Answers to Recommended Problems II

Chapter 13

4.  V₀ = (D₀ * (1 + g)¹ ) / (1 + k)¹ + (D₀ * (1 + g)² + P₂) / (1 + k)²

V₀ = ($1.00 * (1 + 0.20)¹ ) / (1 + 0.085)¹ + (1.00 * (1 + 0.20)² + P₂) / (1 + 0.085)²

P₂ = D₃ / (k - g) = (1.00 * (1 + 0.20)² * (1 + 0.04)) / (0.085 - 0.04) = $33.28

V₀ = ($1.00 * (1 + 0.20)¹ ) / (1 + 0.085)¹ + (1.00 * (1 + 0.20)² + $33.28) / (1 + 0.085)² = $30.60

.

5.  V₀ = D₁ / (k - g) = (D₀ * (1 + g)) / (k - g)

$32.03 = ($1.22 * (1 + 0.05)) / (k - 0.05) => k = 0.09

.

17. 

V₀ = D₁ / (k - g) = (D₀ * (1 + g)) / (k - g)

a. $50.00 = $2.00 / (0.16 - g) => g = 0.12

b.  V₀ = $2.00 / (0.16 - 0.05) = $18.18

.

23.

a. k = r_f + B * (r_m - r_f) = 0.08 + 1.2 * (0.15 - 0.08) = 0.164

g = ROE * b = 0.20 * (1 - 0.40) = 0.12

D₀ = $10 * 0.40 = $4.00

V₀ = D₁ / (k - g) = (D₀ * (1 + g)) / (k - g) = ($4.00 * (1 + 0.12)) / (0.164 - 0.12) = $101.82

b.  V₁ = D₂ / (k - g) = (D₁ * (1 + g)) / (k - g) = ($4.48 * (1 + 0.12)) / (0.164 - 0.12) = $114.04

One year return = ($114.04 - $100.00) / $100.00 = 14.04%

 .

CFA 4.

a. k = r_f + B * (r_m - r_f)  = 0.045 + 1.15 * (0.145 - 0.045) = 0.16

V₀ = (D₀ * (1 + g)¹ ) / (1 + k)¹ + (D₀ * (1 + g)² ) / (1 + k)² + (D₀ * (1 + g)³ + P₃) / (1 + k)³

P₃ = D₄ / (k - g) = (D₃ * (1 + g)) / (k - g) = ($1.72 * (1 + 0.12)³ * (1 + 0.09)) / (0.16 - 0.09) = $37.63

V₀ = ($1.72 * (1 + 0.12)¹) / (1 + 0.16) + ($1.72 * (1 + 0.12)²) / (1 + 0.16)² + ($1.72 * (1 + 0.12)³ + $37.63) / (1 + 0.16)³  = $28.92

b.  Buy QuickBreath since market price < intrinsic value, do not buy SmileWhite since market price > intrinsic value

c.  The two-stage DDM allows an analyst to take into account different stages in a company's life cycle.  One problem with all DDMs is that the future growth rate is difficult to forecast.

. 

Chapter 14

1. 

a.  Inventory turnover ratio = Cost of goods sold / Average inventories = 2,850,000 / [(480,000 + 490,000)/2] = 5.76

b.  Debt / equity ratio = Total liabilities / Shareholders' equity = 3,340,000 / 960,000 = 3.48

c.  Cash flow from operating activities = EBIT + depreciation - taxes = 870,000 + 280,000 - 330,000 = 820,000

d.  Average collection period = Days sales in receivables = Average accounts receivables / Annual sales * 365 = [690,000 + 660,000) / 2] / 5,500,000 * 365 = 44.80 days

e.  Asset turnover ratio = Total asset turnover = Sales / Average total assets = 5,500,000 / [(4,010,000 + 4,300,000) / 2] = 1.32

f.  Interest coverage ratio = EBIT / Interest expense = 870,000 / 130,000 = 6.69

g.  Operating profit margin = EBIT / Sales = 870,000 / 5,500,000 = 15.82%

h.  Return on equity = Net income / Average stockholders' equity = 410,000 / [(810,000 + 960,000) / 2] = 46.33%

i.  Skip

j.  Compound leverage ratio = Interest burden * Leverage = (Pretax profit / EBIT) * (Assets / Equity) = (740,000 / 870,000) * (4,300,000 / 960,000) = 3.81

k.  Skip

.

14. ROE = Tax burden * Interest Burden * Margin * Turnover * Leverage = 0.75 * 0.6 * 0.10 * $2.40 / $1.00 * 1.25 = 0.135 or 13.5%

.

CFA 6.

a.  Tax burden = Net profits / pretax profits = 510 / 805 = 0.63

Interest burden = Pretax profits / EBIT = 805 / 830 = 0.97

Margin = EBIT / sales = 830 / 5140 = 0.16

Turnover = Sales / assets = 5140 / 3100 = 1.66

Leverage = Assets / equity = 3100 / 2200 = 1.41

b.  ROE = 0.63 * 0.97 * 0.16 * 1.66 * 1.41 = 0.232 or 23.2%

c.  g = ROE * b = 0.232 * (1 - 0.60 / 1.96) = 0.16

.

Chapter 9

14.  Trin = (Volume declining / Number declining) / (Volume advancing / Number advancing) = (231,468,687 / 270) / (4,681,742,414 / 2,787) = 0.51

A trin less than one is bullish.

.

15.  Breadth = Number advancing - Number declining = 2787 - 270 = +2517 => bullish

.

17.  Confidence = Aa yield / Baa yield

Confidence1 = 5% / 7% = 0.71

Confidence2 = 6% / 8% = 0.75

The confidence index increased, which is bullish.

.

21.  There is concern because the breadth is negative at 1367 - 1704 = 337.

.

22.

Although still negative, the cumulative breadth is improving, which is a bullish sign.

.

23.  Trin = (Volume declining / Number declining) / (Volume advancing / Number advancing) = (0.9 B / 704) / (1.1 B / 906) = 1.05

A trin greater than one is bearish.

.

24.  Confidence = Aa yield / Baa yield

Confidence1 = 8% / 10.5% = 0.76

Confidence2 = 8.5% / 10% = 0.85

The confidence index increased, which is bullish.

.

Chapter 8

10.  The correct answer is (a).  To exploit (a), the stock should be bought, which is easier to do than short selling the stock, as should be done in (b) and (c).

.

11. 

a.  No reason why 25% of mutual can't outperform the the market in a given year.

b. This would violate the strong form of the efficient market hypothesis.

c. This most contradicts the weak form of the efficient market hypothesis, as past data is not reflected in the price each January.

.

12. The weak form of the efficient market hypothesis says that all previous trading data is reflected in the price.

a.  Does not contradict because there is no reason why the return can't be greater than zero.

b.  Does not contradict because what happened the previous week doesn't affect the current week.

c.  Does contradict because a gain led to a further gain and a loss led to further losses, instead of being immediately reflected in the price.

d.  This contradicts the semi-strong form of the efficient market hypothesis because information about the prospects of the stock was not reflected in the price.

.

17. 

a.  Consistent because on an average, half of managed mutual funds will outperform the market, half will underperform the market.

b.  Violates because a positive result led to another positive result.

c.  Violates because past price trends in January should be reflected in the price of the stock.

d.  Violates because information on earnings should be immediately reflected in the price of the stock.

e.  Consistent because a gain did not lead to another gain.

.

18.   

a. Returns for firms with different P/E ratios should be the same after adjusting for the risk.

b.  There should be no correlation between book-to-market ratio and returns.

c.  Increases in price should not be followed by more increases, and the same for decreases.

d.  Small firms should not consistently outperform the market in early January.

.