Solution fundamentals of corporate finance brealy 4th chapter text solutions ch 6

The stock price today can still reflect the present value of the expected per share stream of dividends.. The value of a common stock equals the present value of dividends received out t

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Solutions to Chapter 6 Valuing Stocks

1. No The dividend discount model allows for the fact that firms may not currently

pay dividends As the market matures, and Rogers Wireless Communication’s growth opportunities moderate, investors may justifiably believe that Rogers Wireless will enjoy high future earnings and will pay dividends then The stock price today can still reflect the present value of the expected per share stream of dividends

2. Dividend yield = Expected dividend/Price = DIV1/P0

So: P0 = DIV1/dividend yield

P0 = $2.4/.08 = $30

3 a The typical preferred stock pays a level perpetuity of dividends The expected

dividend next year is the same as this year’s dividend, $7 Thus the dividend growth rate is zero and the price today is:

P0 = D1/r = 7/.12 = $58.33

b The expected dividend in two years is this year’s dividend, $7

P1= D2/r = 7/.12 = $58.33

c Dividend yield = $7/$58.33 = 12 =12%

Expected capital gains = 0

Expected rate of return = 12%

4 r = DIV1/P0 + g = 8% + 5% = 13%

5 The value of a common stock equals the present value of dividends received out

to the investment horizon, plus the present value of the forecast stock price at the horizon But the stock price at the horizon date depends on expectations of

dividends from that date forward So even if an investor plans to hold a stock for only a year for two, the price ultimately received from another investor depends

on dividends to be paid after the date of purchase Therefore, the stock’s present value is the same for investors with different time horizons

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6 a P0 =  r = + g

r = + 04 = 14 = 14%

b P0 = 2.50/(.165  04) = $20

7 The dividend yield is defined as the annual dividend (or the annualized current

dividend) divided by the current price The current annual dividend is ($2  4) = $8 and the dividend yield is:

DIV1/P0 = 048  $8/ P0 = 048  P0 = $8/.048 = $166.7

To work with the quarterly dividend, divide the dividend yield by 4 and repeat the above steps:

Quarterly DIV/P0 = 048/4 = 012  $2/ P0 = 012 P0 = $2/.012 = $166.7

8 Weak, semi-strong, strong, fundamental, technical

9 True The search for information and insightful analysis is what makes investor

assessments of stock values as reliable as possible Since the rewards accrue to the

investors who uncover relevant information before it is reflected in stock prices,

competition among these investors means that there is always an active search on for mispriced stocks

10 a DIV1 = $1  1.04 = $1.04

DIV2 = $1  1.042 = $1.0816

DIV3 = $1  1.043 = $1.1249

b P0 = DIV1/(r  g) = = $13

c P3 = DIV4/(r  g) = = $14.6237

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d Your payments are:

Sum of PV = $13.00, the same as your answer to (b)

11 Dividend growth rate, g = return on equity × plowback ratio:

g = 15  40 = 06

r = + g = + 06 = 16 = 16%

12 a P0 = = = $21

P0 = = $30

The lower discount rate makes the present value of future dividends higher, raising the value of the stock

13 r = + g  g = r - = 14 – = 04 = 4%

14 a r = + g = + 03 = 0926 = 9.26%

b If r = 10, then 10 = 1.64(1.03)/27 + g So g = 0374 = 3.74%

c g = Return on equity  plowback ratio

5% = Return on equity  4

Return on equity = = = 12.5%

15 P0 = DIV1/(r  g)

= $2/(.12 – 06) = $33.33

16 a P0 = DIV1/(r  g) = 3/[.15 – (.10)] = 3/.25 = $12

b P1 = DIV2/(r  g) = 3(1  10)/.25 = $10.80

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c return = = = 150 = 15.0%

d “Bad” companies may be declining, but if the stock price already reflects this fact, the investor still can earn a fair rate of return, as we saw in part c

17 a (i) reinvest 0% of earnings: g = 0 and DIV1 = $5:

P0 = = = $33.33 (ii) reinvest 40%: g = 15%  40 = 6% and DIV1 = $5  (1 – 40) = $3:

P0 = $3/(.15 – 06) = $33.33 (iii) reinvest 60%: g = 15%  60 = 9% and DIV1 = $5  (1 – 60) = $2:

P0 = 2/(.15 – 09) = $33.33

b (i) reinvest 0%: P0 = 5/(.15 – 0) = $33.33

PVGO = $0 (ii) reinvest 40%: P0 = = $42.86

PVGO = $42.86 – $33.33 = $9.53 (iii) reinvest 60%: P0 = = $66.67

PVGO = $66.67 – $33.33 = $33.34

c In part (a), the return on reinvested earnings is equal to the discount rate

Therefore, the NPV of the firm’s new projects is zero, and PVGO is zero in all cases, regardless of the reinvestment rate While higher reinvestment results in higher growth rates, it does not result in a higher value of growth

opportunities This example illustrates that there is a difference between

growth and growth opportunities

In part (b), the return on reinvested earnings is greater than the discount rate Therefore, the NPV of the firm’s new projects is positive, and PVGO is

positive PVGO is higher when the reinvestment rate is higher in this case, since the firm is taking greater advantage of its opportunities to invest in

positive NPV projects

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18 Stock exchange information

Tips: When accessing stock exchange information at www.fibv.com, you don’t actually click on “Member” but rather place your cursor on the word You click on the region and stock exchange of interest Also, remind the students to click on the symbol of the stock exchange to connect to the Web site of that exchange

Expected results: Students learn about variety of stock exchanges around the world and the types of information provided

19 Hollywood stock exchange

Expected result: A fun experience trading securities

20 a P0 = + + = 18.10

b DIV1/P0 = $1/18.10 = 0552 = 5.52%

21 Stock A Stock B

b g = ROE  plowback 15%  5 = 7.5% 10%  333 = 3.33%

Note: We interpret “recent” to mean in the past The current stock price

depends on future dividends – so the next dividend must be 1 + g times higher

22 a ROE  plowback ratio = 20%  3 = 6%

b E = $2, plowback ratio = 3, r = 12, g = 06  P0 = = $23.33

c No-growth value = E/r = $2/.12 = $16.67

PVGO = P0  no-growth value = $23.33  $16.67 = $6.66

d P/E = 23.33/2 = 11.665

e If all earnings were paid as dividends, price would equal the no-growth value,

$16.67, and P/E would be 16.67/2 = 8.335

f High P/E ratios reflect expectations of high PVGO

23 a =$60

b No-growth value = E/r = $6.20/.12 = $51.67

PVGO = P0  no-growth value = $60  51.67 = $8.33

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24 a Earnings = DIV1 = $4 Growth rate g = 0.

P0 = = $33.33

P/E = 33.33/4 = 8.33

b If r = 10, P0 = = 40, and P/E increases to 40/4 = 10

A decrease in the required rate of return, holding dividends constant, raises the stock price and the P/E ratio

25 a Plowback ratio = 0 implies DIV1 = $3 and g = 0

Therefore, P0 = = $30

and the P/E ratio is 30/3 = 10

b Plowback ratio = 40 implies DIV1 = $3(1 – 40) = $1.80, and g = 10%  40 = 4%

Therefore P0 = $1.80/(.10 – 04) = $30

c Plowback ratio = 80 implies DIV1 = $3(1 – 80) = $.60, and g = 10%  80 = 8% Therefore P0 = $.60/(.10 – 08) = $30

Regardless of the plowback ratio, the stock price = $30 because all projects

offer return on equity just equal to the opportunity cost of capital

26 a P0 = DIV1/(r  g) = $5/(.10 – 06) = $125

b If Trendline followed a zero-plowback strategy, it could pay a perpetual

dividend of $8 Its value would be $8/.10 = $80, and therefore, the value of

assets in place is $80 The remainder of its value must be due to growth

opportunities, so PVGO = $125 – $80 = $45

27 a g = 20%  30 = 6%

DIV1 = $2(1 – 30) = $1.40

P0 = DIV1/(r  g) = $1.40/(.12  06) = $23.33

P/E = 23.33/2 = 11.665

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b If the plowback ratio is reduced to 20, g = 20%  20 = 4%

DIV1 = $2(1 – 20) = $1.60

P0 = DIV1/(r  g) = $1.60/(.12 – 04) = 20

P/E = 20/2 = 10

P/E falls because the firm’s value of growth opportunities is now lower: It takes less advantage of its attractive investment opportunities

c If the plowback ratio = 0, g = 0, and DIV1 = $2,

P0 = $2/.12 = 16.67 and E/P = 2/16.67 = 12

DIV2 = 2(1.20) = 2.40 PV = 2.40/1.102 = 1.983

DIV3 = 2(1.20)2 = 2.88 PV = 2.88/1.103 = 2.164

b This could not continue indefinitely If it did, the stock would be worth an infinite amount Another way to think about the feasible perpetual growth rate

is to compare the company’s growth rate with the growth rate of the economy The economy grows about 3% a year To grow faster than the economy as a whole is feasible when the company is small However, to continue to grow at 20%, the company must take over other companies and eventually become the entire economy But in the long run, it still can only grow as quickly as the entire economy So it is impossible to grow at 20% in perpetuity Think about Microsoft – it has had phenomenal growth partly by acquiring other

companies and partly by growing its own businesses However, even if it were

to own all of the companies in the world, eventually its growth rate would fall

to the growth rate of the world economy We are assuming that Bill Gates is not able to successfully market his software to still to be discovered alien worlds!! Finally, note too that the constant dividend growth model fails when the assumed perpetual growth rate is greater than the discount rate

29 a Book value = $100 million

First year earnings = $100 million  24 = $24 million

Dividends = Earnings  (1 – plowback ratio) = $12 million

g = return on equity  plowback ratio = 24  50 = 12

Market value = = $400 million

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Market-to-book ratio = $400/$100 = 4

b Now g falls to 10  50 = 05, first year earnings decline to $10 million (=$100 million × 1), and dividends decline to $5 million (=$10 million × 5)

Market value = = $50 million

Market-to-book ratio = ½

This makes sense, because the firm now earns less than the required rate of return

on its investments Its project is worth less than it costs

30 P0 = + + = $16.59

31 a DIV1 = $2  1.20 = $2.40

b DIV1 = $2.40 DIV2 = $2.88 DIV3 = $3.456

P3 = = $32.675

P0 = + + = $28.02

c P1 = + = $29.825

d Capital gain = P1  P0 = $29.825  $28.02 = 1.805

r = = 15 = 15%

32 a Note: If students carry at least 4 decimal places, the results will be clearer

Also, it is easier to solve the prices in reverse order

DIV1 = $.5 DIV2 = $.5 DIV3 = $.5

DIV4 = $.5 × 1.04 = $.52 DIV5 = $.5 × 1.042 = $.5408

P4 = = = $7.7257

P3 = = = $7.4286

P2 = = = $7.1429

P1 = = = $6.8855

P0 = = = $6.6536

b Year 0

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Dividend yield = = = 07515

Capital gains yield = = = 03485

Dividend yield + capital gains yield = 07515 + 03485 = 11

Year 1

Year 2

Year 3

Yes, each year the sum of the dividend yield and the capital gains yield equal 11 percent, the required rate of return Once the company hits constant growth rate of

4 percent, both the dividend yield and the capital gains yield also become constant

33 DIV1 = dividend payout × earnings1 = 4 × $3 = $1.2

DIV2 = dividend payout × earnings2 = 4 × $3 × 1.1 = $1.32

P0 = + + + + × = $13.95

34 a BCE preferred shares

Expected results: Students use real data to calculate the current expected (or

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required) rate of return.

b CIBC preferred shares

Expected results: Students will quickly learn that the www.globeinvestor.com does not do a good job on preferred shares The dividend payouts are rounded to 2 digits and hence do not match well the actual dividends listed on the CIBC Web site

35 Expected Results: ATY-T is ATI Technologies and SRF-T is Sun-Rype Foods

Emphasize to the students that they should describe the businesses of these

companies in their own words Encourage students to think about how each

company presents its products Students will look at the investor pages to see the information they provide

36 Tips: The Web site has changed since the textbook went to press Instruct students to click on “Access Public Filings” to get to the insider information General information

on the insiders is found at “View Insider Information” To see current trading by the insiders, click on “View Summary Reports” Pick “insider transaction detail” and click

on “next” Then identify the insider (you will see “insider family” as an option) and go

to the bottom of the page and hit “search” On the next screen select “view” The summary report shows the insider trading of each security of various companies

(“issuers”) For example, in November 2005, the first issuer listed for Frank Stronach was Decoma International Inc Mr Stronach is director or senior officer holding at least 10% of the Class A subordinate voting shares The report shows transactions of Mr Stronach

Expected results: Students will see the information available and wonder whether they can trade on this – do stock purchases and sales provide information of value to outside investors?

37 Before-tax rate of return:

= = = 078 = 7.8%

After-tax rate of return:

=

= = 0596 = 5.96%

38 a An individual can do crazy things, but still not affect the efficiency of markets An

irrational person can give assets away for free or offer to pay twice the market value However, when the person’s supply of assets or money runs out, the price

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will adjust back to its prior level (assuming there is no new, relevant information released by his/her action) If you are lucky enough to trade with such a person you

will receive a positive gain at that investor’s expense You had better not count on

this happening very often though Fortunately, an efficient market protects

irrational investors in cases less extreme than the above Even if they trade in the market in an “irrational” manner, they can be assured of getting a fair price since the price reflects all information

b Yes, and how many people have dropped a bundle? Or more to the point, how many people have made a bundle only to lose it later? People can be lucky and some people can be very lucky; efficient markets do not preclude this

possibility Furthermore, how much risk did they take? You expect to earn a

higher return if you take on more market (beta) risk

c Investor psychology is a slippery concept, more often than not used to explain price movements which the individual invoking it cannot personally explain Even if it exists, is there any way to make money from it? If investor

psychology drives up the price one day, will it do so the next day also? Or will the price drop to a “true” level? Almost no one can tell you beforehand what

“investor psychology” will do Theories based on it have no content

39 There are several thousand mutual funds in Canada and the United States With so many professional managers, it is no surprise that some managers will demonstrate brilliant performance over various periods of time As an analogy, consider a contest in which

10,000 people flip a coin 20 times It would not surprise you if someone managed to flip

heads 18 out of 20 times But it would be surprising if he could repeat that performance Similarly, while many investors have shown excellent performance over relatively short time horizons, and have received favourable publicity for their work, far fewer have demonstrated consistency over long periods

40 If the firm is stable and well run, its price will reflect this information, and the stock may not be a bargain There is a difference between a “good company” and a “good stock.” The best buys in the stock market are not necessarily the best firms; instead, you want

firms that are better than anyone else realizes When the market catches up to your

assessment and prices adjust, you will profit

41 Remember the first lesson of market efficiency: The market has no memory Just because long-term interest rates are high relative to past levels doesn’t mean they won’t

go higher still Unless you have special information indicating that long-term rates are

too high, issuing long-term bonds should be a zero-NPV transaction So should issuing

short-term debt or common stock

42 The stock price will fall The original price would reflect an anticipation of a 25%

increase in earnings The actual increase is a disappointment compared to original

expectations

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