a spreadsheet image for both before-tax (column B) and after-tax (col-
umn C) analysis using the IRR function. The after-tax net cash flow is calculated using
Equation [10.
5]
with Te = 0.5. See the cell tag.
3
57
Q-Solv
358
CHAPT
ER
10
Making Choices: The Method, MARR, and Multiple Attributes
X Microsoft Excel - Example
10
.4 0
iii
Ready
GIS
B
Bond face value
Before tax
$ 1,000 cash flow
Year
0
$
1 $
1
~-
A2'008
~
5 $
6 $
7 $
8 $
9 $
10 $
980 $
(80) $
(80) $
(80) $
(80) $
(80) $
(80)$
(80) $
(80) $
(80) $
(1,080) $
8.30%
c
After tax
cash flow
980
(40)
(40
~
(40) ' =-$-B$-4-*(-1 -- 0-
.5
') I
(40)
(40)
(40)
(40)
(40)
(40)
(1,040)
= IRR(C3:CI3)
Sh~et6
Sheet7
.
.
~
Fi
gure
10-3
Use
of
the
fRR
fu
nction to determine before-tax a
nd
after-tax cost
of
debt cap
it
a
l.
Example J 0.4.
EXAMPLE
10.5
The Hershey Company will purchase a $20,000 10-year-life asset. Company managers
have decided to put
$10,000 down now and borrow $10,000 at
an
interest rate
of
6
%.
The simplified loan repayment plan is $600
in
interest each year, with the entire
$10,000 principal paid
in
year 10. What
is
the after-tax cost
of
debt capital if the effec-
tive tax rate is 42%?
Solution
The after-tax net cash flow for interest on the $10,000 loan is
an
annual amount
of
600(1 - 0.42) = $348 by Equation [10.5]. The loan repayment
is
$10,000
in
year
10.
PW is used to estimate a cost
of
debt capital
of
3.48%.
0 = 10,000 - 348(P/A,i
*,
10) -
1O
,000(P
/F,
i
*,
1O
)
SECTION
lO.5
Determination
of
the Cost
of
Equity Capital and the MARR
Comment
Note that the 6% annual interest on the $10,000 loan
is
not the WACC because 6%
is
paid only on the borrowed funds. Nor
is
3.48% the WACC, since it is only the cost of
debt capital.
10.5
DETERMINATION
OF
THE COST OF EQUITY
CAPITAL
AND
THE MARR
Equity capital
is
usually obtained from the following sources:
Sale
of
preferred stock
Sale
of
common stock
Use
of
retained earnings
L
The cost
of
each type
of
financing is estimated separately and entered into the
WACC computation. A summary
of
one commonly accepted way to estimate
each source's cost
of
capital is presented here. There are additional methods for
estimating the cost
of
equity capital via common stock. There are no tax savings
for
equity capital, because dividends paid to stockholders are not tax-deductible.
Issuance
of
preferred stock carries with it a commitment to pay a stated divi-
dend annually. The cost
of
capital is the stated dividend percentage, for example,
10%, or the dividend amount divided by the price
of
the stock. A $20 dividend
paid on a
$200 share is a 10% cost
of
equity capital. Preferred stock may be sold
at a discount to speed the sale, in which case the actual proceeds from the stock
should be used as the denominator. For example,
if
a 10% dividend preferred
stock with a value
of
$200 is sold at a 5% discount for $190 per share, there is a
cost
of
equity capital
of
($20/ $190) x 100% = 10.53%.
Estimating the cost
of
equity capital for common stock is more involved. The
dividends paid are not a true indication
of
what the stock issue will actually cost
in the future. UsuaJly a valuation
of
the common stock is used to estimate the
cost.
If
Re is the cost
of
equity capital (in decimal form),
R = first-year dividend + expected dividend growth rate
e price
of
stock
DV,
Re =
----p-
+ g
[10.6]
The growth rate g
is
an estimate
of
the annual increase in returns that the share-
holders receive. Stated another way, it
is
the compound growth rate on dividends
that the company believes is required to attract stockholders. For example, as-
sume a multinational corporation plans to raise capital through its U.S. sub-
sidiary for a new plant in South America by selling
$2,500,000 worth
of
common
stock valued at
$20 each.
If
a 5% or
$1
dividend is planned for the first year and
an appreciation
of
4% per year is anticipated for future dividends, the cost
of
cap-
ital for this common stock issue from Equation [10.6] is 9%.
I
Re = 20 + 0.04 = 0.09
359
360
Safe investments
CHAPTER 10 Making Choices: The Method, MARR, and Multiple Attributes
The retained earnings cost
of
equity capital is usually set equal
to
the common
stock cost, since it is the shareholders who will realize any returns from projects
in
which retained earnings are invested.
Once the cost
of
capital for all planned equity sources is estimated, the WACC
is calculated using Equation [10.2].
A second method used to estimate the cost
of
common stock capital
is
the cap-
ital asset pricing model (CAPM). Because
of
the fluctuations in stock prices and
the higher return demanded by some corporations' stocks compared
to
others,
this valuation technique is commonly applied. The cost
of
equity capital from
common stock
Re' using CAPM, is
Re = risk-free
return
+ premium above risk-free
return
= R
f
+
peRm
- R
f
)
[10.7]
where
f3
= volatility
of
a company's stock relative to other stocks
in
the mar-
ket
(f3
= 1.0 is the norm)
Rill
= return on stocks in a defined market portfolio measured
by
a pre-
scribed index
The term
Rf
is
usually the quoted U.
S.
Treasury bill rate, since it
is
considered
a
"safe investment." The term
(Rm
- R
J
)
is the premium paid above the safe or
risk-free rate. The coefficient
f3
(beta) indicates how the stock is expected
to
vary
compared
to
a selected portfolio
of
stocks
in
the same general market area, often
the Standard and
Poor's 500 stock index.
If
f3
< 1.0, the stock is less volatile, so
the resulting premium can be smaller; when
f3
> 1.0, larger price movements are
expected, so the premium is increased.
Security
is
a word which identifies a stock, bond, or any other instrument
used
to
develop capital.
To
better understand how CAPM work
s,
consider
Figure 10-4. This is a plot
of
a market security line, which is a linear
fit
by
Figure
10-4
Exp
ec
ted return on
common stock issue
us
in
gC
APM
Market
Ril
l - - - - - - - - - - - - - - -
-
~
---.---
Premium
in
creases
for more
ri
s
ky
securities
Selected
market
portfolio
L-
__
_
____
~L-
___
~~
o
1.0
SECTION 10.5 Determination
of
the Cost
of
Equity Capital and the MARR
regression ana
ly
sis to indicate the expected return for different
f3
values.
When
f3
= 0, the risk-free return RJ
is
acceptable (no premium). As
f3
increases, the pre-
mium return requirement grows. Beta
values are published periodically for most
stock-issuing corporation
s.
Once complete, this estimated cost
of
common stock
equity
capital can be included
in
the WACC computation in Equation [10.2].
EXAMPLE 10.6
The
lead software engineer
at
SafeSoft, a food industry service corporation, has con-
vinced the president to develop new software technology for the meat and food safety
industry. It is envisioned that processes for prepared meats can be completed more
safe
ly
and faster using this automated control software. A common stock issue is a pos-
sibility
to
raise capital
if
the cost
of
equity capital is below
15
%.
SafeSoft, which has
a
hi
storical beta value
of
1.7, uses CAPM to determine the prem.ium
of
its stock com-
pared
to
other software corporations. The security market line indicates that a 5%
premium above the risk-free rate
is
desirable.
If
U.S. Treasury bills are paying 4%,
estimate the cost
of
common stock capital.
Solution
The premium
of
5% represents the term
Rill
- R
f
in
Equation [10.7].
Re = 4.0 + 1.7(5.0) = 12.5%
Since this cost
is
lower than
15
%, SafeSoft should issue common stock to finance this
new venture.
In theory, a correctly performed engineering economy study uses a
MARR
equal to the cost
of
the capital committed to the specific alternatives in the study.
Of
course, such detail
is
not known. For a combination
of
debt and equity capi-
tal, the calculated WACC sets the minimum
forthe
MARR.
The
most rational ap-
proach
is
to set MARR between the cost
of
equity capital and the corporation's
WACC.
The
risks associated with an alternative should be treated separately
from the
MARR
determination, as stated earlier. This supports the guideline that
the
MARR
should not be arbitrarily increased to account for the various types
of
ri
sk associated with the cash flow estimates. Unfortunately, the
MARR
is often
set above the WACC because management does want to account for risk by in-
creasing the MARR.
EXAMPLE 10.7 .
The Engineering Products Division
of
4M
Corporation has two mutually exclusive
alternatives A and B with
ROR values
of
ij. = 9.2% and
i~
= 5.9%.
The
financing
scenario is yet unsettled, but it will be one
of
the following: plan
I-u
se all equity
funds, which are currently earning 8% for the corporation; plan
2-use
funds from
the corporate capital pool which is 25% debt capital costing 14.5% and the remainder
from the same equity funds mentioned above.
The
cost
of
debt capital
is
currently high
because the compa
ny
has narrowly m.issed its projected revenue on common stock for
361
362
CHAPTER 10 Making Choices: The Method, MARR, and Multiple Attributes
the last two quarters, and banks have increased the borrowing rate for 4M. Make the
economic decision on alternative A versus B under each financing scenario.
Solution
The capital is available for one
of
the two mutually exclusive alternatives. For plan
1,
100% equity, the financing
is
specifically known, so the cost
of
equity capital is the
MARR
, that is, 8%. Only alternative A is acceptable; alternative B is not since the esti-
mated return
of
5.9% does not exceed this MARR.
Under financing plan
2,
with a D-E mix
of
25- 75,
WACC
= 0.25(14.5) + 0.75(8.0) = 9.625%
Now, neither alternative
is
acceptable since both ROR values are less than
MARR
=
WACC = 9.625%. The selected alternative should be to do nothing, unless one alternative
absolutely must be selected, in which case noneconomic attributes must be considered.
10.6
EFFECT OF DEBT-EQUITY
MIX
ON
INVESTMENT
RISK
The O-E mix was introduced in Section 10.3. As the proportion
of
debt capital in-
creases, the calculated cost
of
capital decreases due to the tax advantages
of
debt
capital. Howe
ver,
the leverage offered by larger debt capital percentages in-
creases the riskiness
of
projects undertaken by the company. When large debts
are already present, additional financing using debt (or equity) sources gets more
difficult to justify, and the corporation can be placed in a situation where it owns
a smaller and smaller portion
of
itself. This is sometimes referred to as a highly
leve
ra
ged corporation. Inability to obtain operating and investment capital means
increased difficulty for the company and its projects. Thus, a reasonable balance
between debt and equity financing is important for the financial health
of
a cor-
poration. Example 10.8 illustrates the disadvantages
of
unbalanced O-E mixes.
Three manufacturing companies have the following debt and equity capital amounts
and D-E mixes. Assume all equity capital is in the form
of
common stock.
Comp
any
A
B
C
Amount
of
Capi
tal
Debt
Equity
($ in millions) ($ in millions)
10
20
40
40
20
10
D-E
Mix
(%-%)
20- 80
50- 50
80-20
Assume the annual revenue is $15 million for each one and that, after interest on debt is
considered, the net incomes are $14.4, $13.4, and $10.0 million, respectively. Compute
the return on common stock for each company, and comment on the return relative
to
the D-E mixes.
SECTION
10
.6 Effect
of
Debt-Equity Mix on Inves
tm
ent
Ri
sk
So
lution
Divide the net income by the stock (equity) amount to compute the common stock
return. In
million dollars,
A:
Return =
14.4 =
0.36
40
(36%)
B:
13.4 6
Return =
--
=
O.
7
20
(67%)
C:
10.0 00
R
et
urn =
--
=
l.
10
(100%)
As
expected, the return
is
by far the largest for highly leveraged C, where only 20%
of
the company is
in
dle hands
of
the ownership.
The
return is excellent, but the
ri
sk asso-
ciated with this firm
is
high compared to A, where the
D-E
mix
is
only 20% debt.
The use
of
large percentages
of
debt financing greatly increases the risk taken
by
lenders and stock owners. Long-term confidence in the corporation dimin-
ishes, no matter how large
th
e short-term return on stock.
The
leverage
of
large O-E mixes does increase the return on equity capital, as
shown
in
previous examples; but it can also work against the owners and in-
vestors. A small percentage decrease
in
asset value will more negatively affect
a highly debt-leveraged investment compared to one with small leveraging.
Example 10.9 illustrates
thi
s fact.
EXAMPLE
10.9
~~
Two engineers place $
10
,000 each
in
different investments. MarylYlln invests $10,000
in
airline stock, and Carla leverages the $
10
,000 by purchasing a $100,000 residence to
be used as rental property. Compute the resulting value
of
the $
10
,000 equity capital if
there is a
S% decrease
in
the value
of
both the stock and the residence.
Do
the sa
me
for
a
S%
in
crease. Neglect any
di
vidend, income, or tax considerations.
Solution
The airline slock value decreases by 1O,000(0.OS) =
$SOO,
and the house value de-
creases by
J
OO,OOO(O.OS)
=
$SOOO.
The effect
is
that a smaller amount
of
the $10,000
is returned, if the investment must be sold immediately.
Marylynn
's
lo
ss:
Carla's loss:
~
=
O.OS
(S%)
JO
,
OOO
sooo
=
O.SO
(
SO
%)
10
,000
The
lO
-to- J leveraging by Carla gives her a
SO
% decrease in the equity position, while
Marylynn has only the
S% loss s
in
ce there is no leveraging.
363
364
Decision making
Figure
10-5
Expansion
of
the
decision-making process
to include mUltiple
attributes.
CHAPTER
10
Making Choices:
The
Method, MARR, and Multiple Attributes
The
opposite
is
correct for a
5%
increase; Carla would benefit
by
a 50% gain on her
$10,000, while Marylynn has only a
5%
gain.
The
larger leverage
is
more risky.
It
of-
fers a much higher return
jor
an increase in the value
of
the investment and a much
larger lossjor a decrease
in
the value
of
the investment.
The same principles as discussed above for corporations are applicable to indi-
viduals.
The
person who is highly leveraged has large debts in terms
of
credit card
balances, personal loans, and house mortgages. As an example, assume two
engi-
neers each have a take-home amount
of
$40,000 after all income tax, social security,
and insurance premiums are deducted from their annual salaries. Further, assume
that the cost
of
the debt (money borrowed via credit cards and loans) averages
15% per year and that the current debt principal is being repaid
in
equal amounts
over
20 years.
If
Jamal has a total debt
of
$25,000 and Barry owes $100,000, the
remaining amount
of
the annual take-home pay may be calculated as follows:
Total
Cost
of
Repayment
of
Debt
Amount
Remaining
Person
Debt,
$
Debt
at
15%,
$
over
20-Year Period, $
from
$40,000,
$
Jamal
Barry
25,000
100,000
3,750
15
,000
1,250
5,000
35,000
20,000
Jamal has 87.5%
of
his base available while Barry has only
50%
available.
10.7
MULTIPLE ATTRIBUTE ANALYSIS: IDENTIFICATION
AND
IMPORTANCE OF EACH ATTRIBUTE
In Chapter 1 the role and scope
of
engineering economy in decision making were
outlined.
The
decision-making process explained
in
that chapter included the
seven steps listed on the right side
of
Figure 10-5. Step 4 is to identify the one or
multiple attributes upon which the selection criteria are based. In all prior
evalu-
ations
in
this text, only one
attribute-the
economic
one-has
been identified
Consider multiple
attributes
4-1. Identify the attributes for decision
making.
4-2. Determine the relative
importance (weights)
of
attributes.
4-3.
For
each alternative, determine
each attribute's value rating.
5. Evaluate each alternative using a
multiple-attribute technique.
Use
sensitivity analysis for key
attributes.
Emphasis on one
attribute
I. Understand the problem; define the objective.
2. Collect rel
evant
information.
3. Define alternatives; make estimates.
4. Identify the selection
cr
iteria (one
or
more
attributes).
5. Evaluate each alternative; use sensitivity
analysis.
6.
Select the best alternative.
7. Implement the solution and monitor results.