Cost of Capital

COST OF CAPITAL

• Basic Skills: (Time value of money, Financial Statements)

• Investments: (Stocks, Bonds, Risk and Return)

• Corporate Finance: (The Investment Decision - Capital Budgeting)

What we know…

Liabilities & Equity Assets

Current Liabilities Current assets

Long-term debt Fixed assets

Preferred Stock

Common Equity




Preferred Stock

Common Equity

The investment decision

• Corporate Finance:

(The Financing Decision)

Cost of capital

Leverage

Capital Structure

Dividends

Where we’re going...




Preferred Stock

Common Equity




Preferred Stock

Common Equity

The financing decision




Preferred Stock

Common Equity



Fixed assets

Long-term debt

Preferred Stock

Common Equity}Capital Structure

Cost of Capital

• For Investors, the rate of return on a security is a benefit of investing.

• For Financial Managers, that 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 firm’s cost of capital.

How can the firm raise capital?

• Bonds

• Preferred Stock

• Common Stock

• Each of these offers a rate of return to investors.

• This return is a cost to the firm.

• “Cost of capital” actually refers to the weighted cost of capital - a weighted average cost of financing sources.

Some concept usage

• Systematic Risk: Risk factors that affect the overall market, such as changes in nation’s economy, tax reforms, or a change in the world energy situation. These are risks that affect securities overall where an investor who holds a well-diversified portfolio will be exposed to this type of risk.

• Flotation Costs: The costs associated with issuing securities, such as underwriting, legal, listing, and printing fees.

Cost of Debt

For the issuing firm, the cost of debt is:

• the rate of return required by investors,

• adjusted for flotation costs (any costs associated with issuing new bonds), and

• adjusted for taxes.

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 (30%) (120,000) (105,000)

EAT 280,000 245,000



EBIT 400,000 400,000


EBT 400,000 350,000

- taxes (30%) (120,000) (105,000)

EAT 280,000 245,000

• Now, suppose the firm pays $50,000 in dividends to the stockholders.



EBIT 400,000 400,000


EBT 400,000 350,000

- taxes (30%) (120,000) (105,000)

EAT 280,000 245,000

- dividends (50,000) 0

Retained earnings 230,000 245,000

After-tax Before-tax Marginal % cost of % cost of x tax Debt Debt rate

-= 1


K = k (1 - t)

-= 11

i d


K = k (1 - t)

.06 = .10 (1 - .30)

-= 11

i d

Example: Cost of Debt

• Prescott Corporation issues a $1,000 par, 8 %, 20 year bond whose net proceeds are $940. The tax rate is 40%.

• What is the pre-tax and after-tax cost of debt for Prescott Corporation?

• Pre-tax cost of debt: Use approximate method of YTM on a Bond.

k d =I + (M – V) / n

(M + V) / 2

Where, I = annual interest M = par value per bondV = value or net proceeds form sale of a bondn = bond years

=80 + (1000 – 940) / 20

(1000 + 940) / 2

=83970 = 8.56%

• After-tax cost of debt

K = k (1 -t)

= 8.56% (1 - 0.4)

= 8.56% (0.6)

K = 5.136%

On an almost 9% before-tax cost, the after-tax cost of debt is 5.14%.

i d

i

Cost of Preferred Stock

• Most corporations that issue preferred stock fully intend to pay the stated dividend. The required rate of return for this stock, or simply the yield on preferred stock, serves as the estimate of the cost of preferred stock. Because such stocks have no maturity date.


• It is represented as:

kp = =

D Dividend Price

p

Po

Where, D is the stated annual dividend and P is the current market price of the preferred stock. It also meansnet proceeds from the sale of the stock.

p

o

Example: Cost of Preferred

• Suppose that the Carter Company has preferred stock that pays a $13 dividend per share and sells for $100 per share in the market. The flotation (or underwriting) cost is 3%, or $3 per share. What is the cost of preferred stock?


k = = DividendNet Price

D NPp

=$13

$100 - $3

=$13$97

= 13.4%

o

1

Cost of Common Stock

• There are 2 sources of Common Equity:

1) Internal common equity (retained earnings), and

2) External common equity (new common stock issue)

Do these 2 sources have the same cost?

Cost of Internal Equity

• Since the stockholders own the firm’s retained earnings, the cost is simply the stockholders’ required rate of return.

• Why?

• If managers are investing stockholders’ funds, stockholders will expect to earn an acceptable rate of return.



1) Dividend Growth Model



k = + gD1

Poe



k = + g

2) Capital Asset Pricing Model (CAPM)

D1

Poe



k = + g

2) Capital Asset Pricing Model (CAPM)

Rj = Rf + j(Rm - Rf )

D1

Po

e


Where, Rj = required rate of returnRf = risk-free rateRm = expected r.o.r. for market portfolioj = beta coefficient for stock ‘j’

From market’s aversion to systematic risk, greater the Beta of a stock, the greater its required return. The risk-return relationship in the form of an equation is also known as the security market line.

It implies that in market equilibrium, security prices will be such that there is a linear trade-off between required r.o.r. and Systematic risk, as measured by Beta.

The Capital-Asset Pricing Model Approach

• An alternative approach to measuring the cost of common stock. The steps are:

• Estimate the risk-free rate, Rf.• Estimate the stock’s beta coefficient, , which is

an index of systematic (or non diversifiable market) risk.

• Estimate the r.o.r. on the market portfolio, Rm, such as the Standard & Poor’s 500 Stock Composite Index.

• Use the CAPM equation to find required r.o.r.

Example: Dividend Growth Model

• Assume that the market price of a company’s stock is $40. Dividend to be paid at end of the coming year is $4 per share and is expected to grow at a constant annual rate of 6%. What is cost of common stock?

k e =D1

Po=+ g

$4

$40+ 6% = 16%

Example: CAPM approach

• Assume that risk-free rate is 7%, beta is 1.5, and market portfolio r.o.r. is 13%. Then what is cost of common stock?

Rj = Rf + j(Rm - Rf )= 7% + 1.5(13% - 7%) = 16%

This 16% cost can be viewed as consisting of a 7% risk-free rate plus a 9% risk premium, reflecting firm’s stock price as 1.5 times more volatile than market portfolio to factors affecting systematic risk.

Dividend Growth Model

Cost of External Equity


k = + g


DNPe

o

1


k = + g


DNP

Net proceeds to the firmafter flotation costs!

e1

o

Example: Cost of External Equity

• Assume that the market price of a company’s stock is $40. Dividend to be paid at end of the coming year is $4 per share and is expected to grow at a constant annual rate of 6%. The company is trying to sell new issues and its flotation cost is 10%. What is cost of common stock?

k = + gD1

NPo=

$4$36

+ 6%

= 11.11% + 6% = 17.11%

e

Weighted Cost of Capital

• The weighted cost of capital is just the weighted average cost of all of the financing sources.

K = w k + w k + w k i i p p e e

Where, W = % of total capital supplied by debtW = % of total capital supplied by preferred stockW = % of total capital supplied by equity

ipe

Weighted Cost of Capital

Capital

Source Cost Structure

debt 6% 20%

preferred 10% 10%

common 16% 70%

• Weighted cost of capital =

0.20 (6%) + 0.10 (10%) + 0.70 (16%)

= 13.4%

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

Exercise: Weighted Average Cost of Capital

• Assume the following capital structure of a Company:

Mortgage ($1,000 par) $20,000,000Preferred Stock ($100 par) 5,000,000Common Stock ($40 par) 20,000,000Retained Earnings 5,000,000TOTAL $50,000,000

Calculate book value weights and the Overall cost of capital.

Source Book Value Weights Cost WC (%) (%) (%)

Debt 20,000,000 40 5.14 2.06PS 5,000,000 10 13.14 1.34CS 20,000,000 40 17.11 6.84RE 5,000,000 10 16.00 1.60

Totals 50,000,000 100 11.84

Overall Cost of Capital = 11.84%

Cost of Capital

Documents

interest expense

constant annual

total capital

weighted average

internal equity

raising funds

market price

internal equity1