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Chapter 7 Valuing Stocks 7-1.

We can use Eq. 7.1 to solve for the price of the stock in one year, given the current price of $50.00, the $2 dividend, and the 15% cost of capital.

2 X 1.15 X 55.50

50 

At a current price of $50, we can expect Evco stock to sell for $55.50 immediately after the firm pays the dividend in one year. 7-2. a.

Dividend yield = 1 / 20 = 5%

b.

Capital gain rate = (22 – 20) / 20 = 10%

c.

Equity cost of capital = 5% + 10% = 15%

7-3. a.

P(0) = 2.80 / 1.10 + (3.00 + 52.00) / 1.102 = $48.00

b.

P(1) = (3.00 + 52.00) / 1.10 = $50.00

c.

7-4.

P(0) = (2.80 + 50.00) / 1.10 = $48.00. This is the same as in (a), so the intended holding period does not matter.

Dividend yield = 0.88 / 22.00 = 4% Capital gain rate = (23.54 – 22.00) / 22.00 = 7% Total expected return = rE = 4% + 7% = 11%

7-5.

With the simplifying assumption (as was made in the chapter) that dividends are paid at the end of the year, the stock pays a total of $2.00 in dividends per year. Valuing this dividend as a perpetuity, we have P $2.00 / 0.15 $13.33 . (This only approximates the stock price as it ignores the time value benefits of the earlier quarterly dividends.) Doing the analysis correctly and recognizing that the dividends are paid quarterly, we can value them as a 1

perpetuity, using a quarterly P $0.50 / 0.03556 $14.06 . 7-6.

discount

rate

of

(1.15) 4  1 3.556%

P = 1.50 / (11% – 6%) = $30.00

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(see

Eq.

5.1)

then,

77 Solutions Manual for Berk/DeMarzo/Stangeland  •  Corporate Finance, 4th Canadian Edition

7-7. a. b.

Eq. 7.7 implies rE = Dividend Yield + g, so g = rE – Dividend Yield = 8% – 1.5% = 6.5%. With constant dividend growth, the share price is also expected to grow at rate g = 6.5% (or we can solve this from Eq. 7.2)

7-8. P(Dec. 1, 2020) = Div(Dec. 1, 2021) / (r – g) = 0.40 / (0.11 – 0.05) = $6.67 P(Dec. 1, 2018) = 6.67 / 1.112 = $5.41 7-9.

P = 0.72 / 1.05 + 0.72 / 1.052 + 0.36 / 1.053 + 15.25 / 1.057 = $12.49

7-10. a.

Using Eq. 7.12, g = retention rate × return on new investments = (2 / 5) × 15% = 6%

b.

P = 3 / (12% – 6%) = $50

c.

7-11.

g = (1 / 5) × 15% = 3%, P = 4 / (12% – 3%) = $44.44. The projects have positive NPV (return exceeds cost of capital), so DFB should not raise the dividend as it will cause the stock price to drop in this case.

Estimate rE = Dividend Yield + g = 4 / 50 + 3% = 11% New Price P = 2.50 / (11% – 5%) = $41.67 In this case, cutting the dividend to expand is not a positive NPV decision and the stock price drops.

7-12.

Value of the first five dividend payments: PV1 5

  1.12  5   1    $3.24  0.08  0.12    1.08   . 0.65

Value on date 5 of the rest of the dividend payments: 0.65  1.12 1.02 4

PV5 

0.08  0.02

17.39 .

Discounting this value to the present gives

PV0 

17.39

 1.08 

5

 $11.83 .

So the value of a Procter and Gamble share is

P  PV1 5  PV0  3.24  11.83  $15.07

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.

Chapter 7 Valuing Stocks

7-13.

PV of the first five dividends: PVfirst

5



0.96  1.11  

5  1.11      5.14217 1   0.085  0.11   1.085   .

PV of the remaining dividends in year 5: PVremaining in year 5 

0.96  1.11

5

 1.052 

0.085  0.052

 51.5689 .

Discounting back to the present:

PVremaining 

51.5689

1.085 5

 34.2957 .

Thus the price of Colgate stock is P  PVfirst

7-14.

5

 PVremaining  39.4378

.

Note: it must be the case that r > g2 for the following to hold, otherwise the price is infinite.

n-year,  constant   growth   annuity  PV of terminal value  n n  Div1  1 g 1 g Div   1   1 1 P0  1       r  g1   1  r    1  r  r  g2 

Div1 r  g1



constant growth perpetuity

7-15.

n



 1  g1     1 r 

Div1   Div1     r  g2  r  g1 

pres ent value of difference of perpetuities in year n

See the spreadsheet for Halliford’s dividend forecast:

From year 5 on, dividends grow at a constant rate of 5%. Therefore, P(4) = 4.75 / (10% – 5%) = $95. Then P(0) = 2.34 / 1.103 + (2.64 + 95) / 1.104 = $68.45.

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7-16.

Total payout next year = $5 billion × 1.08 = $5.4 billion. Equity value = $5.4 billion / (12% – 8%) = $135 billion. Share price = $135 billion / 6 billion shares = $22.50.

7-17. a.

Earnings growth = EPS growth = dividend growth = 4%. Thus, P = 3 / (10% – 4%) = $50.

b.

Using the total payout model, P = 3 / (10% – 4%) = $50.

c.

g = rE – dividend yield = 10% – 1 / 50 = 8%

a.

To calculate earnings growth, we can use the formula g = (retention rate) × RONI.

7-18.

In 2008, BMI retains $4 of its $5 in EPS, for a retention rate of 80% and an earnings growth rate of 80% × 15% = 12%. Thus, EPS2009 = $5.00 × (1.12) = $5.60. In 2009, BMI retains $4.60 of its $5.60 in EPS, for a retention rate of 82.14% and an earnings growth rate of 82.14% × 15% = 12.32%. So, EPS2010 = $5.60 × (1.1232) = $6.29. b.

From 2010 on, the firm plans to retain 40% of EPS, for a growth rate of 40% × 15% = 6%. Total Payouts in 2010 are 60% of EPS, or 60% × $6.29 = $3.774. Thus, given the 6% future growth rate, the value of the stock at the end of 2009 is P2009 = $3.77 / (10% – 6%) = $94.35. Given the $1 dividend in 2009, we get a share price in 2008 of P2008 = ($1 + 94.35) / 1.10 = $86.68.

7-19. a.

V(4) = 82 / (14% – 4%) = $820 V(0) = 53 / 1.14 + 68 / 1.142 + 78 / 1.143 + (75 + 820) / 1.144 = $681

b. 7-20.

P = (681 + 0 – 300) / 40 = $9.53

From 2010 on, FCF is expected to grow at a 5% rate. Thus, using the growing perpetuity formula, we can estimate IDX’s terminal enterprise value in 2009 = $50 / (9.4% – 5%) = $1136. Adding the 2009 cash flow and discounting, we have Enterprise value in 2008 = ($45 + $1136) / (1.094) = $1080. Adjusting for cash and debt (net debt), we estimate an equity value of Equity value = $1080 + 110 – 30 = $1160. Dividing by number of shares, Value per share = $1160 / 50 = $23.20.

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Chapter 7 Valuing Stocks

7-21. a.

Terminal value = 33.3 × (1 + 5%) / (10% – 5%) = $699 V(0) = 25.3 / 1.10 + 24.6 / 1.102 + 30.8 / 1.103 + (699 + 33.3) / 1.104 = $567 P(0) = (567 + 40 – 120) / 60 = $8.11

b.

Free cash flows change as follows:

Hence, terminal value = 22.9 × (1+5%) / (10% – 5%) = $481.82 V(0) = 16.88 / 1.10 + 15.32 / 1.102 + 20.94 / 1.103 + (481.82 + 22.9) / 1.104= $388.5 P(0) = (388.5 + 40 – 120) / 60 = $5.14 c.

New FCF:

Hence, terminal value is $988.36, enterprise value V(0) is $803.99, and stock price P(0) is $12.07.

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d.

Increase in NWC in year 1 = 12% Sales(1) – 18% Sales(0) Increase in NWC in later years = 12% × change in sales New FCF:

Hence, terminal value is 733.31, enterprise value V(0) is $620.48, and stock price P(0) is $9.01. 7-22.

See the spreadsheet.

7-23.

a.

$22.85–$25.68

7-24.

b.

$19.60–$27.50

7-25.

c.

$22.24–$28.34

7-26.

d.

$16.55–$32.64

a.

EV = 15.25 × 18.5 – 45 = $237.1 million. FCF = rwacc × EV = 0.11 × $237.1 million = $26.1 million

b.

EBIT = FCF / (1–  c ) = $40.1 million. EBIT Margin = 40.1 / 480 = 8.4%

7-27.

7-28.

PepsiCo P/E = 52.66 / 3.20 = 16.46. Apply to Coca-Cola: $2.49 ×16.46 = $40.98

7-29. a.

Share price = Average P/E × KCP EPS = 15.01 × $1.65 = $24.77

b.

Minimum share price = 8.66 × $1.65 = $14.29; maximum share price = 22.62 × $1.65 = $37.32

c.

KCP’s share price = 2.84 × $12.05 = $34.22

d.

Minimum share price = 1.12 × $12.05 = $13.50, Maximum share price = 8.11 × $12.05 = $97.73

7-30. a.

b.

Estimated enterprise value for KCP = Average EV/Sales × KCP Sales = 1.06 × $518 million = $549 million. Equity Value = EV – Debt + Cash = $549 – 3 + 100 = $646 million. Share price = Equity Value / Shares = $646 / 21 = $30.77 (Note: this is the result calculated with the rounded average EV/Sales of 1.06. Using the non-rounded average from the spreadsheet gives a final result of $30.91 per share.) The range of share prices is $16.21–$58.64.

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Chapter 7 Valuing Stocks

c.

82

Estimated enterprise value for KCP = Average EV/EBITDA × KCP EBITDA = 8.49 × $55.6 million = $472 million. Share Price = ($472 – 3 + 100) / 21 = $27.10.

d.

The range of share prices is $22.25–$33.08.

a.

Using EV/EBITDA: EV = 55.6 × 9.73 = $541 million, P = (541 + 100 – 3) / 21 = $30.38.

7-31. Using P/E: P = 1.65 × 18.4 = $30.36. Thus, KCP appears to be trading at a “discount” relative to Fossil. b.

Using EV/EBITDA: EV = 55.6 × 7.19 = $400 million, P = (400 + 100 – 3) / 21 = $23.66. Using P/E: P = 1.65 × 17.2 = $28.38. Thus, KCP appears to be trading at a “premium” relative to Tommy Hilfiger using EV/EBITDA, but at a slight discount using P/E.

7-32.

All the multiples show a great deal of variation, suggesting that profitability and growth vary widely across firms. This makes the use of multiples problematic. In particular, for several firms, earnings and book value are negative (see cells marked “NM”), making these ratios meaningless.

7-33. a.

New value of share is P = 1.50 / (11% – 3%) = $18.75.

b.

Given that markets are efficient, the new growth rate of dividends will already be incorporated into the stock price, and you would receive $18.75 per share. Once the information about the revised growth rate for Summit Systems reaches the capital market, it will be quickly and efficiently reflected in the stock price.

a.

Expected share price is P = 1.52 / (8% – 7%) = $152

b.

Based on the market price, our growth forecast is probably too high. Growth rate consistent with market price is g = rE – dividend yield = 8% – 1.52 / 46 = 4.70%, which is more reasonable.

7-34.

7-35. a.

PV(change in FCF) = –180 / 1.13 – 60 / 1.132 = –206 Change in V = –206, so if debt value does not change, P drops by 206 / 35 =$5.89 per share.

b.

If this is public information, in an efficient market the share price will drop immediately to reflect the news, and so no trading profit would be possible.

7-36. a.

The market seems to assess a somewhat greater than 50% chance of success.

b.

Yes, Kliner’s fund would profit if they have better information than other investors.

c.

7-37.

Market may be illiquid—no one wants to trade if they know Kliner has better information. Thus Kliner’s trades will move prices significantly, limiting profits.

No. In 2006, investor expectations were likely very different—KCP might have continued to grow. Ex post, the stock is likely to do better or worse than investors’ expectations. The market would be inefficient only if the stock was overpriced relative to what would have been reasonable expectations at the time in 2006.

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83 Solutions Manual for Berk/DeMarzo/Stangeland  •  Corporate Finance, 4th Canadian Edition

7-38. a.

If the market is semi-strong form efficient, then it will reflect publicly known information. Thus the stock price at 9:30 a.m. should be based on the expectations at that time. With a dividend just paid of $2, the expected next quarterly dividend will be $2 × (1 + 0.003) = $2.006. The equity cost of capital is 12% EAR; this needs to be converted to an effective quarterly rate so we can value the growing perpetuity of quarterly dividends. (1 + 0.12) 0.25 – 1 = 0.02873734 = 2.873734% per quarter. The stock price should be equal to the PV of the growing perpetuity of dividends = $2.006 / (0.02873734 – 0.003) = $77.94

b.

If the market is semi-strong form efficient, then it will reflect the newly announced public information. Thus the stock price at 10:30 a.m. should be based on the new expectations at that time. With a dividend just paid of $2, the expected next quarterly dividend will be $2 × (1 + 0.005) = $2.01. As in part (a), the equity cost of capital of 12% EAR is equivalent to 2.873734% effective quarterly rate. The stock price should be equal to the PV of the growing perpetuity of dividends = $2.01 / (0.02873734 – 0.005) = $84.68.

c.

Between 9:30 and 10:30 a.m., SPB’s stock price rose from $77.94 to $84.68. The return over that hour can be calculated as follows: $77.94 1  r  $84.68

84. 68 1.086 77.94  r 8 .6% Even though 8.6% is a very high return over one hour, it is consistent with the efficient market hypothesis because prices are supposed to adjust when new information is realized.

1  r  

d.

The dividend just paid was $2; there is a 75% probability that the next dividend will be $2 × (1.003) = $2.006 and will grow at a rate of 0.3% per quarter, and a 25% chance that there will be no future dividends. So the stock price after the announcement should be as follows: $2.006 0.75   0.25  $0  0.02873734  . 003 0.75 $77.94  0.25 $0 $58. 46 Compared to the stock price at 10:30 a.m., this represents a significant negative return caused by the analyst’s information. $84.68 1 r   $58.46

$58.46 0.69 $84.68  r 0.69  1  0.31  31% Again, this is consistent with the efficient market hypothesis because prices are supposed to adjust when new information is realized.

1  r  

e.

The SD project is not consistent with shareholder wealth maximization because it eroded the value of SPB’s shares. Shareholder wealth maximization requires more than just having one quarter’s earnings be higher; it requires that the present value of all expected future cash flows to be accrued to shareholders is to be maximized. Clearly, the SD project failed in that regard because, once it was disclosed to investors, the stock price dropped.

f.

The CEO might have implemented the SD project because it increased short-term earnings and the CEO may receive a bonus based on these earnings. In addition, if the CEO did not expect to work at SPB much longer and did not hold SPB’s stock, then the CEO might not suffer any long-term loss and would reap the reward of the additional bonus. This would be an example of the principal-agent problem where the CEO’s incentives are not aligned with shareholders’ desire for shareholder wealth maximization.

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