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
EXAMPLE 17.2 (CONT'D)
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
EXAMPLE 17.3 (CONT'D)
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
EXAMPLE 17.4 (CONT'D)
ALTERNATIVE EXAMPLE 17.4 Problem
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?
ALTERNATIVE EXAMPLE 17.4 Solution
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
EXAMPLE 17.5 (CONT'D)
ALTERNATIVE EXAMPLE 17.5 Problem
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
EXAMPLE 17.6
ALTERNATIVE EXAMPLE 17.6 Problem
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?
ALTERNATIVE EXAMPLE 17.6 (CONT’D) Solution
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
EXAMPLE 17.7 (CONT'D)
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
EXAMPLE 17.8 (CONT'D)
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)
17.7 STOCK DIVIDENDS, SPLITS, AND SPIN-OFFS (CONT'D) Stock Dividends and Splits
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.
17.7 STOCK DIVIDENDS, SPLITS, AND SPIN-OFFS (CONT'D) Stock Dividends and Splits
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.
17.7 STOCK DIVIDENDS, SPLITS, AND SPIN-OFFS (CONT'D) Stock Dividends and Splits
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.
17.7 STOCK DIVIDENDS, SPLITS, AND SPIN-OFFS (CONT'D) Stock Dividends and Splits
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
ZERO-COUPON BONDS (CONT'D) Yield to Maturity
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
ZERO-COUPON BONDS (CONT'D) Yield to Maturity
Yield to Maturity of an n-Year Zero-Coupon Bond
1
1
n
nFVYTMP
EXAMPLE 8.1
EXAMPLE 8.1 (CONT'D)
ALTERNATIVE EXAMPLE 8.1 Problem
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
EXAMPLE 8.2 (CONT'D)
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
EXAMPLE 8.3 (CONT'D)
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
ALTERNATIVE EXAMPLE 8.3 Problem
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?
ALTERNATIVE EXAMPLE 8.3 Solution
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
EXAMPLE 8.4 (CONT'D)
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
ALTERNATIVE EXAMPLE 8.4 Problem
Consider the bond in the previous example.
Suppose its yield to maturity has increased to 10%
What is the bond’s new price?
ALTERNATIVE EXAMPLE 8.4 Solution
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
EXAMPLE 8.5 (CONT'D)
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
EXAMPLE 8.6 (CONT'D)
EXAMPLE 8.6 (CONT'D)
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
EXAMPLE 8.7 (CONT'D)
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
FINANCIAL CALCULATOR SOLUTION
N I/YR PV PMT FV
3
4.44
-1153 1000100
Gold P/YR1
EXAMPLE 8.8
EXAMPLE 8.8 (CONT'D)
FINANCIAL CALCULATOR SOLUTION
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
CORPORATE BOND YIELDS (CONT'D) Certain Default
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
CORPORATE BOND YIELDS (CONT'D) Certain Default
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%.
CORPORATE BOND YIELDS (CONT'D) Risk of Default
The price of the bond will be
The yield to maturity will be
950 $903.901.051
P
1000 1 1 .1063903.90
FVYTMP
CORPORATE BOND YIELDS (CONT'D) Risk of Default
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
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
EXAMPLE 9.1 (CONT'D)
ALTERNATIVE EXAMPLE 9.1 Problem
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?
ALTERNATIVE EXAMPLE 9.1 Solution
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
EXAMPLE 9.2 (CONT'D)
ALTERNATIVE EXAMPLE 9.2 Problem
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.
ALTERNATIVE EXAMPLE 9.2 Solution
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
DIVIDENDS VERSUS INVESTMENT AND GROWTH (CONT'D) 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.
DIVIDENDS VERSUS INVESTMENT AND GROWTH (CONT'D) A Simple Model of Growth
Retention Rate Fraction of current earnings that the firm
retains
Change in Earnings New Investment Return on New Investment
New Investment Earnings Retention Rate
DIVIDENDS VERSUS INVESTMENT AND GROWTH (CONT'D) 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.
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 9.3 (CONT'D)
EXAMPLE 9.4
EXAMPLE 9.4 (CONT'D)
ALTERNATIVE EXAMPLE 9.4 Problem
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.
ALTERNATIVE EXAMPLE 9.4 (CONT’D) Solution
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
EXAMPLE 9.5 (CONT'D)
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
EXAMPLE 9.6 (CONT'D)
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
EXAMPLE 9.7 (CONT'D)
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
EXAMPLE 9.8 (CONT'D)
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
EXAMPLE 9.9 (CONT'D)
ALTERNATIVE EXAMPLE 9.9 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.
ALTERNATIVE EXAMPLE 9.9 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
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
EXAMPLE 9.10 (CONT'D)
ALTERNATIVE EXAMPLE 9.10 Problem
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.
ALTERNATIVE EXAMPLE 9.10 Solution
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
EXAMPLE 9.11 (CONT'D)
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
EXAMPLE 9.12 (CONT'D)
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)
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?