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### Chapter 15

Required Returns and the Cost of Capital

© 2001 Prentice-Hall, Inc.

Fundamentals of Financial Management, 11/e

Created by: Gregory A. Kuhlemeyer, Ph.D.

Carroll College, Waukesha, WI

Required Returns and the Cost of Capital

- Creation of Value
- Overall Cost of Capital of the Firm
- Project-Specific Required Rates
- Group-Specific Required Rates
- Total Risk Evaluation

Key Sources of Value Creation

Industry Attractiveness

Other --

e.g., patents,

temporary

monopoly

power,

oligopoly

pricing

Growth

phase of

product

cycle

Barriers to

competitive

entry

Marketing

and

price

Superior

organizational

capability

Perceived

quality

Cost

Competitive Advantage

Overall Cost of Capital of the Firm

Cost of Capital is the required rate of return on the various types of financing. The overall cost of capital is a weighted average of the individual required rates of return (costs).

Market Value of Long-Term Financing

Type of FinancingMkt ValWeight

Long-Term Debt $ 35M 35%

Preferred Stock $ 15M 15%

Common Stock Equity $ 50M 50%

$ 100M 100%

Cost of Debt

Cost of Debt is the required rate of return on investment of the lenders of a company.

ki = kd ( 1 - T )

n

Ij + Pj

S

P0 =

(1 + kd)j

j =1

Determination of the Cost of Debt

Assume that Basket Wonders (BW) has $1,000 par value zero-coupon bonds outstanding. BW bonds are currently trading at $385.54 with 10 years to maturity. BW tax bracket is 40%.

$0 + $1,000

$385.54 =

(1 + kd)10

Determination of the Cost of Debt

(1 + kd)10 = $1,000 / $385.54 = 2.5938

(1 + kd) = (2.5938) (1/10) = 1.1

kd= .1 or 10%

ki = 10% ( 1 - .40 )

ki = 6%

Cost of Preferred Stock

Cost of Preferred Stock is the required rate of return on investment of the preferred shareholders of the company.

kP = DP / P0

Determination of the Cost of Preferred Stock

Assume that Basket Wonders (BW) has preferred stock outstanding with par value of $100, dividend per share of $6.30, and a current market value of $70 per share.

kP = $6.30 / $70

kP = 9%

Cost of Equity Approaches

- Dividend Discount Model
- Capital-Asset Pricing Model
- Before-Tax Cost of Debt plus Risk Premium

Thecost of equity capital, ke, is the discount rate that equates the present value of all expected future dividends with the current market price of the stock.Dividend Discount Model

D1D2D

¥

P0 =

+

+ . . . +

¥

- (1+ke)1 (1+ke)2 (1+ke)

Theconstant dividend growth assumption reduces the model to:

ke = ( D1 / P0 ) + g

Assumes that dividends will grow at the constant rate “g” forever.

Constant Growth ModelDetermination of the Cost of Equity Capital

Assume that Basket Wonders (BW) has common stock outstanding with a current market value of $64.80 per share, current dividend of $3 per share, and a dividend growth rate of 8% forever.

ke = ( D1 / P0 ) + g

ke = ($3(1.08) / $64.80) + .08

ke = .05 + .08 = .13 or 13%

Growth Phases Model

- The growth phases assumption leads to the following formula (assume 3 growth phases):

D0(1+g1)t Da(1+g2)t-a

a

b

P0 =

S

+ S

+

- (1+ke)t (1+ke)t

t=1

t=a+1

¥

Db(1+g3)t-b

S

- (1+ke)t

t=b+1

The cost of equity capital, ke, is equated to the required rate of return in market equilibrium. The risk-return relationship is described by the Security Market Line (SML).

ke = Rj = Rf + (Rm - Rf)bj

Capital Asset Pricing ModelDetermination of the Cost of Equity (CAPM)

Assume that Basket Wonders (BW) has a company beta of 1.25. Research by Julie Miller suggests that the risk-free rate is 4% and the expected return on the market is 11.2%

ke = Rf + (Rm - Rf)bj

= 4% + (11.2% - 4%)1.25

ke = 4% + 9% = 13%

The cost of equity capital, ke, is the sum of the before-tax cost of debt and a risk premium in expected return for common stock over debt.

ke = kd + Risk Premium*

* Risk premium is not the same as CAPM risk premium

Before-Tax Cost of Debt Plus Risk PremiumDetermination of the Cost of Equity (kd + R.P.)

Assume that Basket Wonders (BW) typically adds a 3% premium to the before-tax cost of debt.

ke = kd + Risk Premium

= 10% + 3%

ke = 13%

Comparison of the Cost of Equity Methods

Constant Growth Model 13%

Capital Asset Pricing Model 13%

Cost of Debt + Risk Premium 13%

Generally, the three methods will not agree.

Weighted Average Cost of Capital (WACC)

n

Cost of Capital = kx(Wx)

WACC = .35(6%) + .15(9%) + .50(13%)

WACC = .021 + .0135 + .065 = .0995 or 9.95%

S

x=1

Limitations of the WACC

1.Weighting System

- Marginal Capital Costs
- Capital Raised in Different Proportions than WACC

Limitations of the WACC

2.Flotation Costs are the costs associated with issuing securities such as underwriting, legal, listing, and printing fees.

a. Adjustment to Initial Outlay

b. Adjustment to Discount Rate

Economic Value Added

- A measure of business performance.
- It is another way of measuring that firms are earning returns on their invested capital that exceed their cost of capital.
- Specific measure developed by Stern Stewart and Company in late 1980s.

Economic Value Added

EVA = NOPAT – [ Cost of

Capital x Capital Employed ]

- Since a cost is charged for equity capital also, a positive EVA generally indicates shareholder value is being created.
- Based on Economic NOT Accounting Profit.

Adjustment to Initial Outlay (AIO)

Add Flotation Costs (FC) to the Initial Cash Outlay (ICO).

Impact: Reduces the NPV

n

CFt

S

- ( ICO + FC )

NPV =

(1 + k)t

t=1

Adjustment to Discount Rate (ADR)

Subtract Flotation Costs from the proceeds (price) of the security and recalculate yield figures.

Impact: Increases the cost for any capital component with flotation costs.

Result: Increases the WACC, which decreases the NPV.

Determining Project-Specific Required Rates of Return

Use of CAPM in Project Selection:

- Initially assume all-equity financing.
- Determine project beta.
- Calculate the expected return.
- Adjust for capital structure of firm.
- Compare cost to IRR of project.

Difficulty in Determining the Expected Return

Determining the SML:

- Locate a proxy for the project (much easier if asset is traded).
- Plot the Characteristic Line relationship between the market portfolio and the proxy asset excess returns.
- Estimate beta and create the SML.

Project Acceptance and/or Rejection

Accept

SML

X

X

X

X

X

O

X

X

EXPECTED RATE

OF RETURN

O

O

O

O

Reject

O

Rf

O

SYSTEMATIC RISK (Beta)

Determining Project-Specific Required Rate of Return

1. Calculate the required return for Project k (all-equity financed).

Rk = Rf + (Rm - Rf)bk

2. Adjust for capital structure of the firm (financing weights).

Weighted Average Required Return = [ki][% of Debt] + [Rk][% of Equity]

Project-Specific Required Rate of ReturnExample

Assume a computer networking project is being considered with an IRR of 19%.

Examination of firms in the networking industry allows us to estimate an all-equity beta of 1.5. Our firm is financed with 70% Equity and 30% Debt at ki=6%.

The expected return on the market is 11.2% and the risk-free rate is 4%.

Do You Accept the Project?

ke = Rf + (Rm - Rf)bj

= 4% + (11.2% - 4%)1.5

ke = 4% + 10.8% = 14.8%

WACC = .30(6%) + .70(14.8%) = 1.8% + 10.36% = 12.16%

IRR = 19% > WACC = 12.16%

Determining Group-Specific Required Rates of Return

- Initially assume all-equity financing.
- Determine group beta.
- Calculate the expected return.
- Adjust for capital structure of group.
- Compare cost to IRR of group project.

Use of CAPM in Project Selection:

Comparing Group-Specific Required Rates of Return

Company Cost

of Capital

Expected Rate of Return

Group-Specific

Required Returns

Systematic Risk (Beta)

Qualifications to Using Group-Specific Rates

- Amount of non-equity financing relative to the proxy firm. Adjust project beta if necessary.
- Standard problems in the use of CAPM. Potential insolvency is a total-risk problem rather than just systematic risk (CAPM).

Project Evaluation Based on Total Risk

Risk-Adjusted Discount Rate Approach (RADR)

The required return is increased (decreased) relative to the firm’s overall cost of capital for projects or groups showing greater (smaller) than “average” risk.

Project Evaluation Based on Total Risk

Probability Distribution Approach

Acceptance of a single project with a positive NPV depends on the dispersion of NPVs and the utility preferences of management.

Firm-Portfolio Approach

Indifference

Curves

C

B

EXPECTED VALUE OF NPV

A

Curves show

“HIGH”

Risk Aversion

STANDARD DEVIATION

Firm-Portfolio Approach

Indifference

Curves

C

B

EXPECTED VALUE OF NPV

A

Curves show

“MODERATE”

Risk Aversion

STANDARD DEVIATION

Firm-Portfolio Approach

C

Indifference

Curves

B

EXPECTED VALUE OF NPV

A

Curves show

“LOW”

Risk Aversion

STANDARD DEVIATION

Adjusting Beta for Financial Leverage

bj = bju [ 1 + (B/S)(1-TC) ]

bj: Beta of a levered firm.

bju: Beta of an unlevered firm (an all-equity financed firm).

B/S: Debt-to-Equity ratio in Market Value terms.

TC: The corporate taxrate.

Adjusted Present Value

Adjusted Present Value (APV) is the sum of the discounted value of a project’s operating cash flows plus the value of any tax-shield benefits of interest associated with the project’s financing minus any flotation costs.

Unlevered

Project Value

Value of

Project Financing

APV =

+

NPV and APV Example

Assume Basket Wonders is considering a new $425,000 automated basket weaving machine that will save $100,000 per year for the next 6 years. The required rate on unlevered equity is 11%.

BW can borrow $180,000 at 7% with $10,000 after-tax flotation costs. Principal is repaid at $30,000 per year (+ interest). The firm is in the 40% tax bracket.

Basket Wonders NPV Solution

What is the NPV to an all-equity-financed firm?

NPV = $100,000[PVIFA11%,6] - $425,000

NPV = $423,054-$425,000

NPV = -$1,946

Basket Wonders APV Solution

What is the APV?

First, determine the interest expense.

Int Yr 1 ($180,000)(7%) = $12,600 Int Yr 2 ( 150,000)(7%) = 10,500 Int Yr 3 ( 120,000)(7%) = 8,400 Int Yr 4 ( 90,000)(7%) = 6,300 Int Yr 5 ( 60,000)(7%) = 4,200 Int Yr 6 ( 30,000)(7%) = 2,100

Basket Wonders APV Solution

Second, calculate the tax-shield benefits.

TSB Yr 1 ($12,600)(40%) = $5,040

TSB Yr 2 ( 10,500)(40%) = 4,200

TSB Yr 3 ( 8,400)(40%) = 3,360

TSB Yr 4 ( 6,300)(40%) = 2,520

TSB Yr 5 ( 4,200)(40%) = 1,680

TSB Yr 6 ( 2,100)(40%) = 840

Basket Wonders APV Solution

Third, find the PV of the tax-shield benefits.

TSB Yr 1 ($5,040)(.901) = $4,541

TSB Yr 2 ( 4,200)(.812) = 3,410

TSB Yr 3 ( 3,360)(.731) = 2,456

TSB Yr 4 ( 2,520)(.659) = 1,661

TSB Yr 5 ( 1,680)(.593) = 996

TSB Yr 6 ( 840)(.535) = 449PV = $13,513

Basket Wonders NPV Solution

What is the APV?

APV = NPV +PV of TS - Flotation Cost

APV = -$1,946 +$13,513 - $10,000

APV = $1,567

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