contemporary engineering economics, 4 th edition, © 2007 cost of capital lecture no. 61 chapter 15...

Contemporary Engineering Economics, 4th edition, © 2007

Cost of Capital

Lecture No. 61Chapter 15Contemporary Engineering EconomicsCopyright © 2006


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

Cost of Equity

Cost of Debt

Cos

t of

Cap

ital


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


i c c k c c k

c c ke r e r c e e

p e 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

Calculating the Cost of Equity based on Financing Sources


Calculating the Cost of Equity

Issuing New Common Stock

kD

P fge

c

1

0 1( )

Cost of Preferred Stock

kD

P fpc

*

*( )1

Cost of Equity

i c c k c c k

c c ke r e r c e e

p e p

( / ) ( / )

( / )

kD

Pgr 1

0

Cost of Retained Earnings

Where cr = amount of equity financed from retained earnings,cc = amount of equity financed from issuing new stock,cp = amount of equity financed fromissuing preferred stock, andce = cr + cc + cp


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


Cost of retained earnings: With D1= $5, g = 8%, and P0= $40

Cost of new common stock: With D1= $5, g = 8%, and fc= 12.4%

Cost of preferred stock: With D*= $9, P*= 95, and fc= 0.06

kr 5

400 08 205%. .

ke [ / ( . )] . .5 40 1 0124 0 08 22 27%

kp 9 95 1 0 06 10 08%/ ( . ) .

Cost of equity:

ie

( . )( . ) ( . )( . ) ( . )( . )

.

0167 0 205 0 666 0 2227 0167 01008

19 96%

Solution:


Cost of Debt (id)

( / ) (1 ) ( / ) (1 )d s d s m b d b mi c c k t c c k t

where the amount of the term loan,

the amount of bond financing,

the before-tax interest rate on the term loan,

the before-tax interest rate on the bond,

the firm's marginal tax rate,

s

b

s

b

m

c

c

k

k

t

and

d s bc c c


Example 15.6 Determining the Cost of Debt

Given: Sources of debt financing, tax rate = 38%

Find: A/T cost of debt

Source Amount Fraction Interest

Rate

Flotation

Cost

Term loan $1.33 million

0.333 12% per year

Bonds $2.67 million

0.667 10% per year

6%


Solution

A/T Cost of Issuing Bond (kb):

A/T Cost of Debt:

$940 $100( / , , 20) $1,000( / , , 20)

10.74%b b

b

P A k P F k

k

(0.333)(0.12)(1 0.38) (0.667)(0.1074)(1 0.38)

6.92%di


The Weighted A/T Cost of Capital

d d e ei c i ck

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, andk = Tax-adjusted weighted-average cost of capital.


Process of Calculating the Cost of Capital


Marginal Cost of Capital

• Given: Cd = $4 million, Ce = $6 million, V= $10 millions, id= 6.92%, ie=19.96%• Find: k

k

0 0692 4

10

01996 6

1014 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.


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.


The cost of the capital formula is a composite index reflecting the cost of funds raised from different sources. The formula is

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.

, where d d e ed e

i c i ck V c c

V V

contemporary engineering economics, 4 th edition, © 2007 cost of capital lecture no. 61 chapter 15...

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