Lecture 1 Corporate Finance

Lecture 1FINM7007 Applied Corporate Finance

Fundamentals of Financial ManagementBD Chapters 1,3,4,6,9

1

This Class

• Introduction and course outline• Foundations– Present values and NPV rule– No arbitrage– Separation principle

• Time Value of Money• Valuation of Bonds and Stocks

2

Financial Management

• The study of how financial managers decide– what projects to invest in, and– how these projects should be funded.

• Involves the comparison of risky cash flows through time.

• Success is judged in terms of value.

3

The Tasks of Financial Management

• Tasks– Investment decision– Financing decision– Risk management

• Focus on investment and financing decisions

4

What are the Issues?

Consider:Toll Holdings’ management is evaluating an investment of $20 million in a new complex at Mascot for handling both international and domestic freight. The project has an expected life of 10 years.The investment committee proposed to implement this proposal in two stages, depending upon demand.The committee also raised the possibility of developing a complementary freight facility in the UK and US.Question:What is involved in evaluating this investment opportunity?

5

Cash Flow Estimation

• What are the relevant cash flows associated with the investment proposal.

• How sensitive is the project’s NPV to the projected freight demand?– How do I incorporate this in my analysis?

6

Cash Flow Estimation

• What is the possible impact of competitors?– How do we incorporate this in our analysis?

• How do we allow for the development of freight complexes in both the UK and the US?– Would the analysis change?– Are the risks facing Toll Holdings any

different?

7

The Cost of Capital

• What is the cost of capital against which the project is evaluated?– Estimating the cost of capital• The risk/return trade-off and the CAPM.• Do we do the analysis before or after taxes?• How do we estimate the cost of equity?

– What is the appropriate risk-free rate of return?– How is the market risk premium estimated?– How is beta (factors) estimated?

• How do we estimate the cost of debt?– What is the appropriate risk-free rate of return?

8

What Form of Financing Should be Used?

• Can Toll Holdings’ leverage choice its' value?– current funds from debt rather than equity– Is it optimal to rely predominantly on debt

financing?– Is there an optimal capital structure?– What is the impact of taxes?– Can the choice of financing tell the market

anything about the firm and/or the project?

9

What Form of Financing Should be Used?

• Can Toll Holdings’ choice of financing affect the project’s value?– Are the financing and investments decisions

independent?– What of the differences in obligations and issue

costs for the various security types?• Does it matter where the project is sited or

how it is funded?

10

Foundations: NPV

• The net present value (NPV) of a project or investment is the difference between the present value of its benefits and the present value of its costs.

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(Benefits) (Costs) NPV PV PV

(All project cash flows)NPV PV

The NPV Decision Rule

• When making an investment decision, take the alternative with the highest NPV. Choosing this alternative is equivalent to receiving its NPV in cash today.

• Accepting or Rejecting a Project– Accept those projects with positive NPV because accepting

them is equivalent to receiving their NPV in cash today.

– Reject those projects with negative NPV because accepting them would reduce the wealth of investors.

12

Foundations: Separation Principle

• Financing decisions do not create value but adjust the timing and risk of cash flows to meet the needs of the firm or its investors

• Value is created by undertaking investment opportunities

• Implication: Evaluate investment opportunties separately for the decision as to how to finance them

13

Foundations: No Arbitrage

• Arbitrage– The practice of buying and selling equivalent goods

in different markets to take advantage of a price difference. An arbitrage opportunity occurs when it is possible to make a profit without taking any risk or making any investment.

• Normal Market– A competitive market in which there are no

arbitrage opportunities.

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Determining the No-Arbitrage Price

• Unless the price of the security equals the present value of the security’s cash flows, an arbitrage opportunity will appear.

• No Arbitrage Price of a Security

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Price(Security) (All cash flows paid by the security) PV

Example

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Example (cont'd)

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Foundations: Time Value of Money

18

Example (cont’d)

19

Three Rules of Time Travel

• Financial decisions often require combining cash flows or comparing values. Three rules govern these processes.

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Perpetuities, Annuities, and Other Special Cases

• When a constant cash flow will occur at regular intervals forever it is called a perpetuity.

• The value of a perpetuity is simply the cash flow divided by the interest rate.

• Present Value of a Perpetuity

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( in perpetuity) CPV Cr

Annuities

• When a constant cash flow will occur at regular intervals for N periods it is called an annuity.

• Present Value of an Annuity

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1 1 (annuity of for periods with interest rate ) 1 (1 )

NPV C N r Cr r

• Future Value of an Annuity

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(annuity) V (1 )

1 1 (1 )(1 )

1 (1 ) 1

N

NN

N

FV P r

C rr r

C rr

Growing Perpetuities

• Assume you expect the amount of your perpetual payment to increase at a constant rate, g.

• Present Value of a Growing Perpetuity

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(growing perpetuity)

CPV

r g

Zero-Coupon Bonds

• Zero-Coupon Bond– Does not make coupon payments

– Always sells at a discount (a price lower than face value), so they are also called pure discount bonds

– Treasury Bills are U.S. government zero-coupon bonds with a maturity of up to one year.

25

Zero-Coupon Bonds (cont'd)

• Suppose that a one-year, risk-free, zero-coupon bond with a $100,000 face value has an initial price of $96,618.36. The cash flows would be:

– Although the bond pays no “interest,” your compensation is the difference between the initial price and the face value.

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• Yield to Maturity– The discount rate that sets the present value of

the promised bond payments equal to the current market price of the bond.• Price of a Zero-Coupon bond

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(1 )

n

n

FVPYTM


• Yield to Maturity– For the one-year zero coupon bond:

• Thus, the YTM is 3.5%.

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1

100,00096,618.36 (1 )

YTM

1100,0001 1.035

96,618.36 YTM


• Yield to Maturity– Yield to Maturity of an n-Year Zero-Coupon Bond

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1

1

n

nFVYTMP

Example

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Example (cont'd)

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• Risk-Free Interest Rates– A default-free zero-coupon bond that matures on

date n provides a risk-free return over the same period. Thus, the Law of One Price guarantees that the risk-free interest rate equals the yield to maturity on such a bond.

– Risk-Free Interest Rate with Maturity n

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n nr YTM

Coupon Bonds

• Coupon Bonds– Pay face value at maturity– Pay regular coupon interest payments

• Treasury Notes– U.S. Treasury coupon security with original

maturities of 1–10 years

• Treasury Bonds– U.S. Treasury coupon security with original

maturities over 10 years

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Example

34

Example (cont'd)

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Coupon Bonds (cont'd)

• Yield to Maturity– The YTM is the single discount rate that equates

the present value of the bond’s remaining cash flows to its current price.

– Yield to Maturity of a Coupon Bond

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1 1 1 (1 ) (1 )

N N

FVP CPNy y y

Interest Rate Changes and Bond Prices

• There is an inverse relationship between interest rates and bond prices.– As interest rates and bond yields rise, bond prices

fall.

– As interest rates and bond yields fall, bond prices rise.

37

The Yield Curve and Bond Arbitrage

• Using the Law of One Price and the yields of default-free zero-coupon bonds, one can determine the price and yield of any other default-free bond.

• The yield curve provides sufficient information

to evaluate all such bonds.

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Valuing a Coupon Bond Using Zero-Coupon Yields

• The price of a coupon bond must equal the present value of its coupon payments and face value.– Price of a Coupon Bond

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21 2

(Bond Cash Flows) V

1 (1 ) (1 )

nn

PV PVCPN CPN CPN FYTM YTM YTM

2 3

100 100 100 1000 $11531.035 1.04 1.045

P

Coupon Bond Yields

• Given the yields for zero-coupon bonds, we can price a coupon bond.

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2 3

100 100 100 1000 1153 (1 ) (1 ) (1 )

P

y y y

2 3

100 100 100 1000 $11531.0444 1.0444 1.0444

P

Treasury Yield Curves

• Treasury Coupon-Paying Yield Curve– Often referred to as “the yield curve”

• On-the-Run Bonds– Most recently issued bonds– The yield curve is often a plot of the yields on

these bonds.

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Corporate Bonds

• Corporate Bonds– Issued by corporations

• Credit Risk– Risk of default

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Corporate Bond Yields

• Investors pay less for bonds with credit risk than they would for an otherwise identical default-free bond.

• The yield of bonds with credit risk will be higher than that of otherwise identical default-free bonds.

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Corporate Yield Curves for Various Ratings, September 2005

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Valuation of Shares

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Stock Prices, Returns, and the Investment Horizon

• A One-Year Investor– Potential Cash Flows

• Dividend• Sale of Stock

– Timeline for One-Year Investor

• Since the cash flows are risky, we must discount them at the equity cost of capital.

46

Stock Prices, Returns, and the Investment Horizon (cont'd)

• A One-Year Investor

– If the current stock price were less than this amount, expect investors to rush in and buy it, driving up the stock’s price.

– If the stock price exceeded this amount, selling it would cause the stock price to quickly fall.

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1 10

1

E

Div PPr

Dividend Yields, Capital Gains, and Total Returns

• Dividend Yield• Capital Gain– Capital Gain Rate

• Total Return– Dividend Yield + Capital Gain Rate

• The expected total return of the stock should equal the expected return of other investments available in the market with equivalent risk.

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1 01 1 1

0 0 0

Dividend Yield Capital Gain Rate

1 E

P PDiv P DivrP P P

A Multi-Year Investor (cont'd)

• What is the price if we plan on holding the stock for N years?

– This is known as the Dividend Discount Model.

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1 20 2

E E E E

1 (1 ) (1 ) (1 )

N NN N

Div PDiv DivPr r r r

A Multi-Year Investor (cont'd)

• The price of any stock is equal to the present value of the expected future dividends it will pay.

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31 20 2 3

1E E E E

1 (1 ) (1 ) (1 )

n

nn

Div DivDiv DivPr r r r

The Discount-Dividend Model

• Constant Dividend Growth– The simplest forecast for the firm’s future

dividends states that they will grow at a constant rate, g, forever.

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The Discount-Dividend Model (cont'd)

• Constant Dividend Growth Model

– The value of the firm depends on the current dividend level, the cost of equity, and the growth rate.

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10

E

DivPr g

1E

0

Divr gP

Dividends Versus Investment and Growth

• A Simple Model of Growth– Dividend Payout Ratio• The fraction of earnings paid as dividends each year

53

E

Earnings Dividend Payout Rate Shares Outstanding

t

tt t

t

PS

Div

Dividends Versus Investment and Growth (cont'd)

• A Simple Model of Growth– Assuming the number of shares outstanding is

constant, the firm can do two things to increase its dividend:• Increase its earnings (net income)• Increase its dividend payout rate

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• A Simple Model of Growth– A firm can do one of two things with its earnings: • It can pay them out to investors.• It can retain and reinvest them.

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• A Simple Model of Growth

– Retention Rate• Fraction of current earnings that the firm retains

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Change in Earnings New Investment Return on New Investment

New Investment Earnings Retention Rate


• A Simple Model of Growth

– If the firm keeps its retention rate constant, then the growth rate in dividends will equal the growth rate of earnings.

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Change in EarningsEarnings Growth Rate Earnings

Retention Rate Return on New Investment

Retention Rate Return on New Investment g


• Profitable Growth– If a firm wants to increase its share price, should it

cut its dividend and invest more, or should it cut investment and increase its dividend? • The answer will depend on the profitability of the

firm’s investments.– Cutting the firm’s dividend to increase investment will raise

the stock price if, and only if, the new investments have a positive NPV.

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Example

59

Example (cont'd)

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Changing Growth Rates

• We cannot use the constant dividend growth model to value a stock if the growth rate is not constant.– For example, young firms often have very high

initial earnings growth rates. During this period of high growth, these firms often retain 100% of their earnings to exploit profitable investment opportunities. As they mature, their growth slows. At some point, their earnings exceed their investment needs and they begin to pay dividends.

61

Changing Growth Rates (cont'd)

• Although we cannot use the constant dividend growth model directly when growth is not constant, we can use the general form of the model to value a firm by applying the constant growth model to calculate the future share price of the stock once the expected growth rate stabilizes.

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Changing Growth Rates (cont'd)

• Dividend-Discount Model with Constant Long-Term Growth

63

1

E

N

NDiv

Pr g

11 20 2

E E E E E

1 1 (1 ) (1 ) (1 )

N NN N

Div DivDiv DivPr r r r r g

Example

64

Example (cont'd)

65

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The Discounted Free Cash Flow Model

• Discounted Free Cash Flow Model– Determines the value of the firm to all investors,

including both equity and debt holders

– The enterprise value can be interpreted as the net cost of acquiring the firm’s equity, taking its cash, paying off all debt, and owning the unlevered business.

Enterprise Value Market Value of Equity Debt Cash

67

The Discounted Free Cash Flow Model (cont'd)

• Valuing the Enterprise

• Discounted Free Cash Flow Model

Unlevered Net Income

Free Cash Flow (1 ) Depreciation Capital Expenditures Increases in Net Working Capital

cEBIT

0 (Future Free Cash Flow of Firm)V PV

0 0 00

0

Cash Debt Shares Outstanding

VP

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• Implementing the Model– Since we are discounting cash flows to both equity

holders and debt holders, the free cash flows should be discounted at the firm’s weighted average cost of capital, rwacc. If the firm has no debt, rwacc = rE.

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• Implementing the Model

– Often, the terminal value is estimated by assuming a constant long-run growth rate gFCF for free cash flows beyond year N, so that:

1 20 2

wacc wacc wacc wacc

1 (1 ) (1 ) (1 )

N NN N

FCF VFCF FCFVr r r r

1

wacc wacc

1 ( )

N FCFN N

FCF FCF

FCF gV FCF

r g r g

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Example

71

Example (cont'd)

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• Connection to Capital Budgeting– The firm’s free cash flow is equal to the sum of the

free cash flows from the firm’s current and future investments, so we can interpret the firm’s enterprise value as the total NPV that the firm will earn from continuing its existing projects and initiating new ones. • The NPV of any individual project represents its

contribution to the firm’s enterprise value. To maximize the firm’s share price, we should accept projects that have a positive NPV.

73

Valuation Based on Comparable Firms

• Method of Comparables (Comps)– Estimate the value of the firm based on the value

of other, comparable firms or investments that we expect will generate very similar cash flows in the future.

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Valuation Multiples

• Valuation Multiple– A ratio of firm’s value to some measure of the

firm’s scale or cash flow

• The Price-Earnings Ratio– P/E Ratio• Share price divided by earnings per share

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Valuation Multiples (cont'd)

• Trailing Earnings– Earnings over the last 12 months

• Trailing P/E

• Forward Earnings– Expected earnings over the next 12 months

• Forward P/E

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Valuation Multiples (cont'd)

• Firms with high growth rates, and which generate cash well in excess of their investment needs so that they can maintain high payout rates, should have high P/E multiples.

0 1 1

1 E E

/ Dividend Payout RateForward P/E

P Div EPSEPS r g r g

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Example

• Problem– Best Buy Co. Inc. (BBY) has earnings per share

of $2.22.

– The average P/E of comparable companies’ stocks is 19.7.

– Estimate a value for Best Buy using the P/E as a valuation multiple.

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• Solution– The share price for Best Buy is estimated by

multiplying its earnings per share by the P/E of comparable firms.

– P0 = $2.22 × 19.7 = $43.73

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Stock Valuation Techniques: The Final Word

• No single technique provides a final answer regarding a stock’s true value. All approaches require assumptions or forecasts that are too uncertain to provide a definitive assessment of the firm’s value. – Most real-world practitioners use a combination

of these approaches and gain confidence if the results are consistent across a variety of methods.

Documents

Lecture 1 Corporate Finance