Techniques of Business Negotiation

Cost of Capital

Chapter 7 1^st Paper Samira Sharmin Mahbub Lecturer, Finance Banking & Insurance

Concept of Capital Budgeting

Mr. X is thking to start a business.

He need capital for that.

He can collect that from external sources fund

 Long term loan

 Preferred stock

 Common Stock

But all these sources incur cost.

And the company has to bear this cost for long term

So selecting wrong source of funding hamper business, its owners, employees and investors..

Definition of Cost of Capital

 L. J. Gitman defines the cost of capital as ‘the rate of return a firm must earn on its investment so the market value of the firm remains unchanged’.

 According to Ezra Solomon, ‘the cost of capital is the minimum required rate of earnings or the cut-off rate of capital expenditure’.

 The definition given by Keown et al. refers to the cost of capital as

‘the minimum rate of return necessary to attract an investor to purchase or hold a security’.

 Cost of capital is also referred to as the break-even rate, minimum rate, cut-off rate, target rate, hurdle rate, standard rate, etc.

 Desirable optimum capital structure

 Project evaluation

 Selecting sources of Capital

 Reducing Tax

 Determining discount rate

 Declaration of dividend

 Distribution of fund

 Evaluation of Financial activities

 Evaluation of firm

 Target profit

Significance of Cost of Capital

 Business risk to be unchanged

 Financial risk to be unchanged

 After Tax cost

 Right dividend policy

 Inflation rate

 Short term debt

 Fixed capital structure

 New Investment

Assumptions of Cost of Capital

 Historical Cost

 Future Cost

 Specific Cost

 Explicit Cost

 Implicit cost

 Average Cost of Capital

 Weighted average cost of capital

Concept of Cost of Capital

1. Common Stock

• General shareholders are owner of the company

• They can participate in the management of the company

• They only get dividend from profit and its not guaranteed every year

• They have voting right

2. Preferred Stock

• Get a specified rate of dividend

• Get dividend before all

• They are partially owner

• They don’t enjoy any voting right

Sources of Capital

Sources of Capital

3. Bond or Debenture

 Every year specified rate of interest is paid at specified time

 It is transferable

 Interest is deducted before tax and net income

 Holders don’t participate in Management and enjoys no voting right

4. Retained Earning

 This does not incur any direct expanse

 It has opportunity cost

 Personal tax is adjusted with this

 Usually spend for business expansion

Computation of cost of Capital

This computation of cost of capital consists of two important parts

 Measurement of Specific cost

 Measurement of overall cost of capital

Regarding specific cost we will start with – Cost of Equity

Cost of Equity : Common Stock

The cost of common stock is common stockholders' required rate of return.

We are going to learn 3 types of Cost of Common Stock calculation

 Zero dividend growth model

 Constant growth model

 Capital Asset Pricing Model (CAPM)

Zero Dividend Growth Model

Lets see the formula

𝑲 _𝒆 = ^𝑫

^𝟎

𝑷

_𝟎 ^{X 100}

Where

𝑲

_𝒆 = Cost of Equity

𝑫

_𝟎 = Dividend (It can be present or past or future all same

𝑷

_𝟎 = Current share price

Example

ABC Traders current market price of share is BDT 150, Every year the company provide BDT 12 dividend per share. What will be the cost of equity

𝑲 _𝒆 = ^𝑫

^𝟎

𝑷

_𝟎 ^{X 100 or}

𝑲 _𝒆 = ^𝟏𝟐

𝟏𝟓𝟎

^{X 100}

=

^{8 %}

Where

𝑲

_𝒆 = Cost of Equity

𝑫

_𝟎 = Dividend (It can be present or past or future all same

𝑷

_𝟎 = Current share price

Practice

 A companies current market share price is BDT 120 and every year the company gives BDT 12 dividend. What is the cost of equity(10%)

 Bata company every year gives BDT 10 dividend which in remain unchanged in future and market price is Tk. 110 then what will be the cost of common stock. (9.09%)

 Mr. X purchased ABC companies share at Tk. 150 each and after a year sold that at Tk. 200 each. ABC company paid Tk. 15 dividend that year. What is the return for Mr. X from that share in taka.

Constant Dividend Growth Model

Lets see the formula

𝑲

_𝒆

= 𝑫

_𝟏

𝑷

_𝟎

+ 𝒈 𝑿 𝟏𝟎𝟎 𝑯𝒆𝒓𝒆 𝑫

_𝟏

= 𝑫

_𝟎

(𝟏 + 𝒈)

Where

𝑲

_𝒆 = Cost of Equity

𝑫

_𝟎 = Current Dividend

𝑫

_𝟏 = Expected Dividend

𝑷

_𝟎 = Current share price g = Growth rate

Example

A companies share currently is selling at BDT 105. This year the company provided BDT 10 dividend. It is expected that dividend will grow by 5%. Calculate the cost of general share.

𝑲_𝒆 = ^𝑫𝟏

𝑷_𝟎 + 𝒈 𝑿 𝟏𝟎𝟎 or ^{𝟏𝟎.𝟓𝟎}

𝟏𝟎𝟓 + 𝟎. 𝟎𝟓 𝑿 𝟏𝟎𝟎 = 15%

𝑯𝒆𝒓𝒆 𝑫_𝟏 = 𝑫_𝟎 (𝟏 + 𝒈) or 𝑫_𝟏 = 𝟏𝟎 (𝟏 + 𝟎. 𝟎𝟓) = 10.50

Where

𝑲

_𝒆 = Cost of Equity

𝑫

_𝟎 = Current Dividend

𝑫

_𝟏 = Expected Dividend

𝑷

_𝟎 = Current share price

g

= Growth rate

Example with floating cost

A companies share currently is selling at BDT 90. Last year the company provided BDT 6 dividend. Dividend growth rate is 4%.

Issuance cost is BDT 1. . Calculate the cost of general share.

𝑲_𝒆 = ^𝑫𝟏

𝑷_𝟎 −𝑭𝑪 + 𝒈 𝑿 𝟏𝟎𝟎 or ^{𝟔.𝟐𝟒}

𝟗𝟎 −𝟏 + 𝟎. 𝟎𝟒 𝑿 𝟏𝟎𝟎 = 12%

𝑯𝒆𝒓𝒆 𝑫_𝟏 = 𝑫_𝟎 (𝟏 + 𝒈) or 𝑫_𝟏 = 𝟔 (𝟏 + 𝟎. 𝟎𝟒) = 6.24

Where

𝑲

_𝒆 = Cost of Equity

𝑫

_𝟎 = Current Dividend

𝑫

_𝟏 = Expected Dividend

𝑷

_𝟎 = Current share price

g

= Growth rate

FC

= Issuance cost

Practice

1. Singer Bangladesh current market share price is BDT 120 and share selling cost 1.5%. Expected dividend per share is BDT 10, and growth rate is 5%. What is the cost of equity(13%)

2. Atlas company every year gives BDT 10 dividend which will grow at 2% every year. Current market price is BDT 200 and floating cost 5%.

a) Calculate the cost of general stock? (8.44%)

b) If floatation cost is changed to 3%, than what will be the new cost of general stock? ( 8.309%)

Capital Asset Pricing Model

The Capital Asset Pricing Model (CAPM) is a model that describes the relationship between the expected return. The return on the

investment is an unknown variable that has different values associated with different probabilities. and risk of investing in a security.

𝑲 _𝒆 =

𝑹 _𝒇

+ β ( 𝑹 _𝒎 - 𝑹 _𝒇 )

Where

𝑲

_𝒆 = Cost of Equity

𝑹 _𝒇

= Risk free rate of return

𝑹 _𝒎

= Market return

β = Beta of investment

Condition of CAPM

 Investors are expected to make decisions based solely on risk-return assessments (expected returns and standard deviation measures).

 The purchase and sale transactions can be undertaken in infinitely divisible units.

 Investors can sell short any number of shares without limit.

 There is perfect competition and no single investor can influence prices, with no transactions costs, involved

 Personal income taxation is assumed to be zero.

 Investors can borrow/lend, the desired amount at riskless rates.

Example

ABC companies risk free rate of return is 6.5%, Market return is 13% and beta is 1.62. What will be the cost of equity of ABC company?

ABC companies beta is 0.9, treasury bill rate of return is 7%, Market risk is 10%. What will be the cost of equity of ABC company? ( 16%)

𝑲_𝒆 = 𝑹_𝒇

+

β

(

𝑹_𝒎

-

𝑹_𝒇

)

𝑲_𝒆 = 𝟔. 𝟓%

+

1.62

(

𝟏𝟑%

-

𝟔. 𝟓%

)

= 𝟔. 𝟓%

+

𝟏𝟎. 𝟓𝟑%

= 𝟏𝟕. 𝟎𝟑%

Cost of Preferred Stock

Zero dividend Cost of Preferred Stock formula

𝑲 _𝒆 = ^𝑫

^𝟎

𝑷

_𝟎 ^{X 100}

𝑲 _𝒑 = ^𝑫

^𝒑

𝑷

_𝟎 X 100 With floating cost

𝑲 _𝒆 = ^𝑫

^𝟎

𝑷

_𝟎

−𝑭𝑪

X 100

𝑲 _𝒑 = ^𝑫

^𝒑

𝑷

_𝟎

−𝑭𝑪

X 100 Where

𝑲

_𝒑 = Cost of Preferred Stock

𝑫

_𝒑 = Fixed dividend of Preferred stock (Face value X Dividend rate)

𝑷

_𝟎 = Current Market price

𝑭𝑪

= Floating/ issuance cost

Example

ABC companies is thinking to sale 10% preferred share with face value BDT 1000 at BDT 910 at the market. Share issuance cost will be BDT 5. What will the cost of issuing preference share?

𝑲_𝒑 = ^𝟏𝟎𝟎

𝟗𝟏𝟎−𝟓 X 100

= 𝟏𝟏. 𝟎𝟓%

ABC companies is thinking to sale 15% preferred share with face value BDT 1000. Share issuance cost will be 5%. What will the cost of issuing preference share if

a) Preference stock sold at par value (15.79%) b) Preference share sold at 10% discount (17.54%)

𝑲_𝒑 = ^𝑫𝒑

𝑷_𝟎−𝑭𝑪 X 100

Cost of Retained Earning

Without personal tax, Lets see the formula

𝑲

_𝒓

= 𝑫

_𝟏

𝑷

_𝟎

+ 𝒈 𝑿 𝟏𝟎𝟎 𝑯𝒆𝒓𝒆 𝑫

_𝟏

= 𝑫

_𝟎

(𝟏 + 𝒈)

Where

𝑲

_𝒓 = Cost of Retained Earning

𝑫

_𝟎 = Current Dividend

𝑫

_𝟏 = Expected Dividend

𝑷

_𝟎 = Current share price g = Growth rate

With personal tax, Lets see the formula

𝑲

_𝒓

= 𝑫

_𝟏

(𝟏 − 𝑻

_𝒑

)

𝑷

_𝟎

+ 𝒈 𝑿 𝟏𝟎𝟎 𝑶𝒓 𝑲

_𝒓

= 𝑲

_𝒆

𝟏 − 𝑻

_𝒑

Where

𝑻

_𝒑 = Personal Tax Rate

Example

ABC companies Common stock cost is 8%, personal tax is 15%. What will the cost of retained earnings?

𝑲_𝒓 = 𝑲_𝒆 𝟏 − 𝑻_𝒑 𝑲_𝒓 = 𝟖% 𝟏 − 𝟏𝟓%

= 𝟔. 𝟖𝟎%

Cost of Debt

Irredeemable Cost of Debt, Lets see the formula

𝑲

_𝒅

= 𝑰 (𝟏 − 𝑻)

𝑷

_𝟎

− 𝑭𝑪 𝑿 𝟏𝟎𝟎 𝑯𝒆𝒓𝒆 𝑫

_𝟏

= 𝑫

_𝟎

(𝟏 + 𝒈)

Where

𝑲

_𝒅 = Cost of Debt 𝑰 = Coupon

𝑻 = Corporate Tax

𝑷

_𝟎 = Current share price FC = Floating cost

Redeemable Cost of Debt, Lets see the formula

Or 𝑲_𝒊

=

^𝐼+

𝑀𝑉 −𝑁𝑆𝑉 𝑛 𝑀𝑉+𝑁𝑆𝑉

2

X 100, then

𝑲_𝒅 = 𝑲_𝒊 (𝟏 − 𝑻) Where

𝑴𝑽

= Maturity Value

𝑵𝑺𝑽

= Net Sales Value (SV-FC)

𝒏

= Maturity

𝑲_𝒊 = Cost of Investment

𝑲

_𝒅

=

^{𝐼(1−𝑇) +} 𝑀𝑉+𝑁𝑆𝑉^{𝑀𝑉 −𝑁𝑆𝑉𝑛} 2

X 100

Example with Irredeemable Debt

ABC companies is thinking to sell BDT 1000 face value 10% coupon interest perpetual bond. Company is expecting that bonds will be sold at BDT 930

each. Floatation cost is BDT 5. Corporate tax rate is 30%. What will the cost of debt for the company

𝑲

_𝒅

= 𝑰 (𝟏 − 𝑻)

𝑷

_𝟎

− 𝑭𝑪 𝑿 𝟏𝟎𝟎

𝑲

_𝒅

= 𝟏𝟎𝟎 (𝟏 − 𝟎. 𝟑𝟎)

𝟗𝟑𝟎 − 𝟓 𝑿 𝟏𝟎𝟎

= 𝟕. 𝟓𝟔%

Example with Redeemable Debt

ABC companies is thinking to sell BDT 1000 face value 10% coupon interest 10 years maturity bond. Company is expecting that bonds will be sold at BDT 1100 each. Floatation cost is BDT 20. Corporate tax rate is 30%. What will the cost of debt for the company

𝑲

_𝒅

= 𝐼(1 − 𝑇) + 𝑀𝑉 − 𝑁𝑆𝑉 𝑛

𝑀𝑉 + 𝑁𝑆𝑉 2

X 100

𝑲

_𝒅

= 100(1 − 0.30) + 1000 − 1080 10

1000 + 1080 2

X 100

= 5. 𝟗𝟔%

Practice

1. ABC companies is thinking to sale 7% coupon rate irredeemable bond with face value BDT 1000. Corporate tax rate is 30%. What will the cost of

issuing debt if

a) Bond is sold at par value (4.2%)

b) Bond is sold at 10% premium (3.82%) c) Bond is sold at 10% discount (4.67%)

2. QQ group is considering to sale 12% coupon rate redeemable 10 years maturity bond with face value BDT 1000. At maturity value will be @ 10%

premium but currently it will be sold at 5% discount. Issuance cost is 2%.

Corporate tax rate is 40%. What will the cost of issuing debt? (8.75%)

Summery of Individual Costing

Cost of Common Stock

Zero Dividend Growth

𝑲

_𝒆

=

^𝑫𝟎

𝑷_𝟎

X 100

Constant Dividend Growth

𝑲

_𝒆

=

^𝑫𝟏

𝑷_𝟎

+ 𝒈 𝑿 𝟏𝟎𝟎

CAPM Model

𝑲

_𝒆

= 𝑹

_𝒇

+ β(𝑹

_𝒎

- 𝑹

_𝒇

)

Summery of Individual Costing

Cost of Preferred Stock

𝑲

_𝒑

=

^𝑫𝒑

𝑷_𝟎

X 100

Without Personal Tax 𝑲

_𝒓

= 𝑫

_𝟏

𝑷

_𝟎

+ 𝒈 𝑿 𝟏𝟎𝟎

With Personal Tax

𝑲

_𝒓

= 𝑫

_𝟏

(𝟏 − 𝑻

_𝒑

)

𝑷

_𝟎

+ 𝒈 𝑿 𝟏𝟎𝟎

Cost of Retained Earning

Summery of Individual Costing

Cost of Debt

Irredeemable

𝑲

_𝒅

= 𝑰 (𝟏 − 𝑻)

𝑷

_𝟎

− 𝑭𝑪 𝑿 𝟏𝟎𝟎

Redeemable

𝑲

_𝒅

= 𝑰(𝟏 − 𝑻) + 𝑴𝑽 − 𝑵𝑺𝑽 𝒏

𝑴𝑽 + 𝑵𝑺𝑽 𝟐

X 100

Weighted Average Cost of Capital (WACC)

Weighted Average Cost of Capital (WACC) represents its blended cost of capital across all sources, including

 common shares

 preferred shares and

 debt

The cost of each type of capital is weighted by its percentage of total capital and they are added together.

Fund (in Crore Taka)

70 20 35

Retained Earning 15

15% Debenture 8% Preferred Stock

Common Stock

Sources of Fund Fund (in Crore Taka) Percentage Cost

Common Stock 70 50% 11%

8% Preferred Stock 20 14%

15% Debenture 35 25% TAX 40%

Retained Earning 15 11% P TAX 15%

Total 140 100%

Weighted Average Cost of Capital (WACC)

𝑲_𝒆 = ^𝟕𝟎

𝟏𝟒𝟎= 𝟓𝟎%

𝑲_𝒑 = ^𝟐𝟎

𝟏𝟒𝟎= 𝟏𝟒%

𝑲_𝒅 = ^𝟑𝟓

𝟏𝟎𝟎 = 𝟐𝟓%

𝑲_𝒓 = ^𝟏𝟓

𝟏𝟒𝟎= 𝟏𝟏%

𝑾𝑨𝑪𝑪 = *(𝑾_𝒆 𝑋 𝑲_𝒆) + (𝑾_𝒑 𝑋 𝑲_𝒑) + (𝑾_𝒅 𝑋 𝑲_𝒅) + (𝑾_𝒓 𝑋 𝑲_𝒓)+

= {(0.5X11%)+(0.14X8%)

+(0.25X9%) + (0.11X9.35%) = 9.89%

WACC Example 1

ABC Ltd. Capital Structure is as below:

The market value of common stock is Tk. 200 each. The company has decided to pay Tk. 15 dividend per share next year. Dividend growth rate is 4%. Corporate tax rate is 40%.

a) What will be the cost of common stock of ABC Ltd. [11.5%]

b) What will be the average cost of capital of ABC Ltd. [9.15%]

Sources of Fund Amount (Taka)

General Stock 5,00,000

8% Preferred Stock 2,00,000

10% Bond 3,00,000

Total 10,00,000

WACC Example 1 Solution

a) Solution:

𝑲_𝒆 = ^𝑫𝟏

𝑷_𝟎 + 𝒈 𝑿 𝟏𝟎𝟎 or ^𝟏𝟓

𝟐𝟎𝟎 + 𝟎. 𝟎𝟒 𝑿 𝟏𝟎𝟎 = 11.5%

b) Solution:

Cost of Debt, 𝑲_𝒅 = 𝑰 𝟏 − 𝑻_𝒕 , = 𝟏𝟎% 𝟏 − 𝟎. 𝟒𝟎 , = 6%

Weight

𝑾_𝒆 = 𝑪𝒐𝒎𝒎𝒐𝒏 𝑺𝒕𝒐𝒄𝒌

𝑻𝒐𝒕𝒂𝒍 𝑪𝒂𝒑𝒊𝒕𝒂𝒍 = ^{𝟓,𝟎𝟎,𝟎𝟎𝟎}

𝟏𝟎,𝟎𝟎,𝟎𝟎𝟎 = 0.50 𝑲_𝒆 = 11.5%

𝑾_𝒑 = 𝑷𝒓𝒆𝒇𝒆𝒓𝒓𝒆𝒅 𝑺𝒕𝒐𝒄𝒌

𝑻𝒐𝒕𝒂𝒍 𝑪𝒂𝒑𝒊𝒕𝒂𝒍 = ^{𝟐,𝟎𝟎,𝟎𝟎𝟎}

𝟏𝟎,𝟎𝟎,𝟎𝟎𝟎 = 0.20 𝑲_𝒑 = 8%

𝑾_𝒅 = ^{𝑩𝒐𝒏𝒅}

𝑻𝒐𝒕𝒂𝒍 𝑪𝒂𝒑𝒊𝒕𝒂𝒍 = ^{𝟑,𝟎𝟎,𝟎𝟎𝟎}

𝟏𝟎,𝟎𝟎,𝟎𝟎𝟎 = 0.30 𝑲_𝒅 = 𝟔%

𝑾𝑨𝑪𝑪 = *(𝑾_𝒆 𝑋 𝑲_𝒆) + (𝑾_𝒑 𝑋 𝑲_𝒑) + (𝑾_𝒅 𝑋 𝑲_𝒅)+

= {(0.5X11.5%)+(0.2X8%)+(0.3X6%)}

= 9.15%

WACC Example 2

ABC Ltd. issued 12% coupon interest 5 years maturity bond with face value TK. 1000. Selling cost of each bond will be 2%. On the other hand PWC Company operates business with debenture, preferred share and common share. Its cost of fund and weight are as 12%, 14% & 15% and 30%, 30% & 40%. Corporate tax for both company is 30%

a) What will be the cost of bond for ABC Ltd. [8.89%]

b) What will be the average cost of capital of PWC Ltd. [12.72%]

WACC Example 3

ABC Ltd. Capital Structure is as below:

Company Beta value is 2. Market portfolio return is 15% and risk free return is 7%. Corporate tax rate is 40%. Companies expected profit is 25%. While taking funding decision financial manager will consider overall cost of capital.

a) What will be the cost of common stock of ABC Ltd. [23%]

b) What will be the average cost of capital of ABC Ltd. [16.63%]

Sources of Fund Amount (Taka)

General Stock 20,00,000

14% Preferred Stock 5,00,000

15% Debenture 15,00,000

Total 40,00,000

WACC HW

 Book page 7-24 Theory 1-22

 Book page 7-25 to 7-51 example 1 to 40

 Book page 7-51 Theory extra question 1 to 12

Simple Mathematical

1. Mr. ‘X’ is owner of ABC Group. His cost of common stock 15% and personal tax rate is 30%.

 What will be his cost of retained earnings?

 If Personal tax is 20%, then what will be the cost of Retained earnings ? 2. What will be the cost of common stock market return is 15%, treasury bill

return is 5% and beta is 2?

3. ABC Company Ltd. uses Common Stock, Preference stock and debenture for funding their capital. Their desired capital structure is 30% Common stock, 20% Preference Stock and 50% Debenture and cost are 10.6%, 9%

and 7% respectively.

 What will be the WACC of ABC Ltd.?

 If the company reduced Common stock ratio by 5% and increased Debenture ratio by 5%, then what will the new WACC ?

10.5%

12%

25%

8.48%

8.3%

Simple Mathematical

4. ABC Ltd Market price of share is Tk. 120, expected dividend is Tk. 10 and growth rate is 5%.

 What will be his cost of Common Stock?

 If selling cost of share is 5% of market price, then what will be the cost?

5. ABC Company Ltd. would like to sale 10% preference share to collect

additional capital with face value Tk. 500, market price Tk. 450 and selling cost Tk. 20 per share.

 What will be the cost of preference share for ABC Ltd.?

 If the company sales share at 10% discounted price and there is no additional selling cost, then what will the cost of preference share?

13.33%

13.77%

11.63%

11.11%