Cost of capitalCh 14

Any returns for investors are costs for the

company

NPV

What is the required rate of return? What does it

mean?

What is the difference between: required rate of

return / appropriate discount rate and cost of

capital?

Require return versus cost of capital

Require rate of return (RRR): the minimum annual percentage earned by the an investment that will induce individual or companies to put money into a particular security or project.

Appropriate discount rate: the interest rate used in discounted cash flow(DCF) analysis to determine the present value of future cash flows.

Cost of capital: the cost of funds used for financing a business. (cost of equity or cost debt).

In a risk free project the cost of capital is the risk free rate.

In a risky project the cost of capital is greater than than risk free rate, and the appropriate discount rate would exceed the risk free rate.

The cost capital depend primarily in the use of the funds, not the source.

Cost of capital will reflect both its cost of debt and cost of equity.

Capital structure

Common stock

Debt

Preferred stock

Cost of common equity (Re) is the rate of return that an

investor requires when investing in common shares of a

company

The cost of common equity is the return required by

equity investors given the risk of the cash flows from the

firm

Business risk

Financial risk

Cost of equity

There are two major methods for

determining the cost of common equity

1. Dividend growth model

2. SML

Cost of equity

Reminder

Debt • Interest

Preferred stock

• Preferred dividends

Common stock

• Dividends• Capital

gain

1- Dividend growth model

Cost of equity

ggDP

Re)1(00g

P

DRE

0

1

D1: expected dividend for upcoming

year

Po: current share price

g: growth rate

Suppose STC paid a dividend of 4$ per share last year. The stock is currently sells for 60 $ per share. You estimate that the dividend will grow steadily at a rate if 6% per year into the infinite future. What is the cost of equity for STC?

Suppose that your company is expected to pay a dividend of $1.50 per share next year. You bought the common stock for 20 and expect to sell it next year worth $25. What is your required rate of return?

Cost of equity

Estimating g:

There are two ways of estimating g

1. Use historical growth rates

2. Use analysts’ forecasts of future growth

rates

Cost of equity

Year Dividend

2005 1.10$

2006 1,20$

2007 1.35$

2008 1.40$

2009 1.55$

Advantages and Disadvantages of Dividend Growth Model

Advantages: simplicity

Disadvantages:

1. Only applicable to companies currently paying dividends

2. Not applicable if dividends aren’t growing at a reasonably

constant rate

3. Extremely sensitive to the estimated growth rate – an

increase in g of 1% increases the cost of equity by 1%

4. Does not explicitly consider risk

Cost of equity

2. The Security Market Line Approach (SML)

The SML essentially tells us the reward (return) for

bearing risk in financial markets – what return is

expected for a given level of risk

required return is a function of 3 things:

1. risk free rate

2. market risk premium

3. systematic risk of the asset relative to the average

risk - called the ‘beta’ coefficient

Cost of equity

1. risk free rate: return on a risk free asset

2. market risk premium - reflecting the return associated

with the market as a whole e.g. the Saudi market return

3. systematic risk of the asset relative to the average risk

called the ‘beta’ coefficient : A measure of the

systematic risk, of a security or a portfolio in comparison

to the market as a whole - so if the stock historically is

much more volatile (risky) than the market then the return

should reflect that incremental risk

Cost of equity

From the SML comes the Capital Asset Pricing Model (CAPM)

According to the CAPM:

RE = Rf + bE (ERM - Rf)

Rf = risk free rate of return

Rm = expected market return

Rm-RF = market risk premium

BE = estimate of systematic risk, the risk for an individual security

relative to the market risk as a whole

Cost of equity

Get the risk-free rate (Rf ) from financial press—many use

the 1-year Treasury bill rate, T-bond rates

Get estimates of market risk premium and security beta.

Historical risk premium — RM - Rf =

Beta — historical

(1) Investment information services

(2) Estimate from historical data

Cost of equity

Suppose your company has an equity beta of .58 and the current risk-free rate is 6.1%. If the expected market risk premium is 8.6%, what is your cost of equity capital?

Cost of equity

Advantages and Disadvantages of SML

Advantages

Explicitly adjusts for systematic risk

Applicable to all companies, as long as we can estimate beta

Disadvantages

Have to estimate the expected market risk premium, which

does vary over time

Have to estimate beta, which also varies over time

We are using the past to predict the future, which is not

always reliable

Cost of equity

The Down and Out Co. just issued a dividend of 2.40$ per share on its common stock. The company is expected to maintain a constant 5.5 percent growth rate in its dividends indefinitely. If the stock sells for 52$ a share , what is the company’s cost of capital?

Ex 1 Page 465

Stock in Country Road Industries has a beta of 0.85. the market risk premium is 8 percent, and T-bills are currently yielding 5 percent. The company’s most recent dividend was 1.6$ per share, and dividends are expected to grow at a 6 percent annual rate indefinitely. If the stock sells for 37$ per share, what is your best estimate of the company’s cost of capital?

Ex3 Page 465

Suppose In a Found Ltd. Just issued a dividend of 1.43$ per share on its common stocks. The company paid dividends of 1.05$ , 1.12$, 1.19$, and 1.30$ per share in the last four years. If the stock currently sells for 45$, what is your best estimate of the company’s cost of equity?

Ex4 Page 465

Debt

1. Bank loans

2. Bonds

Equity

1. Preferred stock

2. Common stock

Reminder

Cost of capital is the rate that must be earned to satisfy the required rate of return of the firm's investors ( fund providers)

Cost of Debt

Cost

Required

return

What is rate of return?

Required rate of return versus expected rate of

return

RRR : The minimum annual percentage earned by

an investment that will induce individuals or

companies to put money into a particular security

or project.

Cost of Debt

Do you accept the project?

Cost of Debt

ERR 20%

RRR 25%

Do you accept the project?

Cost of Debt

ERR 30%

RRR 25%

What is required rate of return based on?

The required rate of return is used to determine if

the reward is worth the risk.

Risk free rate is required return on a risk-free asset,

it is implied that any additional risk taken by an

investor should be rewarded with an interest rate

higher than the risk-free rate

Cost of Debt

Cost of debt is simply the interest rate the

firm must pay on new borrowing.

The current interest rate in the market

The cost of debt is the required return on a

company’s liabilities

Cost of Debt

Loans: Decreasing interest

Bonds: Fixed interest

Cost of Debt

Loans

Ki= 2mD/ P(n+1)

m= number of payments per-year

D= total interest amount

P= value of loan

n= total number of payments throughout loan period

Cost of debt

You borrowed 10m$ with a 5% interest rate for 5 years from a bank were you will be repaying the loan as fixed payments. These payments include the principal and interest of the loan. What is the cost of your debt if you are to pay the payments every 3 months across the 5 year period.

Example

Bond: is an interest only loan

Bonds features and prices:

For example: suppose the Beck Corporation

wants to borrow 1,000$ for 30 years. The

interest rate on similar corporation is 12

percent.

Bonds

Features:

1. Coupon: the stated interest payment made on a bond

(120$)

2. Face value: the principle amount of a bond that is repaid

at the end of the term. Also called par value (1,000$)

3. Coupon rate: the annual coupon divided by the face

value of a bond. 120$/ 1,000$ = (12%)

4. Maturity: the specified date on which the principle

amount of a bond is paid.

Bonds

There is an inverse relation ship between

interest rates and the present value of a bond

To determine the value of a bond we need to know:

1. The number of periods left to maturity

2. Par value

3. Interest rate

4. coupon

Bond values and yields

Yield to maturity (YTM): the rate required in the market on a bond

Bond values and yields

V Pmtk

k

FV

kB

d

N

d d

N

1 11

1

Example: suppose a company were to issue a

bond with 10 years to maturity. This company has

an annual coupon of 80$. Similar bonds have a

yield of maturity of 8%. What will the bond sell

for?

Suppose a year has gone by. And interest rate has

risen to 10 percent, what will the bond be worth?

What would the bond sell for if interest rates had

dropped by 2 percent?

Bond values and yields

The required return is best estimated by

computing the yield-to-maturity on the

existing debt

The cost of debt is NOT the coupon rate

What is the cost of new debt Rd for a

company if the current interest rate is 12%?

Cost of debt

Trial and Error

Suppose we have a bond issue currently

outstanding that has 10 years left to maturity and

a face value of $1,000. The coupon rate is 10%

and coupons are paid annually. The bond is

currently selling for $941. What is the cost of debt

Rd?

Cost of debt

If the Price is Higher than face value

Rd= YTM = int - ( rs/n)

(p+FV) / 2

int= interest payment

rs= raise in value of bond

n= years to maturity

p= market value of bond

FV= face value of bond

Cost of debt

Trial and Error

Suppose we have a bond issue currently

outstanding that has 10 years left to maturity and

a face value of $1,000. The coupon rate is 10%

and coupons are paid annually. The bond is

currently selling for $1,134. What is the cost of

debt Rd?

Cost of debt

If the Price is Higher than face value

Rd= YTM = int - ( rs/n)

(p+FV) / 2

int= interest payment

rs= raise in value of bond

n= years to maturity

p= market value of bond

FV= face value of bond

Cost of debt

Suppose we are interested in a six-year , 8 percent

coupon bond that is paid annually with a face value

of 1,000$. The current price is 955.14$. What is the

yield to maturity on this bond?

Suppose that the current price for the bond is

1250$. What is the yield to maturity on this bond?

Cost of debt

Tax Deduction:

An item or expense subtracted from gross

income to reduce the amount of income

subject to tax.

Interest expense is tax deductible

Therefore, when a company pays interest,

the actual cost is less than the expense

Cost of debt

Note that Rd is not the appropriate cost of

debt to use in calculating the WACC, instead

we should use the after-tax cost of debt

Rdt = Rd ( 1- T)

Cost of debt

Reminders

Preferred stock generally pays a constant dividend each period

Dividends are expected to be paid every period forever

Preferred stock is a perpetuity, so we take the

perpetuity formula, rearrange and solve for RP

po = Dp/Rp

Rp = required return on preferred stock

Cost of preferred stocks

RP = DP / P0

Rp cost of preferred stock

Dp dividends paid

Po current price not face value

Cost of preferred stocks

On May 30,2008 Alabama Power Co. had two issues of ordinary preferred stock with a 25$ par value that traded on the NYSE. One issue paid 1.30$ annually per share and sold for 21.05$ per share. The other paid 1.46$ per share annually and sold for 24.35$ per share. What is Alabama Power’s cost of preferred stock?

Example 14.3

Holdup bank has an issue of preferred stock with a 6$ stated dividend that just sold for 96$ per share. What is the bank’s cost of preferred stock?

Ex5 Page 465

We know that the return earned on assets

depends on the risk of those assets

The return to an investor is the same as the cost

to the company

Our cost of capital provides us with an indication

of how the market views the risk of our assets

Why Cost of Capital Is Important

We said previously that the capital of a company

composes of different elements, debt – preferred stock

– common stock

As we have seen, a given firm may have more than one

provider of capital, each with its own required return

The question here is what is the total cost of capital for

a firm putting into consideration all the types of capital

that a firm uses

Reminder

We can use the individual costs of capital that we have

computed to get our “average” cost of capital for the firm.

This “average” is the required return on the firm’s assets,

based on the market’s perception of the risk of those

assets

The weights are determined by how much of each type of

financing is used

The Weighted Average Cost of Capital

A calculation of a firm's cost of capital in which each category

of capital is proportionately weighted. All capital sources

- common stock, preferred stock, bonds and any other long-

term debt - are included in a WACC calculation.

The WACC is the minimum return that a company must earn

on an existing asset base to satisfy its creditors, owners, and

other providers of capital, or they will invest elsewhere

When we talk about the “cost” of capital, we are talking about

the required rate of return on invested funds

WACC

The weights are determined by how much of each type

of financing is used

The weights that we use to calculate the WACC will

obviously affect the result

Therefore, the obvious question is: “where do the

weights come from?”

There are two possibilities:

Book-value weights

Market-value weights

WACC

Notation

E = market value of equity = # of outstanding shares times price

per share

D = market value of debt = # of outstanding bonds times bond price

V = market value of the firm = D + E

Weights

wE = E/V = percent financed with equity

wD = D/V = percent financed with debt

Capital Structure Weights

Suppose you have a market value of equity

equal to $500 million and a market value of

debt equal to $475 million.

What are the capital structure weights?

Example: Capital Structure Weights

One potential source of these weights is the firm’s

balance sheet, since it lists the total amount of

long-term debt, preferred equity, and common

equity

We can calculate the weights by simply

determining the proportion that each source of

capital is of the total capital

Book value weights

What are the weights if you had the following balance sheet

Book value weights

Source Total Book Value Long-term Debt $400,000 Preferred Equity $100,000 Common Equity $500,000 Grand Totals $1,000,000

The problem with book-value weights is that the book values are

historical, not current, values

The market recalculates the values of each type of capital on a

continuous basis. Therefore, market values are more appropriate

Calculation of market-value weights is very similar to the

calculation of the book-value weights

The main difference is that we need to first calculate the total

market value (price times quantity) of each type of capital

Market-value Weights

What are the weights if you had the following market values?

Market-value Weights

Source Price per Unit

Number of shares

Debt $ 905 400 Preferred $ 100 1,000 Common $ 70 10,000 Totals

It is important to note that market-values is always

preferred over book-value

The reason is that book-values represent the historical

amount of securities sold, whereas market-values

represent the current amount of securities outstanding

For some companies, the difference can be much more

dramatic than others

Market versus book values

We are concerned with after-tax cash flows, so we also

need to consider the effect of taxes on the various costs of

capital

Interest expense reduces our tax liability

This reduction in taxes reduces our cost of debt

After-tax cost of debt = RD(1-TC)

Dividends are not tax deductible, so there is no tax impact

on the cost of equity

WACC = wERE + wPRP+ wDRD(1-TC)

Taxes and the WACC

The capital structure of a certain firm consists of 30% debt, 10% preferred stock and 60% common stock . The cost of debt is 10%, preferred stock 12% and 15% for common stock. What is the weighted average cost of capital if you knew that the company pays 40% in taxes?

Example

Company A has issued 10,000 bonds and 200,000 common stocks with face values 1000, 50 respectively. The coupon rate for the bonds is 10% and has a 8 year maturity date. The company just paid $6 in dividends which are expected to grow 5% in the upcoming years. The current price for the bonds are $800 and $60 for the common stock. What is the WACC of the company if it pays 35% in taxes?

Example

The B.B Lean Co. has 1.4 million shares of stocks outstanding. The stock currently sells for 20$ per share. The firm’s debt is publicly traded and was recently quoted at 93 percent of face value. It has a total face value of 5$ million, and is currently priced to yield 11 percent. The risk free rate is 8 percent, and the market risk premium is 7 percent. You’ve estimated that Lean has a beta of .74. if the corporate tax rate is 34 percent, what is the WACC of Lean Coo?

Ex 14.4

It is the appropriate discount rate to use for

cash flows with risk that is similar to that of

the overall firm

Evaluate projects and investments

Evaluation of firm

What is WACC used for

Using the WACC as our discount rate is only

appropriate for projects that have the same risk as

the firm’s current operations

If we are looking at a project that does NOT have

the same risk as the firm, then we need to

determine the appropriate discount rate for that

project

Drawbacks

The required return depends on the risk, not how the

money is raised

However, the cost of issuing new securities should not

just be ignored either

Basic Approach

Compute the weighted average flotation cost

Use the target weights because the firm will issue securities in

these percentages over the long term

Flotation Costs- Basic Approach

The Spatt Company, an all equity firm, has a cost of equity of 20

percent. What is the WACC for this company?

The Spatt is considering a large-scale expansion of 100$ million, this

expansion is going to be funded by selling new stocks with flotation

costs of 10 percent. What is the amount that Spatt should raise?

Suppose that Spatt’s target capital structure is 60 percent equity,

40 percent debt. The flotation cost of equity is still 10percent while

the flotation cost of debt is 5 percent. What is the amount that Spatt

should raise?

Example

ABC co. has a target capital structure that is 80% common equity, 20% debt. The flotation cost for equity issues are 20% of the amount raised; the flotation costs for debt issues are 6%. If the company needs $65 million for a new manufacturing facility, what is the true cost once flotation costs are considered?

Example

Suppose the Tripleday Printing company is currently at its target

debt-ratio of 100 percent. It is considering building a new 500,000

printing plant in Kansas. This new plant is expected to generate

after-tax cash flows of 73,150$ per year forever. The tax rate is 34

percent. There are two financing options:

1. A 500,000$ new issue of common stock: the issuance costs of the

new common stock would be about 10 percent of the amount

raised. The required return on the company’s new equity is 20

percent.

2. A 500,000$ issue of 30-year bonds: the issuance costs of the new

debt would be 2 percent of the proceeds. The company can raise

new debt at 10 percent.

What is the NPV of the new printing plant?

Flotation Costs & NPV

Mullineaux Corporation has a target capital structure of 60 percent

common stocks, 5 percent preferred stocks, and 35 percent debt. Its

cost of equity is 14 percent, the cost of preferred stock is 6 percent,

and the cost of debt is 8 percent. The relevant tax rate is 35 percent

A. What is the WACC?

B. The company’s president has approached you about Mullineaux’s

capital structure. He wants to know why the company doesn’t use

more preferred stock financing because its costs less than debt.

What would you tell the president?

Ex 9 Page 465

Sixx AM Manufacturing has a target debt-equity ratio of 0.65. its cost of equity is 15 percent, and its cost of debt is 9 percent. If the tax rate is 35 percent, what is the company’s WACC?

Ex 10 Page466

Fama’s Llamas has a WACC of 8.9 percent. The company’s cost of equity is 12 percent, and its pretax cost of debt is 7.9 percent. The tax rate is 35 percent. What is the company’s target debt-equity ratio?

Ex 11 Page 466

Filer Manufacturing has 11 million shares of common stock out standing.

The current share price is 68$, and the book value per share is 6$. Filer

Manufacturing also has two bond issues outstanding. The first bond issue

has a face value of 70$ million, has a 7 percent coupon, and sells for 93

percent of par. The second issue has a face value of 55$ million, has an 8

percent coupon, and sells for 104 percent of par. The first issue matures in

21 years, the second in 6 years.

A. What are Filer’s capital structure weights on a book value biases?

B. What are Filer’s capital structure weights on a market value biases?

C. Which are more relevant, the book or market value weights? Why?

EX 12 Page 466

Suppose your company needs 20$million to build a new assembly line. Your

target debt-equity ratio is .75. the flotation cost for new equity is 8 percent, but

the flotation cost for debt is only 5 percent. Your boss decided to fund the project

by borrowing money because the flotation costs are lower and the needed fund

are relatively small.

A. What do you think about the rationale behind borrowing the entire amount?

B. What is your company weighted average flotation costs, assuming all equity is

raised externally?

C. What is the true cost of building the new assembly line after taking flotation

costs into account? Does it matter in this case that the entire amount is being

raised from debt?

Ex 18 Page 467

Floyd industries stock has a beta of 1.5. the company just paid a

dividend of .8$, and the dividends are expected to grow at 5

percent. The expected return of the market is 12 percent, and the

Treasury bill are yielding 5.5 percent. The most recent stock price

for Floyd is 61$.

A. Calculate the cost of equity using DCF method

B. Calculate the cost of equity using SML method

C. Why do you think your estimates in (a) and (b) are so different?

Ex 23 Page 468