lecture five – the dividend decision

LECTURE FIVE – THE DIVIDEND DECISION

Tuesday 23rd

LEARNING OBJECTIVES1. List two ways a company can distribute

cash to its shareholders.2. Describe the dividend payment process

and the open-market repurchase process.3. Define stock split, reverse stock split, and

stock dividend; describe the effect of those actions on stock price.

4. Discuss the effect of dividend payment or share repurchase in a perfect world.

LEARNING OBJECTIVES (CONT'D)5. Assuming perfect capital markets, describe

what Modigliani and Miller (1961) found about payout policy.

6. Discuss the effect of taxes on dividend policy; compute the effective dividend tax rate.

7. Provide reasons why firms might accumulate cash balances rather than pay dividends.

8. Describe the effect of agency costs on payout policy.

9. Assess the impact of information asymmetry on payout policy.

17.1 DISTRIBUTION TO SHAREHOLDERS Payout Policy

The way a firm chooses between the alternative ways to distribute free cash flow to equity holders

FIGURE 17.1 USES OF FREE CASH FLOW

DIVIDENDS Declaration Date

The date on which the board of directors authorizes the payment of a dividend

Record Date When a firm pays a dividend, only

shareholders on record on this date receive the dividend.

DIVIDENDS (CONT'D) Ex-dividend Date

A date, two days prior to a dividend’s record date, on or after which anyone buying the stock will not be eligible for the dividend

Payable Date (Distribution Date) A date, generally within a month after

the record date, on which a firm mails dividend checks to its registered stockholders

FIGURE 17.2 IMPORTANT DATES FOR MICROSOFT’S SPECIAL DIVIDEND

DIVIDENDS (CONT'D) Special Dividend

A one-time dividend payment a firm makes, which is usually much larger than a regular dividend

Stock Split (Stock Dividend) When a company issues a dividend in

shares of stock rather than cash to its shareholders

FIGURE 17.3 DIVIDEND HISTORY FOR GM STOCK, 1983–2008

DIVIDENDS (CONT'D) Return of Capital

When a firm, instead of paying dividends out of current earnings (or accumulated retained earnings), pays dividends from other sources, such as paid-in-capital or the liquidation of assets

Liquidating Dividend A return of capital to shareholders from a

business operation that is being terminated

SHARE REPURCHASES An alternative way to pay cash to

investors is through a share repurchase or buyback. The firm uses cash to buy shares of its

own outstanding stock.

SHARE REPURCHASES (CONT'D) Open Market Repurchase

When a firm repurchases shares by buying shares in the open market

Open market share repurchases represent about 95% of all repurchase transactions.

SHARE REPURCHASES (CONT'D) Tender Offer

A public announcement of an offer to all existing security holders to buy back a specified amount of outstanding securities at a prespecified price (typically set at a 10%-20% premium to the current market price) over a prespecified period of time (usually about 20 days)

If shareholders do not tender enough shares, the firm may cancel the offer and no buyback occurs.

SHARE REPURCHASES (CONT'D) Dutch Auction

A share repurchase method in which the firm lists different prices at which it is prepared to buy shares, and shareholders in turn indicate how many shares they are willing to sell at each price. The firm then pays the lowest price at which it can buy back its desired number of shares

SHARE REPURCHASES (CONT'D) Targeted Repurchase

When a firm purchases shares directly from a specific shareholder

Greenmail When a firm avoids a threat of takeover

and removal of its management by a major shareholder by buying out the shareholder, often at a large premium over the current market price

17.2 COMPARISON OF DIVIDENDS AND SHARE REPURCHASES Consider Genron Corporation. The

firm’s board is meeting to decide how to pay out $20 million in excess cash to shareholders.

Genron has no debt, its equity cost of capital equals its unlevered cost of capital of 12%.

ALTERNATIVE POLICY 1: PAY DIVIDEND WITH EXCESS CASH With 10 million shares outstanding,

Genron will be able to pay a $2 dividend immediately.

The firm expects to generate future free cash flows of $48 million per year, thus it anticipates paying a dividend of $4.80 per share each year thereafter.

ALTERNATIVE POLICY 1: PAY DIVIDEND WITH EXCESS CASH (CONT'D) Cum-dividend

When a stock trades before the ex-dividend date, entitling anyone who buys the stock to the dividend

The cum-dividend price of Genron will be 4.80 Current Dividend (Future Dividends) 2 2 40 $42

0.12cumP PV

ALTERNATIVE POLICY 1: PAY DIVIDEND WITH EXCESS CASH (CONT'D) After the ex-dividend date, new

buyers will not receive the current dividend and the share price and the price of Genron will be 4.80 (Future Dividends) $40

0.12exP PV

ALTERNATIVE POLICY 1: PAY DIVIDEND WITH EXCESS CASH (CONT'D)

ALTERNATIVE POLICY 1: PAY DIVIDEND WITH EXCESS CASH (CONT'D) In a perfect capital market, when a

dividend is paid, the share price drops by the amount of the dividend when the stock begins to trade ex-dividend.

ALTERNATIVE POLICY 2: SHARE REPURCHASE (NO DIVIDEND) Suppose that instead of paying a dividend

this year, Genron uses the $20 million to repurchase its shares on the open market. With an initial share price of $42, Genron will

repurchase 476,000 shares. $20 million ÷ $42 per share = 0.476 million shares

This will leave only 9.524 million shares outstanding.

10 million − 0.476 million = 9.524 million

ALTERNATIVE POLICY 2: SHARE REPURCHASE (NO DIVIDEND) (CONT'D) The net effect is that the share price

remains unchanged.

ALTERNATIVE POLICY 2: SHARE REPURCHASE (NO DIVIDEND) (CONT'D) Genron’s Future Dividends

It should not be surprising that the repurchase had not effect on the stock price.

After the repurchase, the future dividend would rise to $5.04 per share.

$48 million ÷ 9.524 million shares = $5.04 per share

Genron’s share price is

5.04 $420.12repP

ALTERNATIVE POLICY 2: SHARE REPURCHASE (NO DIVIDEND) (CONT'D) Genron’s Future Dividends

In perfect capital markets, an open market share repurchase has no effect on the stock price, and the stock price is the same as the cum-dividend price if a dividend were paid instead.

ALTERNATIVE POLICY 2: SHARE REPURCHASE (NO DIVIDEND) (CONT'D) Investor Preferences

In perfect capital markets, investors are indifferent between the firm distributing funds via dividends or share repurchases. By reinvesting dividends or selling shares, they can replicate either payout method on their own.

ALTERNATIVE POLICY 2: SHARE REPURCHASE (NO DIVIDEND) (CONT'D) Investor Preferences

In the case of Genron, if the firm repurchases shares and the investor wants cash, the investor can raise cash by selling shares.

This is called a homemade dividend.

If the firm pays a dividend and the investor would prefer stock, they can use the dividend to purchase additional shares.

EXAMPLE 17.1

EXAMPLE 17.1 (CONT'D)

ALTERNATIVE POLICY 3: HIGH DIVIDEND (EQUITY ISSUE) Suppose Genron wants to pay

dividend larger than $2 per share right now, but it only has $20 million in cash today. Thus, Genron needs an additional $28

million to pay the larger dividend now. To do this, the firm decides to raise the cash by selling new shares.

ALTERNATIVE POLICY 3: HIGH DIVIDEND (EQUITY ISSUE) (CONT'D) Given a current share price of $42,

Genron could raise $28 million by selling 0.67 million shares. $28 million ÷ $42 per share = 0.67

million shares This will increase the total number of shares

to 10.67 million.

ALTERNATIVE POLICY 3: HIGH DIVIDEND (EQUITY ISSUE) (CONT'D) The new dividend per share will be

And the cum-dividend share price will be

Again, the share value is unchanged.

$48 million $4.50 per share10.67 million shares

4.50 4.50 4.50 37.50 $420.12cumP

MODIGLIANI–MILLER AND DIVIDEND POLICY IRRELEVANCE There is a trade-off between current

and future dividends. If Genron pays a higher current

dividend, future dividends will be lower. If Genron pays a lower current dividend,

future dividends will be higher.

TABLE 17.1 GENRON’S DIVIDENDS PER SHARE EACH YEAR UNDER THE THREE ALTERNATIVE POLICIES

MODIGLIANI–MILLER AND DIVIDEND POLICY IRRELEVANCE (CONT'D) MM Dividend Irrelevance

In perfect capital markets, holding fixed the investment policy of a firm, the firm’s choice of dividend policy is irrelevant and does not affect the initial share price.

DIVIDEND POLICY WITH PERFECT CAPITAL MARKETS A firm’s free cash flow determines

the level of payouts that it can make to its investors. In a perfect capital market, the type of

payout is irrelevant.

In reality, capital markets are not perfect and it is these imperfections that should determine the firm’s payout policy.

17.3 THE TAX DISADVANTAGE OF DIVIDENDS Taxes on Dividends and Capital Gains

Shareholders must pay taxes on the dividends they receive and they must also pay capital gains taxes when they sell their shares.

Dividends are typically taxed at a higher rate than capital gains. In fact, long-term investors can defer the capital gains tax forever by not selling.

TABLE 17.2 LONG-TERM CAPITAL GAINS VERSUS DIVIDEND TAX RATES IN THE UNITED STATES, 1971–2009

17.3 THE TAX DISADVANTAGE OF DIVIDENDS (CONT'D) Taxes on Dividends and Capital Gains

The higher tax rate on dividends makes it undesirable for a firm to raise funds to pay a dividend.

When dividends are taxed at a higher rate than capital gains, if a firm raises money by issuing shares and then gives that money back to shareholders as a dividend, shareholders are hurt because they will receive less than their initial investment.

EXAMPLE 17.2

ALTERNATIVE EXAMPLE 17.2 Problem

Assume: A firm raises $25 million from shareholders

and uses this cash to pay them $25 million in dividends.

Dividends are taxed at a 39% tax rate Capital gains are taxed at a 20% tax rate.

How much will shareholders receive after taxes?

ALTERNATIVE EXAMPLE 17.2 Solution

On dividends, shareholders will owe: 39% × $25 million = $9.75 million in

dividend taxes. Shareholders will lower their capital

gains taxes by: 20% × $25 million = $5 million

Note: The value of the firm will fall when the dividend is paid, lowering the shareholders’ capital gains.

ALTERNATIVE EXAMPLE 17.2 Solution (continued)

Shareholders will pay a total of $4.75 million in taxes.

$9.75 − $5.00 = $4.75 million Shareholders will receive back only

$20.25 million of their $25 million investment.

$25 − $4.75 = $20.25 million

OPTIMAL DIVIDEND POLICY WITH TAXES When the tax rate on dividends is

greater than the tax rate on capital gains, shareholders will pay lower taxes if a firm uses share repurchases rather than dividends. This tax savings will increase the value

of a firm that uses share repurchases rather than dividends.

OPTIMAL DIVIDEND POLICY WITH TAXES (CONT'D) The optimal dividend policy when the

dividend tax rate exceeds the capital gain tax rate is to pay no dividends at all. The payment of dividends has declined

on average over the last 30 years while the use of repurchases has increased.

FIGURE 17.4 THE DECLINE IN PAYOUTS AND THE USE OF DIVIDENDS

Source: Compustat.

FIGURE 17.5 THE CHANGING COMPOSITION OF SHAREHOLDER PAYOUTS

Source: Compustat data for U.S. firms, excluding financial firms and utilities.

OPTIMAL DIVIDEND POLICY WITH TAXES (CONT'D) Dividend Puzzle

When firms continue to issue dividends despite their tax disadvantage

17.4 DIVIDEND CAPTURE AND TAX CLIENTELES The preference for share repurchases

rather than dividends depends on the difference between the dividend tax rate and the capital gains tax rate. Tax rates vary by income, by

jurisdiction, and by whether the stock is held in a retirement account.

Given these differences, firms may attract different groups of investors depending on their dividend policy.

THE EFFECTIVE DIVIDEND TAX RATE Consider buying a stock just before it goes ex-

dividend and selling the stock just after. The equilibrium condition must be:

Which can be stated as

Where Pcum is the cum-dividend price, Pex is the ex-dividend price, g is the capital gains rate tax, d is the dividend tax rate.

( ) (1 ) (1 )cum ex g dP P Div

* 1 1 1

1 1 d

d gdcum ex

g g

P P Div Div Div

THE EFFECTIVE DIVIDEND TAX RATE (CONT'D) Thus, the effective dividend tax

rate is

This measures the additional tax paid by the investor per dollar of after-tax capital gains income that is instead received as a dividend.

*

1 d g

dg

EXAMPLE 17.3

TAX DIFFERENCES ACROSS INVESTORS The effective dividend tax rate differs

across investors for a variety of reasons. Income Level Investment Horizon Tax Jurisdiction Type of Investor or Investment Account

As a result of their different tax rates investors will have varying preferences regarding dividends.

CLIENTELE EFFECTS Clientele Effect

When the dividend policy of a firm reflects the tax preference of its investor clientele

Individuals in the highest tax brackets have a preference for stocks that pay no or low dividends, whereas tax-free investors and corporations have a preference for stocks with high dividends.

TABLE 17.3 DIFFERING DIVIDEND POLICY PREFERENCES ACROSS INVESTOR GROUPS

CLIENTELE EFFECTS (CONT'D) Dividend-Capture Theory

The theory that absent transaction costs, investors can trade shares at the time of the dividend so that non-taxed investors receive the dividend

An implication of this theory is that we should see large trading volume in a stock around the ex-dividend day, as high-tax investors sell and low-tax investors buy the stock in anticipation of the dividend, and then reverse those trades just after the ex-dividend date.

FIGURE 17.6 VOLUME AND SHARE PRICE EFFECTS OF VALUE LINE’S SPECIAL DIVIDEND

17.5 PAYOUT VERSUS RETENTION OF CASH In perfect capital markets, once a

firm has taken all positive-NPV investments, it is indifferent between saving excess cash and paying it out.

With market imperfections, there is a tradeoff: Retaining cash can reduce the costs of raising capital in the future, but it can also increase taxes and agency costs.

RETAINING CASH WITH PERFECT CAPITAL MARKETS If a firm has already taken all

positive-NPV projects, any additional projects it takes on are zero or negative-NPV investments. Rather than waste excess cash on

negative-NPV projects, a firm can use the cash to purchase financial assets.

In perfect capital markets, buying and selling securities is a zero-NPV transaction, so it should not affect firm value.

RETAINING CASH WITH PERFECT CAPITAL MARKETS (CONT'D)

Thus, with perfect capital markets, the retention versus payout decision is irrelevant.

EXAMPLE 17.4


Payne Enterprises has $20,000,000 in excess cash.

Payne is considering investing the cash in one-year Treasury bills paying 5% interest, and then using the cash to pay a dividend next year.

ALTERNATIVE EXAMPLE 17.4 Problem (continued)

Alternatively, the firm can pay a dividend immediately and shareholders can invest the cash on their own.

In a perfect capital market, which option will shareholders prefer?


If Payne pays an immediate dividend, the shareholders receive $20,000,000 today.

If Payne retains the cash, at the end of one year the company will be able to pay a dividend of $21,000,000.

$20,000,000 × (1.05) = $21,000,000

ALTERNATIVE EXAMPLE 17.4 Solution (continued)

If shareholders invest the $20,000,000 in Treasury bills themselves, they would have $21,000,000 at the end of 1 year.

$20,000,000 × (1.05) = $21,000,000 The present value in either scenario is:

$21,000,000 ÷ 1.05 = $20,000,000 Thus shareholders are indifferent about

whether the firm pays the dividend immediately or retains the cash.

RETAINING CASH WITH PERFECT CAPITAL MARKETS (CONT'D) MM Payout Irrelevance

In perfect capital markets, if a firm invests excess cash flows in financial securities, the firm’s choice of payout versus retention is irrelevant and does not affect the initial share price.

TAXES AND CASH RETENTION Corporate taxes make it costly for a

firm to retain excess cash. Cash is equivalent to negative leverage,

so the tax advantage of leverage implies a tax disadvantage to holding cash.

EXAMPLE 17.5


What if Payne, from Alternative Example 17.4, has a marginal tax rate of 39%. Would a tax-exempt endowment prefer that Payne use its excess cash to pay the dividend immediately or invest the cash in a Treasury bill paying 5% interest and then pay out a dividend?

ALTERNATIVE EXAMPLE 17.5 (CONT’D) Solution

If Payne pays a dividend today, shareholders receive $20,000,000. If Payne retains the cash for one year, it will earn an after-tax return on the Treasury bills of:

5% × (1 − 0.39) = 3.05% At the end of the year, Payne will pay a dividend

of $20,000,000 × (1.0305) = $20,610,000. This amount is less than the $21,000,000 the endowment would have earned if they had invested the $20,000,000 in the Treasury bills themselves.

EXAMPLE 17.6


What if Payne, from Alternative Examples 17.4 and 17.5, were to pay a special dividend of $20,000,000. How would this affect the present value of the taxes Payne must pay?


If Payne retains the $20,000,000 and invests in Treasury Bills, the interest will be taxed at 39%. The present value of the tax payments on Payne’s additional interest income will be:$20,000,000 5% 39% $7,800,000

5%

ADJUSTING FOR INVESTOR TAXES The decision to pay out versus retain

cash may also affect the taxes paid by shareholders. When a firm retains cash, it must pay

corporate tax on the interest it earns. In addition, the investor will owe capital gains tax on the increased value of the firm. In essence, the interest on retained cash is taxed twice.

ADJUSTING FOR INVESTOR TAXES (CONT'D)

If the firm paid the cash to its shareholders instead, they could invest it and be taxed only once on the interest that they earn.

The cost of retaining cash therefore depends on the combined effect of the corporate and capital gains taxes, compared to the single tax on interest income.

*1 1

1 1

c gretain

i

ISSUANCE AND DISTRESS COSTS Generally, firms retain cash balances

to cover potential future cash shortfalls, despite the tax disadvantage to retaining cash. A firm might accumulate a large cash

balance if there is a reasonable chance that future earnings will be insufficient to fund future positive-NPV investment opportunities.

ISSUANCE AND DISTRESS COSTS (CONT'D) The cost of holding cash to cover

future potential cash needs should be compared to the reduction in transaction, agency, and adverse selection costs of raising new capital through new debt or equity issues.

AGENCY COSTS OF RETAINING CASH When firms have excessive cash,

managers may use the funds inefficiently by paying excessive executive perks, over-paying for acquisitions, etc. Paying out excess cash through

dividends or share repurchases, rather than retaining cash, can boost the stock price by reducing managers’ ability and temptation to waste resources.

EXAMPLE 17.7

AGENCY COSTS OF RETAINING CASH (CONT'D) Firms should choose to retain to help

with future growth opportunities and to avoid financial distress costs. It is not surprising that high-tech and

biotechnology firms tend to retain and accumulate large amounts of cash.

TABLE 17.4 FIRMS WITH LARGE CASH BALANCES (APRIL 2009)

17.6 SIGNALING WITH PAYOUT POLICY Dividend Smoothing

The practice of maintaining relatively constant dividends

Firm change dividends infrequently and dividends are much less volatile than earnings.

FIGURE 17.7 GM’S EARNINGS AND DIVIDENDS PER SHARE, 1985–2008

Source: Compustat and CapitalIQ.

17.6 SIGNALING WITH PAYOUT POLICY (CONT'D) Research has found that

Management believes that investors prefer stable dividends with sustained growth.

Management desires to maintain a long-term target level of dividends as a fraction of earnings.

Thus, firms raise their dividends only when they perceive a long-term sustainable increase in the expected level of future earnings, and cut them only as a last resort.

DIVIDEND SIGNALING Dividend Signaling Hypothesis

The idea that dividend changes reflect managers’ views about a firm’s future earning prospects

If firms smooth dividends, the firm’s dividend choice will contain information regarding management’s expectations of future earnings.

DIVIDEND SIGNALING (CONT'D) When a firm increases its dividend, it

sends a positive signal to investors that management expects to be able to afford the higher dividend for the foreseeable future.

When a firm decreases its dividend, it may signal that management has given up hope that earnings will rebound in the near term and so need to reduce the dividend to save cash.

DIVIDEND SIGNALING (CONT'D) While an increase of a firm’s dividend may

signal management’s optimism regarding its future cash flows, it might also signal a lack of investment opportunities.

Conversely, a firm might cut its dividend to exploit new positive-NPV investment opportunities. In this case, the dividend decrease might lead

to a positive, rather than negative, stock price reaction.

SIGNALING AND SHARE REPURCHASES Share repurchases are a credible signal that

the shares are under-priced, because if they are over-priced a share repurchase is costly for current shareholders. If investors believe that managers have better

information regarding the firm’s prospects and act on behalf of current shareholders, then investors will react favorably to share repurchase announcements.

EXAMPLE 17.8

17.7 STOCK DIVIDENDS, SPLITS, AND SPIN-OFFS Stock Dividends and Splits

With a stock dividend, a firm does not pay out any cash to shareholders.

As a result, the total market value of the firm’s equity is unchanged. The only thing that is different is the number of shares outstanding.

The stock price will therefore fall because the same total equity value is now divided over a larger number of shares.

17.7 STOCK DIVIDENDS, SPLITS, AND SPIN-OFFS (CONT'D) Stock Dividends and Splits

Suppose Genron paid a 50% stock dividend (a 3:2 stock split) rather than a cash dividend.

A shareholder who owns 100 shares before the dividend has a portfolio worth $4,200.

$42 × 100 = $4,200. After the dividend, the shareholder owns 150

shares. Since the portfolio is still worth $4,200, the stock price will fall to $28.

$4,200 ÷ 150 = $28

TABLE 17.5 CUM- AND EX-DIVIDEND SHARE PRICE FOR GENRON WITH A 50% STOCK DIVIDEND ($ MILLION)


Stock dividends are not taxed, so from both the firm’s and shareholders’ perspectives, there is no real consequence to a stock dividend.

The number of shares is proportionally increased and the price per share is proportionally reduced so that there is no change in value.


The typical motivation for a stock split is to keep the share price in a range thought to be attractive to small investors.

If the share price rises “too high,” it might be difficult for small investors to invest in the stock.


Keeping the price “low” may make the stock more attractive to small investors and can increase the demand for and the liquidity of the stock, which may in turn boost the stock price.

On average, announcements of stock splits are associated with a 2% increase in the stock price.


Reverse Split When the price of a company’s stock falls

too low and the company reduces the number of outstanding shares

FIGURE 17.8 DISTRIBUTION OF STOCK PRICES FOR NYSE FIRMS (JUNE 2009)

SPIN-OFFS Spin-off

When a firm sells a subsidiary by selling shares in the subsidiary alone

Non-cash special dividends are commonly used to spin off assets or a subsidiary as a separate company.

SPIN-OFFS (CONT'D) Spin-offs offer two advantages

It avoids the transaction costs associated with a subsidiary sale.

The special dividend is not taxed as a cash distribution.

DISCUSSION OF DATA CASE KEY TOPIC If Congress were to pass legislation

eliminating the capital gains tax, what would be the impact on your analysis? What if taxes on dividends were eliminated instead?

How would your analysis change if capital gains and dividends were both taxed at the same rate as ordinary income?

QUIZ1. What is a targeted repurchase?2. How important is the firm’s decision to pay

dividends versus repurchase shares, assuming perfect capital markets?

3. What is “the dividend puzzle”?4. Why would investors have a tax preference for

share repurchases rather than dividends?5. Is there an advantage for a firm to retain its cash

instead of paying it out to shareholders in perfect capital markets? What if capital markets are not perfect?

QUIZ

6. What possible signals does a firm give when it cuts its dividend?

7. What is the difference between a stock dividend and a stock split?

8. Why would a firm initiate a reverse stock split?

LECTURE SIX – VALUING BONDSWednesday 24th April 2013

LEARNING OBJECTIVES1. Identify the cash flows for both coupon bonds

and zero-coupon bonds, and calculate the value for each type of bond.

2. Calculate the yield to maturity for both coupon and zero-coupon bonds, and interpret its meaning for each.

3. Given coupon rate and yield to maturity, determine whether a coupon bond will sell at a premium or a discount; describe the time path the bond’s price will follow as it approaches maturity, assuming prevailing interest rates remain the same over the life of the bond.

LEARNING OBJECTIVES4. Illustrate the change in bond price that will occur

as a result of changes in interest rates; differentiate between the effect of such a change on long-term versus short-term bonds.

5. Discuss the effect of coupon rate to the sensitivity of a bond price to changes in interest rates.

6. Define duration, and discuss its use by finance practitioners.

7. Calculate the price of a coupon bond using the Law of One Price and a series of zero-coupon bonds.

LEARNING OBJECTIVES8. Discuss the relation between a corporate bond’s

expected return and the yield to maturity; define default risk and explain how these rates incorporate default risk.

9. Assess the creditworthiness of a corporate bond using its bond rating; define default risk.

8.1 BOND CASH FLOWS, PRICES, AND YIELDS Bond Terminology

Bond Certificate States the terms of the bond

Maturity Date Final repayment date

Term The time remaining until the repayment date

Coupon Promised interest payments

8.1 BOND CASH FLOWS, PRICES, AND YIELDS (CONT'D) Bond Terminology

Face Value Notional amount used to compute the

interest payments Coupon Rate

Determines the amount of each coupon payment, expressed as an APR

Coupon PaymentCoupon Rate Face Value Number of Coupon Payments per Year

CPN

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.

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.

ZERO-COUPON BONDS (CONT'D) 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 (1 )

n

n

FVPYTM


For the one-year zero coupon bond:

Thus, the YTM is 3.5%.

1

100,00096,618.36 (1 )

YTM

1100,0001 1.035

96,618.36 YTM


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

1

1

n

nFVYTMP

EXAMPLE 8.1


Suppose that the following zero-coupon bonds are selling at the prices shown below per $100 face value. Determine the corresponding yield to maturity for each bond. Maturity 1 year 2 years 3 years 4 years

Price $98.04 $95.18 $91.51 $87.14

ALTERNATIVE EXAMPLE 8.1 (CONT'D) Solution:

1/2

1/3

1/4

YTM (100 / 98.04) 1 0.02 2%YTM (100 / 95.18) 1 0.025 2.5%YTM (100 / 91.51) 1 0.03 3%YTM (100 / 87.14) 1 0.035 3.5%

ZERO-COUPON BONDS (CONT'D) 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 n nr YTM

ZERO-COUPON BONDS (CONT'D) Risk-Free Interest Rates

Spot Interest Rate Another term for a default-free, zero-coupon

yield Zero-Coupon Yield Curve

A plot of the yield of risk-free zero-coupon bonds as a function of the bond’s maturity date

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

EXAMPLE 8.2

ALTERNATIVE EXAMPLE 8.2The U.S. Treasury has just issued a ten-year, $1000 bond with a 4% coupon and semi-annual coupon payments. What cash flows will you receive if you hold the bond until maturity?

ALTERNATIVE EXAMPLE 8.2 (CONT'D)

The face value of this bond is $1000. Because this bond pays coupons semiannually, from Eq. 8.1 you will receive a coupon payment every six months of CPN = $1000 X 4%/2 = $20. Here is the timeline, based on a six-month period:

Note that the last payment occurs ten years (twenty six-month periods) from now and is composed of both a coupon payment of $20 and the face value payment of $1000.

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 Bond1 1 1

(1 ) (1 )

N N

FVP CPNy y y

EXAMPLE 8.3

FINANCIAL CALCULATOR SOLUTION Since the bond pays interest semi-

annually, the calculator should be set to 2 periods per year.

N I/YR PV PMT FV

10

6

-957.35 1,00025

Gold P/YR2


Consider the following semi-annual bond:

$1000 par value 7 years until maturity 9% coupon rate Price is $1,080.55

What is the bond’s yield to maturity?


N = 7 years × 2 = 14 PMT = (9% × $1000) ÷ 2 = $45

Gold P/YR2

N I/YR PV PMT FV

14

7.5

-1,080.55 1,00045

EXAMPLE 8.4

FINANCIAL CALCULATOR SOLUTION Since the bond pays interest semi-

annually, the calculator should be set to 2 periods per year.

N I/YR PV PMT FV

10 6.3

-944.98

1,00025

Gold P/YR2


Consider the bond in the previous example.

Suppose its yield to maturity has increased to 10%

What is the bond’s new price?


N = 7 years × 2 = 14 PMT = (9% × $1000) ÷ 2 = $45

Gold P/YR2

N I/YR PV PMT FV

14 10

-950.51

1,00045

8.2 DYNAMIC BEHAVIOR OF BOND PRICES Discount

A bond is selling at a discount if the price is less than the face value.

Par A bond is selling at par if the price is

equal to the face value. Premium

A bond is selling at a premium if the price is greater than the face value.

DISCOUNTS AND PREMIUMS If a coupon bond trades at a

discount, an investor will earn a return both from receiving the coupons and from receiving a face value that exceeds the price paid for the bond. If a bond trades at a discount, its yield

to maturity will exceed its coupon rate.

DISCOUNTS AND PREMIUMS (CONT'D) If a coupon bond trades at a premium it will

earn a return from receiving the coupons but this return will be diminished by receiving a face value less than the price paid for the bond.

Most coupon bonds have a coupon rate so that the bonds will initially trade at, or very close to, par.

DISCOUNTS AND PREMIUMS (CONT'D)

Table 8.1 Bond Prices Immediately After a Coupon Payment

EXAMPLE 8.5

FINANCIAL CALCULATOR SOLUTION

N I/YR PV PMT FV

30 5

-176.86

10010

Gold P/YR1

FINANCIAL CALCULATOR SOLUTION (CONT'D)

N I/YR PV PMT FV

30 5

-100

1005

Gold P/YR1

FINANCIAL CALCULATOR SOLUTION (CONT'D)

N I/YR PV PMT FV

30 5

-69.26

1003

Gold P/YR1

TIME AND BOND PRICES Holding all other things constant, a

bond’s yield to maturity will not change over time.

Holding all other things constant, the price of discount or premium bond will move towards par value over time.

If a bond’s yield to maturity has not changed, then the IRR of an investment in the bond equals its yield to maturity even if you sell the bond early.

EXAMPLE 8.6

N I/YR PV PMT FV

30 5

-176.86

10010

FINANCIAL CALCULATOR SOLUTION Initial Price

FINANCIAL CALCULATOR SOLUTION (CONT'D) Price just after first coupon

Price just before first coupon $175.71 + $10 = $185.71

N I/YR PV PMT FV

29 5

-175.71

10010

FIGURE 8.1 THE EFFECT OF TIME ON BOND PRICES

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.

INTEREST RATE CHANGES AND BOND PRICES (CONT'D) The sensitivity of a bond’s price to

changes in interest rates is measured by the bond’s duration. Bonds with high durations are highly

sensitive to interest rate changes. Bonds with low durations are less

sensitive to interest rate changes.

EXAMPLE 8.7

FIGURE 8.2 YIELD TO MATURITY AND BOND PRICE FLUCTUATIONS OVER TIME

8.3 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.

REPLICATING A COUPON BOND Replicating a three-year $1000 bond

that pays 10% annual coupon using three zero-coupon bonds:

REPLICATING A COUPON BOND (CONT'D) Yields and Prices (per $100 Face

Value) for Zero Coupon BondsTable 8.2 Yields and Prices (per $100 Face Value) for Zero-Coupon Bonds

REPLICATING A COUPON BOND (CONT'D)

By the Law of One Price, the three-year coupon bond must trade for a price of $1153.

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

21 2

(Bond Cash Flows) V

1 (1 ) (1 )

nn

PV PVCPN CPN CPN F

YTM 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.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


N I/YR PV PMT FV

3

4.44

-1153 1000100

Gold P/YR1

EXAMPLE 8.8


N I/YR PV PMT FV

3

4.47

-986.98 100040

Gold P/YR1

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.

8.4 CORPORATE BONDS Corporate Bonds

Issued by corporations Credit Risk

Risk of default

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.

CORPORATE BOND YIELDS (CONT'D) No Default

Consider a 1-year, zero coupon Treasury Bill with a YTM of 4%.

What is the price?

N I/YR PV PMT FV

1 4

-961.54

1000

1

1000 1000 $961.541 1.04

PYTM

CORPORATE BOND YIELDS (CONT'D) Certain Default

Suppose now bond issuer will pay 90% of the obligation.

What is the price?

N I/YR PV PMT FV

1 4

-865.38

900

1

900 900 $865.381 1.04

PYTM


When computing the yield to maturity for a bond with certain default, the promised rather than the actual cash flows are used. 1000 1 1 15.56%

865.38

FVYTMP

900 1.04865.38


The yield to maturity of a certain default bond is not equal to the expected return of investing in the bond. The yield to maturity will always be higher than the expected return of investing in the bond.

CORPORATE BOND YIELDS (CONT'D) Risk of Default

Consider a one-year, $1000, zero-coupon bond issued. Assume that the bond payoffs are uncertain.

There is a 50% chance that the bond will repay its face value in full and a 50% chance that the bond will default and you will receive $900. Thus, you would expect to receive $950.

Because of the uncertainty, the discount rate is 5.1%.


The price of the bond will be

The yield to maturity will be

950 $903.901.051

P

1000 1 1 .1063903.90

FVYTMP


A bond’s expected return will be less than the yield to maturity if there is a risk of default.

A higher yield to maturity does not necessarily imply that a bond’s expected return is higher.

CORPORATE BOND YIELDS (CONT'D)

Table 8.3 Price, Expected Return, and Yield to Maturity of a One-Year, Zero-Coupon Avant Bond with Different Likelihoods of Default

BOND RATINGS Investment Grade Bonds Speculative Bonds

Also known as Junk Bonds or High-Yield Bonds

Table 8.4 Bond Ratings

Table 8.4 Bond Ratings (cont’d)

CORPORATE YIELD CURVES Default Spread

Also known as Credit Spread The difference between the yield on

corporate bonds and Treasury yields

FIGURE 8.3 CORPORATE YIELD CURVES FOR VARIOUS RATINGS, FEBRUARY 2009

Source: Reuters

FIGURE 8.4 YIELD SPREADS AND THE FINANCIAL CRISIS

Source: Bloomberg.com

DISCUSSION OF DATA CASE KEY TOPIC

Look at the Financial Industry Regulatory Authority’s website. What bond issues does Sirius Satellite Radio (ticker: SIRI) currently have outstanding? What are their yields? What are their ratings?

Source: FINRA

http://cxa.marketwatch.com/finra/bondcenter/default.aspx

QUIZ1. What is the relationship between a bond’s price and

its yield to maturity?2. If a bond’s yield to maturity does not change, how

does its cash price change between coupon payments?

3. How does a bond’s coupon rate affect its duration – the bond price’s sensitivity to interest rate changes?

4. Explain why two coupon bonds with the same maturity may each have a different yield to maturity.

5. There are two reasons the yield of a defaultable bond exceeds the yield of an otherwise identical default-free bond. What are they?

Copyright © 2011 Pearson Education. All rights reserved.

8

Appendix

FORWARD INTEREST RATES 8A.1 Computing Forward Rates

A forward interest rate (or forward rate) is an interest rate that we can guarantee today for a loan or investment that will occur in the future.

In this , we consider interest rate forward contracts for one-year investments, so the forward rate for year 5 means the rate available today on a one-year investment that begins four years from today.

COMPUTING FORWARD RATES By the Law of one price, the forward

rate for year 1 is equivalent to an investment in a one-year, zero-coupon bond.

1 1f YTM

COMPUTING FORWARD RATES Consider a two-year forward rate. Suppose the one-year, zero-coupon yield is 5.5%

and the two-year, zero-coupon yield is 7.0%. We can invest in the two-year, zero-coupon bond

at 7.0% and earn $(1.07)2 after two years. Or, we can invest in the one-year bond and earn

$1.055 at the end of the year. We can simultaneously enter into a one-year interest rate forward contract for year 2 at a rate of f2.

COMPUTING FORWARD RATES At then end of two years, we will

have $(1.055)(1+f2). Since both strategies are risk free, by

the Law of One Price they should have the same return:2

2(1.07) (1.055)(1 )f

COMPUTING FORWARD RATES

Rearranging, we have:

The forward rate for year 2 is f2=8.52%.

2

2

1.07(1 ) 1.08521.055

f

COMPUTING FORWARD RATES

In general:

Rearranging, we get the general formula for the forward interest rate:

(1 ) (1 ) (1 )n n-1n n-1 nYTM YTM f

11

1 -11

nn

n n-n-

( +YTM )f =( +YTM )

EXAMPLE 8A.1

EXAMPLE 8A.1 (CONT’D)

8A.2 COMPUTING BOND YIELDS FROM FORWARD RATES It is also possible to compute the zero-coupon

yields from the forward interest rates:

For example, using the forward rates from Example 8A.1, the four-year zero-coupon yield is:

(1 ) (1 ) ... (1 ) (1 )n1 2 n nf f f YTM

14

4 1 2 3 4

14

1 (1 )(1 )(1 )(1 )

(1.05)(1.0701)(1.06)(1.05)1.0575

YTM f f f f

8A.3 FORWARD RATES AND FUTURE INTEREST RATES How does the forward rate compare

to the interest rate that will actually prevail in the future?

It is a good predictor only when investors do not care about risk.

EXAMPLE 8A.2

EXAMPLE 8A.2 (CONT’D)

FORWARD RATES AND FUTURE INTEREST RATES We can think of the forward rate as a

break-even rate. Since investors do care about risk:

Expected Future Spot Interest Rate = Forward Interest Rate + Risk Premium

LECTURE SEVEN – VALUING SHARESThursday 25th April 2013

LEARNING OBJECTIVES1. Describe, in words, the Law of One Price value for a

common stock, including the discount rate that should be used.

2. Calculate the total return of a stock, given the dividend payment, the current price, and the previous price.

3. Use the dividend-discount model to compute the value of a dividend-paying company’s stock, whether the dividends grow at a constant rate starting now or at some time in the future.

4. Discuss the determinants of future dividends and growth rate in dividends, and the sensitivity of the stock price to estimates of those two factors.

LEARNING OBJECTIVES (CONT'D)5. Given the retention rate and the return on new investment,

calculate the growth rate in dividends, earnings, and share price.6. Describe circumstances in which cutting the firm’s dividend will

raise the stock price.7. Assuming a firm has a long-term constant growth rate after time

N + 1, use the constant growth model to calculate the terminal value of the stock at time N.

8. Compute the stock value of a firm that pays dividends as well as repurchasing shares.

9. Use the discounted free cash flow model to calculate the value of stock in a company with leverage.

10. Use comparable firm multiples to estimate stock value.

LEARNING OBJECTIVES (CONT'D)11. Explain why several valuation models are required to

value a stock.12. Describe the impact of efficient markets hypothesis on

positive-NPV trades by individuals with no inside information.

13. Discuss why investors who identify positive-NPV trades should be skeptical about their findings, unless they have inside information or a competitive advantage. As part of that, describe the return the average investor should expect to get.

14. Assess the impact of stock valuation on recommended managerial actions.

9.1 THE DIVIDEND DISCOUNT MODEL 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.

9.1 THE DIVIDEND DISCOUNT MODEL (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.

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.

1 01 1 1

0 0 0

Dividend Yield Capital Gain Rate

1 E

P PDiv P DivrP P P

EXAMPLE 9.1


3M (MMM) is expected to pay paid dividends of $1.92 per share in the coming year.

You expect the stock price to be $85 per share at the end of the year.

Investments with equivalent risk have an expected return of 11%.

What is the most you would pay today for 3M stock?

What dividend yield and capital gain rate would you expect at this price?


Total Return = 2.45% + 8.54% = 10.99% ≈ 11%

1 10

E

$1.92 $85 $78.31(1 ) (1 .11)

Div PP

r

1

0

$1.92Dividend Yield 2.45%$78.31

Div

P

1 0

0

$85.00 $78.31Capital Gains Yield 8.54%$78.31

P PP

A MULTI-YEAR INVESTOR What is the price if we plan on

holding the stock for two years?

1 2 20 2

E E

1 (1 )

Div Div PP

r r

THE DIVIDEND-DISCOUNT MODEL EQUATION What is the price if we plan on holding the

stock for N years?

This is known as the Dividend Discount Model. Note that the above equation (9.4) holds for any

horizon N. Thus all investors (with the same beliefs) will attach the same value to the stock, independent of their investment horizons.

1 20 2

E E E E

1 (1 ) (1 ) (1 )

N NN N

Div PDiv DivPr r r r

THE DIVIDEND-DISCOUNT MODEL EQUATION (CONT'D)

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

31 20 2 3

1E E E E

1 (1 ) (1 ) (1 )

n

nn

Div DivDiv DivPr r r r

9.2 APPLYING 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.

9.2 APPLYING 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.

10

E

DivPr g

1E

0

Divr gP

EXAMPLE 9.2


AT&T plans to pay $1.44 per share in dividends in the coming year.

Its equity cost of capital is 8%. Dividends are expected to grow by 4%

per year in the future.

Estimate the value of AT&T’s stock.


10

E

$1.44 $36.00 .08 .04

DivPr g

DIVIDENDS VERSUS INVESTMENT AND GROWTH A Simple Model of Growth

Dividend Payout Ratio The fraction of earnings paid as dividends

each year

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


A firm can do one of two things with its earnings:

It can pay them out to investors. It can retain and reinvest them.


Retention Rate Fraction of current earnings that the firm

retains

Change in Earnings New Investment Return on New Investment

New Investment Earnings Retention Rate


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

Change in EarningsEarnings Growth Rate Earnings

Retention Rate Return on New Investment

Retention Rate Return on New Investment g

DIVIDENDS VERSUS INVESTMENT AND GROWTH (CONT'D) 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.

EXAMPLE 9.3

EXAMPLE 9.4


Dren Industries is considering expanding into a new product line. Earnings per share are expected to be $5 in the coming year and are expected to grow annually at 5% without the new product line but growth would increase to 7% if the new product line is introduced. To finance the expansion, Dren would need to cut its dividend payout ratio from 80% to 50%. If Dren’s equity cost of capital is 11%, what would be the impact on Dren’s stock price if they introduce the new product line? Assume the equity cost of capital will remain unchanged.


First, calculate the current price for Dren if they do not introduce the new product. To calculate the price, D1 is needed. To find D1, EPS1 is required:EPS1 = EPS0 × (1 + g) = $5.00 × 1.05 =

$5.25D1 = EPS1 × Payout Ratio = $5.25 × 0.8 =

$4.20 P0 = D1/(rE-g) = $4.20/(.11 - .05) = $70.00 Thus, the current price without the new

product should be $70 per share.

ALTERNATIVE EXAMPLE 9.4 (CONT’D)

Solution Next, calculate the expected current price

for Dren if they introduce the new product:EPS1 = EPS0 × (1 + g) = $5.00 × 1.07 =

$5.35D1 = EPS1 × Payout Ratio = $5.35 × 0.50 =

$2.675 P0 = D1/(rE-g) = $2.675/(.11 - .07) = $66.875 Thus, the current price is expected to fall

from $70 to $66.875 if the new product line is introduced.

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.

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.

CHANGING GROWTH RATES (CONT'D)

Dividend-Discount Model with Constant Long-Term Growth

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 9.5

LIMITATIONS OF THE DIVIDEND-DISCOUNT MODEL There is a tremendous amount of

uncertainty associated with forecasting a firm’s dividend growth rate and future dividends.

Small changes in the assumed dividend growth rate can lead to large changes in the estimated stock price.

9.3 TOTAL PAYOUT AND FREE CASH FLOW VALUATION MODELS Share Repurchases and the Total

Payout Model Share Repurchase

When the firm uses excess cash to buy back its own stock

Implications for the Dividend-Discount Model

The more cash the firm uses to repurchase shares, the less it has available to pay dividends.

By repurchasing, the firm decreases the number of shares outstanding, which increases its earnings per and dividends per share.

9.3 TOTAL PAYOUT AND FREE CASH FLOW VALUATION MODELS (CONT'D) Share Repurchases and the Total

Payout Model0 (Future Dividends per Share)PV PV

9.3 TOTAL PAYOUT AND FREE CASH FLOW VALUATION MODELS (CONT'D) Share Repurchases and the Total Payout Model

Total Payout Model

Values all of the firm’s equity, rather than a single share. You discount total dividends and share repurchases and use the growth rate of earnings (rather than earnings per share) when forecasting the growth of the firm’s total payouts.

00

(Future Total Dividends and Repurchases) Shares Outstanding

PVPV

EXAMPLE 9.6

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

THE DISCOUNTED FREE CASH FLOW MODEL (CONT'D) Valuing the Enterprise

Free Cash Flow Cash flow available to pay both debt holders

and equity holders

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

THE DISCOUNTED FREE CASH FLOW MODEL (CONT'D) 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.

THE DISCOUNTED FREE CASH FLOW MODEL (CONT'D) 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 FCFr g r g

EXAMPLE 9.7

THE DISCOUNTED FREE CASH FLOW MODEL (CONT'D) 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.

EXAMPLE 9.8

FIGURE 9.1 A COMPARISON OF DISCOUNTED CASH FLOW MODELS OF STOCK VALUATION

9.4 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.

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

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

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

EXAMPLE 9.9


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.


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

VALUATION MULTIPLES (CONT'D) Enterprise Value Multiples

This valuation multiple is higher for firms with high growth rates and low capital requirements (so that free cash flow is high in proportion to EBITDA).

0 1 1

1

/

wacc FCF

V FCF EBITDAEBITDA r g

EXAMPLE 9.10


Best Buy Co. Inc. (BBY) has EBITDA of $2,766,000,000 and 410 million shares outstanding.

Best Buy also has $1,963,000,000 in debt and $509,000,000 in cash.

If Best Buy has an enterprise value to EBITDA multiple of 7.7, estimate the value for a share of Best Buy stock.


Using the enterprise value to EBITDA multiple, Best Buy’s enterprise value is $2,766 million × 7.7 = $21,298.20 million.

Subtract out the debt, add the cash and divide by the number of shares to estimate the Best Buy’s share price.0

$21, 298.2 $1,963 $509 $48.40410

P

VALUATION MULTIPLES (CONT'D) Other Multiples

Multiple of sales Price to book value of equity per share Enterprise value per subscriber

Used in cable TV industry

LIMITATIONS OF MULTIPLES When valuing a firm using multiples,

there is no clear guidance about how to adjust for differences in expected future growth rates, risk, or differences in accounting policies.

Comparables only provide information regarding the value of a firm relative to other firms in the comparison set. Using multiples will not help us

determine if an entire industry is overvalued,

COMPARISON WITH DISCOUNTED CASH FLOW METHODS Discounted cash flows methods have

the advantage that they can incorporate specific information about the firm’s cost of capital or future growth. The discounted cash flow methods have

the potential to be more accurate than the use of a valuation multiple.

Table 9.1 Stock Prices and Multiples for the Footwear Industry, January 2006

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.

FIGURE 9.2 RANGE OF VALUATION METHODS FOR KCP STOCK USING ALTERNATIVE VALUATION METHODS

9.5 INFORMATION, COMPETITION, AND STOCK PRICES Information in Stock Prices

Our valuation model links the firm’s future cash flows, its cost of capital, and its share price. Given accurate information about any two of these variables, a valuation model allows us to make inferences about the third variable.

FIGURE 9.3 THE VALUATION TRIAD

9.5 INFORMATION, COMPETITION, AND STOCK PRICES (CONT'D) Information in Stock Prices

For a publicly traded firm, its current stock price should already provide very accurate information, aggregated from a multitude of investors, regarding the true value of its shares.

Based on its current stock price, a valuation model will tell us something about the firm’s future cash flows or cost of capital.

EXAMPLE 9.11

COMPETITION AND EFFICIENT MARKETS Efficient Markets Hypothesis

Implies that securities will be fairly priced, based on their future cash flows, given all information that is available to investors.

COMPETITION AND EFFICIENT MARKETS (CONT'D) Public, Easily Interpretable

Information If the impact of information that is

available to all investors (news reports, financials statements, etc.) on the firm’s future cash flows can be readily ascertained, then all investors can determine the effect of this information on the firm’s value.

In this situation, we expect the stock price to react nearly instantaneously to such news.

EXAMPLE 9.12

COMPETITION AND EFFICIENT MARKETS (CONT'D) Private or Difficult-to-Interpret

Information Private information will be held by a

relatively small number of investors. These investors may be able to profit by trading on their information.

In this case, the efficient markets hypothesis will not hold in the strict sense. However, as these informed traders begin to trade, they will tend to move prices, so over time prices will begin to reflect their information as well.

COMPETITION AND EFFICIENT MARKETS (CONT'D) Private or Difficult-to-Interpret

Information If the profit opportunities from having

private information are large, others will devote the resources needed to acquire it.

In the long run, we should expect that the degree of “inefficiency” in the market will be limited by the costs of obtaining the private information.

EXAMPLE 9.13

EXAMPLE 9.13 (CONT’D)FIGURE 9.4 POSSIBLE STOCK PRICE PATHS

LESSONS FOR INVESTORS AND CORPORATE MANAGERS Consequences for Investors

If stocks are fairly priced, then investors who buy stocks can expect to receive future cash flows that fairly compensate them for the risk of their investment.

In such cases the average investor can invest with confidence, even if he is not fully informed.

LESSONS FOR INVESTORS AND CORPORATE MANAGERS (CONT'D) Implications for Corporate Managers

Focus on NPV and free cash flow Avoid accounting illusions Use financial transactions to support

investment

THE EFFICIENT MARKETS HYPOTHESIS VERSUS NO ARBITRAGE The efficient markets hypothesis

states that securities with equivalent risk should have the same expected return.

An arbitrage opportunity is a situation in which two securities with identical cash flows have different prices.

DISCUSSION OF DATA CASE KEY TOPIC How do the assumptions regarding

the cost of equity, cost of debt, and expected return on investments impact your decision?

How sensitive are your estimates for GE’s stock price and enterprise value to these assumptions?

QUIZ1. What discount rate do you use to discount

the future cash flows of a stock?2. Does an investor’s expected holding period

affect the amount they would be willing to pay for a stock?

3. How can a firm increase its future dividend per share?

4. What is the enterprise value of a firm?5. What are the implicit assumptions made

when valuing a firm using multiples?

QUIZ

6. What is the efficient market hypothesis? What are its implications for corporate managers?

lecture five – the dividend decision

Documents

dividend policy

dividend decisiontuesday

dividend history

shares of stock

effect of dividend payment

dividend payment process

firm mails dividend

dividend decision lecture