Lec8.Cost of Capital

8/13/2019 Lec8.Cost of Capital

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Liabilities Assets

Current Liabilities Current assets

Long-term debt Fixed assets

Preference Capital

Equity Capital

Retained Earnings

BALANCE SHEET


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Liabilities & Equity Assets


Long-term debt Fixed assets

Preference Capital

Equity Capital

Retained Earnings

The financing decision

The Investment Decision


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Liabilities & Equity Assets


Long-term debt

Preferred Stock

Common Equity

Capital Structure

}


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For Investorsthe rate of return on a

security is a benefit of investing.

For the Companythat same rate of

return is a cost of raising funds that

are needed to operate the firm.

In other words, the cost of raising

funds is the firms cost of capital.


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How can the firm raise capital?

Debt Preference Capital

Equity Capital

Each of these offers a rate of returntoinvestors

This return is a costto the firm

Cost of capital actually refers to theweighted cost of capital - a weightedaverage cost of financing sources


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Cost of capital can be defined as the

minimum rate of return that the

firm must earn on its investment forthe market value of the firm to

remain unchanged.


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Cost of

Debt


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Cost of Debt

For the issuing firm, the cost of debtis:

the rate of returnrequired by

investors adjusted for flotation costs(any costs

associated with issuing new bonds),

and

adjusted for taxes


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Example: Tax effects of financing

with debt

with stock with debt

EBIT 400,000 400,000

- interest expense 0 (50,000)

EBT 400,000 350,000

- taxes (34%) (136,000) (119,000)

EAT 264,000 231,000


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Example: Tax effects of

financing with debt


EBIT 400,000 400,000

- interest expense 0 (50,000)EBT 400,000 350,000

- taxes (34%) (136,000) (119,000)

EAT 264,000 231,000

Now, suppose the firm pays $50,000 in dividends

to the stockholders


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Example: Tax effects of

financing with debt


EBIT 400,000 400,000

- interest expense 0 (50,000)EBT 400,000 350,000

- taxes (34%) (136,000) (119,000)

EAT 264,000 231,000- dividends (50,000) 0

Retained earnings 214,000 231,000


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After-tax cost Before-tax cost Tax

of Debt of Debt Savings-=


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of Debt of Debt Savings

33,000 = 50,000 - 17,000

-=


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33,000 = 50,000 - 17,000

OR

-=


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33,000 = 50,000 - 17,000

OR33,000 = 50,000 ( 1 - .34)

-=


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33,000 = 50,000 - 17,000

OR

33,000 = 50,000 ( 1 - .34)

Or, if we want to look at percentage costs:

-=


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After-tax Before-tax

% cost of % cost of x tax

Debt Debt rate

-= 1


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After-tax Before-tax

% cost of % cost of x tax

Debt Debt rate

Kd = k

d(1 - T)

-= 1


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After-tax before-tax

% cost of % cost of x taxdebt debt rate

Kd = kd (1 - T)

= .10 (1 - .34)

= .066

-= 1


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Cost of debt is the discount rate that equates

the present value of post-tax interest and

principle repayments with the net proceeds

of the debt issue

n

d

n

tt

d )k(F

)k(T)C(P

111

1


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For Perpetual Debt - Cost of Debt

P

TC

kd)1(


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A company has 15%perpetual debt of Rs

1,00,000. The tax rate is 35%.Determine

the cost of capital (before tax & after tax)assuming the debt is issued at :

A at par

B at 10% discount C at 10% premium

Problem


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At par:

Before Tax cost: 15000/100000 = 15%

After Tax cost: 0.15*(1-0.35) = 9.75%

At discount:

Before Tax cost: 15000/90000 = 16.7%After Tax cost: 0.167*(1-0.35) = 10.85%

At premium:Before Tax cost: 15000/110000 = 13.6%

After Tax cost: 0.136*(1-0.35) = 8.84%

E l C t f D bt


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Example: Cost of Debt

Prescott Corporation issues a $1,000par, 20 yearbond paying the market

rate of 10%. Coupons (interest) are

annual. The bond will sell at par, butflotation costs amount to $50per bond.

The tax rate is 34%.

What is the pre-tax and after-tax cost of

debt for Prescott Corporation?


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Pre-tax cost of debt:

950 = 100(PVIFA 20, kd) + 1000(PVIF 20, kd)

kd= 10.61%

After-tax cost of debt:

Kd = kd (1 - T)

Kd = .1061 (1 - .34)

Kd = .07 = 7%


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2

)(

)()1(

PFn

PFTC

kd

Approximation for after tax cost of debt


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Problem

Vikas limited issues 14% debentures,

Face value Rs.100. The net amount

realized per debenture is Rs.94. Thedebentures are redeemable at par after

10 years. The firm pays 50% tax on its

income. What is the cost of debt?

7.88%


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Cost of Preferred Capital


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Redeemable Preference Capital

n

n

t

t

p pk

F

k

DP

)1()1(1

2/)(

/)(

PF

nPFDkp

Approximation


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Cost of Perpetual

Preferred Capital

kp = =D

Po

Dividend

Net amount

realized


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Example: Cost of Preferred

If Prescott Corporation issues

preferred capital, it will pay a

dividend of $8 per year and shouldbe valued at $75 per share. If

flotation costs amount to $1 per

share, what is the cost of preferredcapital for Prescott?


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Cost of Preferred Capital

kp = =

= = 10.81%

Dividend

Net Price

D

Po

8.00

74.00


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Cost of Equity

The cost of equity capital, may bedefined as the minimum rate of return

that the firm must earn on the equity

financed portion of an investment

project in order to leave unchanged the

market price of the shares (or net

proceeds of the sale).


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Cost of Equity

)1(...)1()1( 221

eee

o

k

D

k

D

k

D

P

o

e

P

Dk

1

DDDIf ..., 21

Dividend Capitalization Method


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Cost of Equity

Dividend Growth ModelIf Dividend is growing @ g% per year

then,

n

t

t

e

t

k

gD

1

1

1

)1(

)1(

n

e

n

o

e

o

e

o

k

gD

k

gD

k

gDP

)1(

)1(...

)1(

)1(

)1(

)1(2

2

1

1

0


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gk

DP

e

o

1

g

P

Dke

0

1

Assumptions:

market value of shares depends upon

the expected dividends

Do>0

dividend pay-out ratio is constant


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Example

Suppose that dividend per share of afirm is expected to be Rs.1per share

and is expected to grow at 6%per

year perpetually. Determine the costof equity capital, assuming the

market price per share is Rs. 25

1/25 + .06 = 10.0%


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Weighted Cost of Capital

The weighted cost of capital is just

the weighted average cost of all of

the financing sources.


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Weighted Cost of Capital

Capital

Source Cost Structure

debt 6% 20%

preferred 10% 10%equity 16% 70%


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Weighted cost of capital

=.20 (6%) + .10 (10%) + .70 (16%)

= 13.4%

Weighted Cost of Capital(20% debt, 10% preferred, 70% equity)


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Problem

A company issues 15%debentures of

Rs.100for an amount aggregating

Rs.1,00,000at 10%premium,redeemable at par after 5 years. The

company's tax rate is 35%.Determine

the cost of debt.


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Solution

2

)(

)()1(

PF

n

PFTC

kd

15(1-.35) + (100-110)/5

(110+100)/2

= 7.4%

=


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A company issues 14%irredeemable

preference shares of the face value of Rs.

100each. Flotation costs are estimated at

5%of the expected sale price.What is thecost of preference capital, if preference

shares are issued at:

i) parvalue ii) 10%premium

iii) 5%discount

Problem


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i) 14 / 100*(1 - 0.05)= 14.7%

ii) 14 / 110*(1 - 0.05)

= 13.4%

iii) 14 / 95*(1 - 0.05)

= 15.5%

Solution

P bl


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Given the information determine the cost of new

equity shares of Company X: Current market price of a share = Rs. 150

Cost of flotation per share on new share = Rs.3

Dividend paid over past 5 years:1 2 3 4 5

10.50 11.02 11.58 12.16 12.76

Assume fixed dividend pay-out ratio Expected dividend on new shares at the end of

current year = Rs. 14.10

Problem


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Solution

Annual growth = 5%(app)

= 14.10/147 + 5%

= 14.6%


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Example

GA Ltd. has got Rs. 100 lakhs of retained

earnings and Rs. 100 lakhs of equity

through a fresh issue, in its capital structure.The equity investors expect a rate of return

of 18%. The cost of issuing equity is 5%.

Find the cost of retained earnings and cost

of equity.


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Solution

Cost of retained earnings:

kr = ke = 18%

Cost of external equity raised by thecompany:

ke = kr/ (1-f) = 0.18/ (1-0.05) = 18.95%


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Example

A company is considering raising Rs. 80 lakhs

by 14% institutional term loan. Calculate

the cost of the term loan. Tax rate is 35%.


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Solution

Cost of term loan = .14*80 (1-.35)/ 80

= .14*(1-.35)

= 9.1%= Interest Rate * (1-T)

Lec8.Cost of Capital

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