Question 1

The Farmer's Market recently announced that it will pay its first annual dividend two years from today.The first dividend will be $0.50 a share with that amount doubling each year for the following two years.After that,the dividend is expected to increase by 4 percent annually.What is the value of this stock today if the required return is 10 percent?

Accepted Answer

P₄ = ($0.50 × 2² × 1.04)/(0.10 - 0.04) = $34.67; P₀ = [$0.50/1.10²] + [$1/1.10³] + [($2 + $34.67)/1.10⁴] = $26.21

Question 2

A stock has paid dividends of $1.80,$1.85,$2.00,$2.20,and $2.25 over the past five years,respectively.What is the average capital gains yield?

Accepted Answer

The average capital gains yield is calculated by dividing the total capital gains by the average stock price over the period. The total capital gains is the difference between the current stock price and the purchase price. The average stock price is the average of the stock prices at the beginning and end of the period. In this case, the total capital gains is $2.25 - $1.80 = $0.45. The average stock price is ($1.80 + $2.25) / 2 = $2.025. Therefore, the average capital gains yield is $0.45 / $2.025 = 5.79%.

Question 3

A firm expects to increase its annual dividend by 20 percent per year for the next two years and by 15 percent per year for the following two years.After that,the company plans to pay a constant annual dividend of $3 a share.The last dividend paid was $1 a share.What is the current value of this stock if the required rate of return is 12 percent?

Accepted Answer

P₀ = [(1 × 1.2)/1.12] + [(1 × 1.2²)/1.12²] + [(1 × 1.2² × 1.15)/1.12³] + [(1 × 1.2² × 1.15²)/1.12⁴] + [($3/0.12)/1.12⁴ = $20.50

Question 4

This morning,you purchased a stock that will pay an annual dividend of $1.90 per share next year.You require a 12 percent rate of return and the annual dividend increases at 3.5 percent annually.What will your capital gain be on this stock if you sell it three years from now?

Accepted Answer

P₀ = $1.90/(0.12 - 0.035) = $22.35; P₃ = [$1.90 × (1.035)³]/(0.12 - 0.035) = $24.78; Capital gain = $24.78 - $22.35 = $2.43

Question 5

New Gadgets is growing at a very fast pace.As a result,the company expects to pay annual dividends of $0.55,0.80,and $1.10 per share over the next three years,respectively.After that,the dividend is projected to increase by 5 percent annually.The last annual dividend the firm paid was $0.40 a share.What is the current value of this stock if the required return is 16 percent?

Accepted Answer

P₃ = ($1.10 × 1.05)/(0.16 - 0.05) = $10.50; P₀ = [$0.55/1.16] + [$0.80/1.16²] + [($1.10 + $10.50)/1.16³] = $8.50

Question 6

The Sports Club plans to pay an annual dividend of $1.20 per share next year,$1.00 per share a year for the following two years,and then cease paying dividends altogether.How much is one share of this stock worth to you today if you require a 19 percent rate of return?

Accepted Answer

P₀ = ($1.20/1.19¹) + ($1/1.19²) + ($1/1.19³) = $2.31

Question 7

Lamey Headstones increases its annual dividend by 1.5 percent annually.The stock sells for $28.40 a share at a required return of 14 percent.What is the amount of the last dividend this company paid?

Accepted Answer

$28.40 = (D₀ × 1.015)/(0.14 - 0.015); D₀ = $3.50

Question 8

The common stock of Sweet Treats is valued at $10.80 a share.The company increases its dividend by 8 percent annually and expects its next dividend to be $0.40 per share.What is the total rate of return on this stock?

Accepted Answer

R = ($0.40/$10.80) + 0.08 = 11.70 percent

Question 9

General Importers announced today that its next annual dividend will be $2.60 per share.After that dividend is paid,the company expects to encounter some financial difficulties and is going to suspend dividends for five years.Following the suspension period,the company expects to pay a constant annual dividend of $1.30 per share.What is the current value of this stock if the required return is 18 percent?

Accepted Answer

P₆ = $1.30/0.18 = $7.22; P₀ = ($2.60/1.18¹) + ($7.22/1.18⁶) = $4.88

Question 10

For the past six years,the price of Slippery Rock stock has been increasing at a rate of 9.6 percent a year.Currently,the stock is priced at $67 a share and has a required return of 14 percent.What is the dividend yield?

Accepted Answer

Dividend yield = 0.14 - 0.096 = 4.4 percent

Question 11

Investors receive a total return of 13.7 percent on the common stock of Dexter International.The stock is selling for $41.68 a share.What is the dividend growth rate if the company plans to pay an annual dividend of $2.10 a share next year?

Accepted Answer

Capital gains yield = 0.137 - ($2.10/$41.68) = 8.66 percent

Question 12

Business Solutions,Inc.is expected to pay its first annual dividend of $1.00 per share three years from now.Starting in year 6,the company is expected to start increasing the dividend by 2 percent per year.What is the value of this stock today at a required return of 12 percent?

Accepted Answer

P₅ = ($1.00 × 1.02)/(0.12 - 0.02) = $10.20; P₀ = [$1.00/1.12³] + [$1.00/1.12⁴] + [($1.00 + $10.20)/1.12⁵] = $7.70

Question 13

The Toy Chest pays an annual dividend of $4.80 per share and sells for $93.20 a share based on a market rate of return of 15 percent.What is the capital gains yield?

Accepted Answer

Capital gains yield = 0.15 - ($4.80/$93.20) = 9.85 percent

Question 14

The required return on Mountain Brook stock is 14 percent and the dividend growth rate is 5.5 percent.The stock is currently selling for $18.80 a share.What is the dividend yield?

Accepted Answer

Dividend yield = 0.13 - 0.055 = 7.5 percent

Question 15

The Three Amigos Restaurant just paid an annual dividend of $4.20 per share and is expected to pay annual dividends of $4.40 and $4.50 per share the next two years,respectively.After that,the firm expects to maintain a constant dividend growth rate of 2 percent per year.What is the value of this stock today if the required return is 15 percent?

Accepted Answer

P₂ = ($4.50 × 1.02)/(0.15 - 0.02) = $35.31; P₀ = [$4.40/1.15] + [($4.50 + $35.31)/1.15² = $33.93

Question 16

River Rock,Inc.just paid an annual dividend of $2.80.The company has increased its dividend by 2.5 percent a year for the past 10 years and expects to continue doing so.What will a share of this stock be worth 6 years from now if the required return is 16 percent?

Accepted Answer

P₆ = ($2.80 × 1.025⁷)/(0.16 - 0.025) = $24.65

Question 17

Horseshoe Stables is losing significant market share and thus its managers have decided to decrease the firm's annual dividend.The last annual dividend was $0.90 a share but all future dividends will be decreased by 10 percent annually.What is a share of this stock worth today at a required return of 15 percent?

Accepted Answer

P₀ = ($0.90 × (1 - 0.10)/[0.15 - (-0.10] = $3.24

Question 18

Brickhouse is expected to pay annual dividends of $1.90 and $2.10 over the next two years,respectively.After that,the company expects to pay a constant dividend of $2.30 a share.What is the value of this stock at a required return of 16 percent?

Accepted Answer

P₂ = ($2.30/0.16) = $14.38; P₀ = [$1.90/1.16] + [($2.10 + $14.38)/1.16²] = $13.89

Question 19

A stock has a market price of $46.10 and pays a $2.40 annual dividend.What is the dividend yield?

Accepted Answer

Dividend yield = $2.40/$46.10 = 5.21 percent

Question 20

Atlas Home Supply has paid a constant annual dividend of $2.40 a share for the past 15 years.Yesterday,the firm announced the dividend will increase next year by 10 percent and will stay at the level through year 3,after which time the dividends will increase by 2 percent annually.The required return on this stock is 12 percent.What is the current value per share?

Accepted Answer

P₃ = ($2.40 × 1.10 × 1.02)/(0.12 - 0.02) = $26.928P₀ = {($2.40 × 1.10)/1.12} + {($2.40 × 1.1)/1.12²} + {[($2.40 × 1.1) + $26.928]/1.12³} = $25.51

Quiz 7: Equity Markets and Stock Valuation