Cost of Capital
Lecture No. 61
Chapter 15
Contemporary Engineering Economics
Copyright © 2006
Contemporary Engineering Economics, 4th
edition, © 2007
Cost of Capital (k)



Cost of Equity (ie) –
Opportunity cost associated
with using shareholders’
capital
Cost of Debt (id) – Cost
associated with borrowing
capital from creditors
Cost of Capital (k) –
Weighted average of ie and
id
Contemporary Engineering Economics, 4th
edition, © 2007
Cost of Debt
Cost of Equity
Cost of Equity (ie)




Cost of Retained
Earnings (kr)
Cost of issuing New
Common Stock(ke)
Cost of Preferred Stock
(kp)
Cost of equity:
weighted average of kr
ke, and kp
Contemporary Engineering Economics, 4th
edition, © 2007
Calculating the Cost of Equity based on
Financing Sources
ie  (cr / ce ) kr  (cc / ce ) ke
(c p / ce ) k p
Where Cr = amount of equity financed
from retained earnings,
Cc = amount of equity financed from
issuing new stock,
Cp = amount of equity financed from
issuing preferred stock, and
Ce = Cr + Cc + Cp
Contemporary Engineering Economics, 4th
edition, © 2007
Calculating the Cost of Equity
Cost of Retained Earnings
D1
kr 
g
P0
Issuing New Common Stock
D1
ke 
g
P0 (1  f c )
Cost of Preferred Stock
D*
kp 
P *(1  f c )
Cost of Equity
ie  (cr / ce ) kr  (cc / ce ) ke
(c p / ce ) k p
Where cr = amount of equity financed
from retained earnings,
cc = amount of equity financed from
issuing new stock,
cp = amount of equity financed from
issuing preferred stock, and
ce = cr + cc + cp
Contemporary Engineering Economics, 4th
edition, © 2007
Example 15.4 Determining the Cost of
Equity – Alpha Corporation
Source
Amount
Fraction of Total
Equity
Retained
earnings
$1 million
0.167
New common
stock
$4 million
0.666
Preferred
stock
$1 million
0.167
Contemporary Engineering Economics, 4th
edition, © 2007
Solution:
Cost of retained earnings: With D1= $5, g = 8%, and P0= $40
5
kr 
 0.08  20.5%
40
Cost of new common stock: With D1= $5, g = 8%, and fc= 12.4%
k e  [5 / 40(1  0124
. )]  0.08  22.27%
Cost of preferred stock: With D*= $9, P*= 95, and fc= 0.06
k p  9 / 95(1  0.06)  10.08%
Cost of equity:
ie  (0167
. )(0.205)  (0.666)(0.2227)  (0167
. )(01008
.
)
 19.96%
Contemporary Engineering Economics, 4th
edition, © 2007
Cost of Debt (id)
id  (cs / cd )ks (1  tm )  (cb / cd )kb (1  tm )
where cs  the amount of the term loan,
cb  the amount of bond financing,
ks  the before-tax interest rate on the term loan,
kb  the before-tax interest rate on the bond,
tm  the firm's marginal tax rate, and
cd  cs  cb
Contemporary Engineering Economics, 4th
edition, © 2007
Example 15.6 Determining the Cost of Debt

Given: Sources of debt financing, tax rate =
38%
Source

Amount
Fraction
Interest
Rate
Term loan
$1.33
million
0.333
12% per
year
Bonds
$2.67
million
0.667
10% per
year
Find: A/T cost of debt
Contemporary Engineering Economics, 4th
edition, © 2007
Flotation
Cost
6%
Solution

A/T Cost of Issuing Bond (kb):
$940  $100( P / A, kb ,20)  $1,000( P / F , kb ,20)
kb  10.74%

A/T Cost of Debt:
id  (0.333)(0.12)(1  0.38)  (0.667)(0.1074)(1  0.38)
 6.92%
Contemporary Engineering Economics, 4th
edition, © 2007
The Weighted A/T Cost of Capital
id cd ie ce
k

V
V
cd= Total debt capital(such as bonds) in dollars,
ce=Total equity capital in dollars,
V = cd+ ce,
ie= Average equity interest rate per period considering
all equity sources,
id = After-tax average borrowing interest rate per
period considering all debt sources, and
k = Tax-adjusted weighted-average cost of capital.
Contemporary Engineering Economics, 4th
edition, © 2007
Process of Calculating the Cost of Capital
Contemporary Engineering Economics, 4th
edition, © 2007
Marginal Cost of Capital
• Given: Cd = $4 million, Ce = $6 million, V= $10 millions,
id= 6.92%, ie=19.96%
• Find: k
0.0692(4) 01996
.
(6)
k

10
10
 14.74%
Comments: This 14.74% would be the marginal cost
of capital that a company with this financial structure
would expect to pay to raise $10 million.
Contemporary Engineering Economics, 4th
edition, © 2007
Summary
•
•
Methods of financing:
1. Equity financing uses retained earnings or
funds raised from an issuance of stock to
finance a capital investment.
2. Debt financing uses money raised through
loans or by an issuance of bonds to finance a
capital investment.
Companies do not simply borrow all funds to
finance projects. Well-managed firms usually
establish a target capital structure and strive to
maintain the debt ratio when individual projects
are financed.
Contemporary Engineering Economics, 4th
edition, © 2007

The cost of the capital formula is a composite
index reflecting the cost of funds raised from
different sources. The formula is
id cd ie ce
k

,
V
V

where V  cd  ce
The marginal cost of capital is defined as the cost
of obtaining another dollar of new capital. The
marginal cost rises as more and more capital is
raised during a given period.
Contemporary Engineering Economics, 4th
edition, © 2007