C H 1 4

COST OF CAPITAL

REQUIRE RETURN VERSUS COST OF CAPITAL

• 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 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 stockDebtPreferred stock

COST OF EQUITY

• 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 equity1. Dividend growth model2. SML

REMINDER

Debt • Interest

Preferred stock

• Preferred dividends

Common stock

• Dividends• Capital

gain

COST OF EQUITY

1- Dividend growth model

ggDP

Re)1(00

gPD

RE 0

1

D1: expected dividend for upcoming yearPo: current share priceg: growth rate

COST OF EQUITY

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 rates2. Use analysts’ forecasts of future growth

rates Year Dividend2005 1.10$2006 1,20$2007 1.35$2008 1.40$2009 1.55$

COST OF EQUITY

Advantages and Disadvantages of Dividend Growth Model• Advantages: simplicity• Disadvantages:

1. Only applicable to companies currently paying dividends2. Not applicable if dividends aren’t growing at a reasonably

constant rate3. 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 rate2. market risk premium3. 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 asset2. market risk premium - reflecting the return associated

with the market as a whole e.g. the Saudi market return3. 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

EX 1 PAGE 465

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?

EX3 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?

EX4 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?

REMINDER

• Debt

1. Bank loans2. Bonds• Equity

1. Preferred stock2. Common stock

• Cost of capital is the rate that must be earned to satisfy the required rate of

return of the firm’s investors (fund providers).

Rate of return: The gain or loss of an investment over a specified period,

expressed as a percentage increase over the initial investment cost.

Required rate of return (RRR) versus expected rate of return:

• RRR: is the minimum annual percentage earned by an investment that will

induce individuals or companies to put money into a particular security or a

project.

• In other words, RRR sets the minimum return an investor should accept given

all other options available and the capital structure of the firm

Why the required rate of return is important? To determine if the reward is

worth the risk.

Example: Risk free rate is required return on a risk free asset. Any additional risk

taken by an investor should be rewarded with an interest rate higher than the

risk free rate.

• Expected rate of return (ERR): The projected percentage return on an investment,

based on the weighted probability of all-possible rates of return.

•  

• Exercise: Do you accept a project that has an ERR of 20% and RRR of 25%?

• Do you accept a project that has an ERR of 30% and RRR of 25%?

COST OF DEBT

• Cost of Debt: The interest rate the firm must pay on a

new borrowing. Or, the required return on a firm’s

liabilities. Cost of debt is usually in a form of bonds.

• Bonds: is an interest only loan, meaning that the

borrower will pay the interest every period, but none of

the principle will be repaid until the end of the loan.

COST OF DEBT • Example:

• Suppose the Eric Corporation wants to borrow $1000 for 6 years. The interest

rate for a similar corporation is 4%.

• Features:•  

1. Coupon: The stated interest payment made on a bond ($40).2. Coupon rate: The annual coupon divided by the face value of the bond. $40/$1000 = 4% 3. Face value: The principle amount of a bond that is repaid at the end of the term. Also

called par value. ($1000)4. Maturity: The specified date on which the principle amount of a bond is paid. (6 years).

COST OF DEBT There is an inverse relationship 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 value3. Interest rate (YTM)4. Coupon•  • Bond value = present value of the coupons present value of the face amount • = C + • C= interest payment (coupon)• r= interest rate• t= number of years until maturity • F= face value or par value

The required return on a bond or the cost of it is best estimated by computing the yield to maturity rate on the existing debt (It is Not the coupon rate)

•   Yield to Maturity YTM; the rate required in the market on a bond.

COST OF DEBT • 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?•  • To find what will the bond sell for, we find the bond value.•  • = $80 + = $1000•  • $463.19 + 536.81•  •  • Suppose a year has gone by and interest rate has risen to 10 percent, what will the bond be worth?•  • = $80 + = $884.82 (discounted bond by $115)•  • $424.10 + 460.72•  • What would the bond sell for if interest rates had dropped by 2 %?•  • = $80 + = $1,136.03 (premium bond by 136)

COST OF DEBT Finding the YTM (Trail 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?

•  • To find the cost of debt or the YTM:• 1. If the Price is lower than face value• • Rd= YTM = C +( d/n)• (p+F) / 2•  • C= payment• d= decrease in value of bond• n= years to maturity• p= market value of bond• F= face value of bond•  • Rd= YTM= 100 +( 59/10) = 11%• (941+1000) / 2

COST OF DEBT • 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?

•  • 2. If the Price is Higher than face value • Rd= YTM = C - ( rs/n)• (p+F) / 2• C= payment• rs= raise in value of bond• n= years to maturity• p= market value of bond•  • Rd= YTM = 100 - ( 134/10) = 8%• (1134+1000) / 2

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 PREFERRED STOCKS

• 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 stockDp dividends paidPo current price not face value

EXAMPLE 14.3

• 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?

EX5 PAGE 465

• 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?

WHY COST OF CAPITAL IS IMPORTANT

cost of capital can be used as a discount rate

cost of capital has a significant role in making investment decisions.

cost of capital helps to design the capital structure of the firm

• cost of capital help to evaluate the performance

REMINDER

• 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

THE WEIGHTED AVERAGE COST OF CAPITAL

• 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

WACC

• 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

CAPITAL STRUCTURE WEIGHTS

• 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

EXAMPLE: 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?

BOOK VALUE 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

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

MARKET-VALUE WEIGHTS

• 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?

Source Price per Unit

Number of shares

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

MARKET VERSUS BOOK VALUES

• 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

TAXES AND THE WACC

• 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)

EXAMPLE

• 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?

EX 14.4

• 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?

WHAT IS WACC USED FOR

• 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

DRAWBACKS

• 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

FLOTATION COSTS- BASIC APPROACH

• 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

EXAMPLE

• 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?

FLOTATION COSTS & NPV

• 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?

EX 9 PAGE 465

• 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 10 PAGE466

• 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 11 PAGE 466

• 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 12 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 18 PAGE 467

• 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 23 PAGE 468

• 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 methodB. Calculate the cost of equity using SML methodC. Why do you think your estimates in (a) and (b) are so

different?