2201AFE VW Week 10 Cost of Capital

7/27/2019 2201AFE VW Week 10 Cost of Capital

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2201AFE Corporate FinanceWeek 10:

Cost of Capital

Readings: Chapter 17


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Agenda

Last Week

Cost of Capital Key Concepts and Skills

Real World Application

Investors Need A Good WACC

Next Week

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Last Lecture

Expected Returns and Variances

Single asset & Portfolios Using probabilities & Historical returns

Principle of Diversification

Systematic and Unsystematic Risk

Beta

CAPM = Capital Asset Pricing Model

SML = Security Market Line

Reward-to-Risk Ratio Deciding if assets are undervalued or overvalued?

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Cost of Capital

Chapter 17

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1. Introduction & Financial

Statements

2. Time Value of Money

3. Valuing Shares & Bonds

7. Mid-semester Exam

8. Some Lessons from Capital

Market History

11. Financial Leverage & Capital

Structure Policy

13. Options & Revision

9. Return, Risk & the Security

Market Line

5. Making Capital Investment

Decisions & Project Analysis

12. Dividends & Dividend Policy

6. Revision for Mid-sem Exam

4. Net Present Value & Other

Investment Criteria

10. Cost of Capital


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Key Concepts and Skills

Cost of Capital: Introduction

Cost of Equity

Cost of Debt

Cost of Preferred Stock

Weighted Average Cost of Capital (WACC)

Divisional and Project Costs of Capital

Flotation Costs (cost of issuing shares)

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Why Cost of Capital Is Important

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.

Knowing our cost of capital can also help us determine our

required return for capital budgeting projects.

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Required Return = Cost of Capital

The Required Rate of Return = Discount Rate = Hurdle Rate

= Cost of Capital

Need to know the required return for an investment so we

can compute the NPV and decide whether or not to take

the investment.

Need to earn at least the required return to compensate

investors for their financing.

Required returnfrom the investors point ofview.

Cost of capitalfrom the firms point ofview.

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Cost of Capital

The firm is financed by a mixture of equity and debt (i.e.

capital structure).

Cost of Capital is a mix of Cost of Equity and Cost of Debt.

These costs are determined by the market.

The firm determines the mix, Debt/Equity (D/E) reflecting

its target capital structure.

To calculate cost of capital:

Calculate cost of equity

Calculate cost of debt

Combine them

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Cost of Equity

The cost of equity is the return required by equity

investors, the shareholders on their investment in the firm.

Since this cost is not directly observable, it must be

estimated.

There are two main methods for determining the cost of

equity:

Dividend Growth Model

CAPM

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Cost of Equity DGM Approach

Start with the dividend growth model formula whereg is

constant:

where: REis the required return for shareholders,P0 is the

current price, D0is the current/last dividend, D1 is the nextdividend. Rearranging to solve for RE:

where D1 / P0 is the dividend yield, and g is the growth rate ofdividends.

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gR

D

gR

g)1(DP

E

1

E

00

gP

DR

0

1E


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DGM Example 1

Bentex Ltd. recently paid a dividend of 40 cents per share.

This dividend is expected to grow at 6% per year

indefinitely. If the current market price of Bentex shares is

$6 per share, estimate its cost of equity.

D0 = $0.40, g = 6%, P0 = $6, RE = ?

D1 = D0(1 + g) = $0.40(1.06) = $0.424

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equityofcost=13.07%or13070=060+

006

4240=+=

0

1 ..g

P

DRE

.

.


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DGM Example 2

Suppose ABC company is expected to pay a dividend of

$1.50 per share next year. There has been a steady growth

in dividends of 5.1% per year. The current price is $25.

What is the cost of equity?

D1 = $1.50, g = 5.1%, P0 = $25, RE = ?

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%1.11111.0051.02550.1g

PDR

gR

DP

0

1E

E

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Example Estimating the Dividend Growth Rate g

One method for estimating the growth rate is to use the

historical average:

Another way is use analysts forecast of growth (g).

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Year Dividend Change Return

2000 1.23 -

2001 1.30 (1.30-1.23) / 1.23 = 5.7%

2002 1.36 (1.36-1.30) / 1.30 = 4.6%

2003 1.43 (1.43-1.36) / 1.36 = 5.1%

2004 1.50 (1.50-1.43) / 1.43 = 4.9%

Average return = (5.7 + 4.6 + 5.1 + 4.9) / 4 = 5.1%


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Advantages and Disadvantages of Dividend Growth Model

Advantage:

Easy to understand and use.

Disadvantages:

Only applicable to companies currently paying dividends.

Assumes dividend growth is constant. Cost of equity is sensitive to growth estimate.

Does not explicitly consider risk.

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Cost of Equity CAPM or SML Approach

Recall CAPM for any asset i is:

E(Ri) = Rf+ i[E(Rm) Rf]

The CAPM cost of equity (RE) is:

RE = Rf+ E[E(Rm) Rf]

Where:

RE = Required return for shareholders

Rf= Risk-free rate

E(RM) Rf= Market risk premium

E= Systematic risk of firms equity relative to the market

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CAPM Example

Suppose our ABC company has an equity beta of 0.58 and

the current risk-free rate is 6.1%. If the expected market

risk premium is 8.6%, what is the cost of equity capital?

E = 0.58, Rf= 6.1%, E(RM) Rf= 8.6%

RE = Rf+ E[E(Rm) Rf]RE = 0.061 + 0.58(0.086) = 11.1%

What if the expected market return E(Rm) is 8.6%?

RE = 0.061 + 0.58(0.086 0.061) = 7.55%

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Advantages and Disadvantages of CAPM

Advantages:

Explicitly adjusts for risk.

Applicable to all companies.

Disadvantages:

Have to estimate the expectedmarket risk premium, whichdoes 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.

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Example Cost of Equity

Suppose our company has a beta of 1.5. The market risk

premium is expected to be 9% and the current risk-free

rate is 6%. The market believes our dividends will grow at

6% per year and our last dividend was $2. The stock is

currently selling for $15.65. What is the cost of equity?

Using CAPM:

RE = Rf+ E[E(Rm) Rf]

Using DGM:

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gP

gDRE +

+1=

0

0)(


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Cost of Preferred Stock

Reminders:

Preferred stock pays a constant dividend.

Dividends are expected to be paid forever.

Preferred stock return = Perpetuity = RP

P0 = D / Rp RP = D / P0

Example: Your company has preferred stock that has an

annual dividend of $3. If the current price is $25, what is

the cost of preferred stock?

25 = 3 / Rp therefore, RP = 3 / 25 = 12%

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Cost of Debt

The cost of debt is the required return on our companys

debt.

We usually focus on the cost of long-term debt or bonds.

The required return is best estimated by computing the

yield-to-maturity or YTM.

The cost of debt is NOT the coupon rate.

For publicly listed debt use YTM.

If the firm has no publicly traded debt, use YTM on similar

debt that is traded.

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YTM of Bond

In general:

Where:

C = coupon interest payment

RD = required market return or YTM

T = the number of periods left until repayment

F = face value

Need to solve for RD22

TDD

TD

0)R1(

F

R

)R1(

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CP


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l f b


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Example Cost of Debt

Suppose a firm has a bond issue currently outstanding that

has 25 years left to maturity and pays coupons semi-

annually. The coupon rate is 9% per year. The bondscurrent price is $90.87 per $100 bond. What is the cost of

debt?

t = 25 years 2 = 50; C = $9 / 2 = 4.5;

F = $100; Bond Price or P = $90.87;

RD or YTM = ?

By trial and error semiannual yield = 5% YTM = RD = 5% 2 = 10%

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W i h d A C f C i l


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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.

WACC is the required return on our assets, based on the

markets perception of the risk of those assets

The weights are determined by how much of each type offinancing we use:

WACC = wE RE + wP RP + wD RD

WACC = (E/V) RE + (P/V) RP + (D/V) RD

where V = E + P + D

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W i ht d A C t f C it l


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Weighted Average Cost of Capital

Notations:

E = market value of equity

no. of outstanding shares price per share

P = market value of preference shares

no. of outstanding preference shares price per share

D = market value of debt

no. of outstanding bonds bond price

V = market value of the firm = E + P + D

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C it l St t W i ht


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Capital Structure Weights

Weights:

wE = E/V = percent financed with equity

wP = P/V = percent financed with preference stock

wD = D/V = percent financed with debt

wE + wP + wD = 1

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E l W i ht & WACC


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Example Weights & WACC

Cost of debt = 5.7 %, Cost of equity = 14.0 %

Cost of preference shares = 9.0 %

WACC = (E/V) RE + (P/V) RP + (D/V) RD

= (0.5)0.14 + (0.1)0.09 + (0.4)0.057

= 0.1018 or 10.18% (Unadjusted for taxation effects)

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Source of Capital Market Value Weight

Long term debt $40m 40%

Preference shares $10m 10%

Equity $50m 50%Total $100m 100%

WACC Adjusted


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WACC Adjusted

The company gets a tax deduction for interest on debt,

reducing the effective cost of debt.

IfTC is the corporate tax rate then the after tax cost of debt

is RD(1 TC), and the WACC adjusted for taxation effects

is given by:

WACC = wE

RE + wP

RP + wD

RD(1Tc)or

WACC = (E/V) RE + (P/V) RP + (D/V) RD(1Tc)

Previous example: If tax rate is 30%, thenWACC = (0.5)0.14 + (0.1)0.09 + (0.4)0.057(10.3)

= 0.0950 or 9.5%.29

WACC Extended Example (1)


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Equity Information:

50 million shares

$80 per share

Beta = 1.15

Market risk premium = 9%

Risk-free rate = 5%

Step 1: Calculate cost of equity and cost of debt.

Step 2: Calculate the market value of each source of financing andthe weights.

Step 3: Calculate the WACC adjusting for tax.

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Debt Information:

$1 billion in outstanding

debt (face value) Current quote = 110%

Coupon rate = 9%,

semiannual coupons

15 years to maturity Tax rate = 40%



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What is the cost of equity?

E = 1.15; Rf= 5%; RM Rf= 9%; RE = ?

RE = 5% + 1.15(0.09) = 0.1535 or 15.35%

What is the cost of debt?

t = 15 years 2=30; Price = $110; C = $9 / 2 = 4.5;

F = $100; by trial & error semi yield = 3.9268%

RD = 0.03927 2 = 0.07854 or 7.854%

What is the after-tax cost of debt?

RD(1 TC) = 7.854(1 0.4) = 0.04712 or 4.712%

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What are the capital structure weights?

E = 50 million $80 = $4 billion

D = $1 billion 110% = $1.1 billion or

$1 billion / 100 = 10 million bonds issued

10 million bonds $110 = $1.1 billion

V = 4 + 1.1 = 5.1 billion

wE = (E / V) = (4 / 5.1) = 0.7843

wD = (D / V) = (1.1 / 5.1) = 0.2157

What is the WACC?

WACC = wE RE + wD RD(1Tc)

WACC = 0.7843(0.1535) + 0.2157(0.04712)

= 0.1336 or 13.06%32

Finding the Weights from D/E


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Finding the Weights from D/E

Suppose Belo Corp has a target D/E ratio of 0.33. Cost of Debt is

10% and cost of equity is 20%. If tax is 34%, what is WACC?

First calculate WE and WD .

If D / E = 0.33 what is E = ? D = ?

Assign any value to equity, E = 1

D / 1= 0.33 then D = 0.33 and V = 1.33E / V = 1 / 1.33 = 0.7519 and

D / V = 0.33 / 1.33 = 0.2481

WACC = wE RE + wD RD(1Tc)

WACC = 0.750.20 + 0.250.10(10.34) = 0.1665 or 16.65%

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Finding D/E


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Finding D/E

If BHP has a WACC of 21.67% and the cost of equity is 29.2%,

cost of debt is 10%, what is its target D/E ratio? Assume tax is

34%.

We know that:

E + D = V or WE + WD = 1

We express one in terms of another:

WE = 1 - WD

And insert in WACC equation:

0.2167 = WE 0.292 + WD 0.10 (10.34)

0.2167 = (1-WD) 0.292 + WD 0.10 (10.34)

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Finding D/E


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Finding D/E

0.2167 = (1-WD) 0.292 + WD 0.10 (1-0.34)

Solve for WD the only unknown variable:

0.2167 = 0.292 WD 0.292 + WD 0.066

0.2167 0.292 = -WD 0.292 + WD 0.066

-0.0753 = -WD (0.292 - 0.066)0.0753 = WD 0.226

WD = 0.0753/0.2260 = 0.333

Therefore WE = 1 WD, WE = 1 0.333 = 0.667D/E = 0.333/0.667 = 0.5

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Using the WACC as our discount rate is only appropriate for

projects that have the same risk as the firms 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.

Divisions also often require separate discount rates

(Divisions Overview).

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Using WACC for All Projects Example
http://www.ge.com/products_services/index.htmlhttp://www.ge.com/products_services/index.html


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Using WACC for All Projects Example

Assume the WACC = 15%.

If we use the WACC for all projects regardless of risk

Accept A and B, reject C

If correct required return based on specific risk is usedAccept B and C, reject A

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Project Required Return IRR WACC

A 20% reject 17% accept 15%

B 15% accept 18% accept 15%

C 10% accept 12% reject 15%

Divisional and Project costs of capital


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Divisional and Project costs of capital

WACC is the appropriate discount rate only when the

project is about the same risk as the firm.

Other approaches to estimating a discount rate:

Divisional cost of capital used if a company has more

than one division with different levels of risk;

Pure play approach a discount rate that is unique to a

particular project is used;

Subjective approach projects are allocated to specific

risk classes which, in turn, have specified discount rates.

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Other Approaches


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Other Approaches

Pure Play Approach:

Look at companies in the same line of business as the new

project.

Calculate an average WACC for all the companies and use

this rate as the discount rate of the new project.

Subjective Approach: Consider the projects risk relative to the firm overall risk.

If the project risk > firm risk,

use a discount rate > WACC

If the project risk < firm risk,

use a discount rate < WACC

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Flotation Costs


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The required return depends on the risk, not how the money is

raised.

However, the cost of issuing new securities should not just beignored either.

Basic Approach:

Compute the weighted average flotation cost

Use the target weights because the firm will issue securities inthese percentages over the long term

fA = (E/V) fE + (D/V) fD

where fA is the weighted average flotation cost, fE is the equity

flotation cost proportion, and fD is debt flotation cost proportion.

True cost of project = Cost / (1 fA)

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Flotation Costs Example


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p

A firm has a target structure that is 80% equity and 20% debt.

The costs for raising equity are 20% and the cost of raising debt

are 6%. If the firm needs $65 million for a new facility, what is the true

cost after accounting for flotation costs?

fA = (E/V) fE + (D/V) fD

= 0.80.2 + 0.20.06 = 0.172 or 17.2%

If the flotation cost is 17.2%, and we need to raise $65 million

net, this would be only 82.8% or (117.2%) of amount raised

$65m = (1 fA) True amount raised True amount raised = $65 / (1 fA) = 65 / 0.828 = $78.50 million

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Flotation Costs Example


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p

The firm needs to raise

$78.5 million to account for flotation costs and to have $65

million left to invest.

Since 78.5 / 65 = 1.2077, this suggests that:

for every dollar required by the project, the firm must raise

$1.2077 to finance its projects and to cover the cost of

raising the funds.

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Quick Quiz


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What are the two approaches for computing the cost of equity?

What is the cost of debt?

How do you compute the after-tax cost of debt?

When is appropriate to use WACC as the discount rate for

projects?

What is the proportion of E and D if we have a D/E ratio of 1.2?

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Real World Application


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During the dotcom era, there were predictions of the Dow Jones

Index soaring to 30,000!

Around five times greater than current value.

But this was a time when the market lost itself to the hype.

Role of psychology and behavioural finance?

When investors, along with their valuations, come back down toearth from such heights, there can be a loud thump, reminding

everyone that it's time to get back to fundamentals and take a

look at a key aspect of share valuations.

the weighted average cost of capital (WACC)

Source: http://www.investopedia.com/articles/fundamental/03/061103.asp

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To understand WACC, think of a company as a bag of money. The money in the bagcomes from two sources: debt and equity
http://www.investopedia.com/articles/fundamental/03/061103.asphttp://www.investopedia.com/articles/fundamental/03/061103.asphttp://www.investopedia.com/articles/fundamental/03/061103.asphttp://www.investopedia.com/articles/fundamental/03/061103.asp


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Money from business operations is not a third source because, after paying for debt,any cash left over that is not returned to shareholders in the form of dividends is keptin the bag on behalf of shareholders

If debt holders require a 10% return on their investment and shareholders requirea 20% return, then, on average, projects funded by the bag of money will have toreturn 15% to satisfy debt and equity holders - the 15% is the WACC

If the only money the bag held was $50 from debt holders and $50 fromshareholders, and the company invested $100 in a project, the return from thisproject, to meet expectations, would have to return $5 a year to debt holders and

$10 a year to shareholders - this would require a total return of $15 a year, or a15% WACC

Investors use WACC as a tool to decide whether to invest. The WACC represents theminimum rate of return at which a company produces value for its investors

Let's say a company produces a return of 20% and has a WACC of 11%. Thatmeans that for every dollar the company invests into capital, the company is

creating $0.09 of value By contrast, if the company's return is less than WACC, the company is shedding

value, which indicates that investors should put their money elsewhere

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Next Week


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Next week we look at the role of leverage and the Nobel

Prize winning work on selecting a capital structure.

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2201AFE VW Week 10 Cost of Capital

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