Ch 8 Assessment

What type of problem is this?

A firm expects its dividends to grow at 25 percent per year for the next seven years before levelling off to a constant 3 percent growth rate. The required return is 11 percent. What is the current stock price if the annual dividend per share that was just paid was $1.05?

This is a two stage problem

How do we solve this two stage problem?

A firm expects its dividends to grow at 25 percent per year for the next seven years before levelling off to a constant 3 percent growth rate. The required return is 11 percent. What is the current stock price if the annual dividend per share that was just paid was $1.05?

 We first gotta find the stock price 7 years from now

P 7 = D0 x (1 + g1) ^ t x (1 + g2) / r - g2

= $1.05 x ( 1 + .25) ^ 7 x (1 + .03) / .11 - .03

= 5.157 / .08

= 64.4625

P0 = D1 / R - g1 x [1 - ( 1 + g1 / 1 + R ) ^ t ] + pt / (1 + R) ^ t

P0 = [1.05 (1.25) / (.11 - .25) ] [ 1 - ( 1.25 / 1.11 ) ] ^ 7 + 64.46 / 1.11 ^ 7 

43.21 is the answer

There are two steps in a two stage problem:

1. We want to calculate the price at the end of the high growth period

   1. pt = (dividend) (1 + g1 ^ t) (g2) / (r - g2)

2. We plug in

   1. Then P0 = [dividend (g1) / (r - g1) ] [1 - (g1 / 1 + r) ^ t] + pt / 1 + r ^ t

1. We want to calculate the price at the end of the high growth period

   1. pt = (dividend) (g1 ^ t) (g2) / (r - g2)

2. We plug in

   1. Then P0 = [dividend (g1) / (r - g1) ] [1 - (g1 / 1 + r) ^ t] + pt / 1 + r ^ t

There are two steps in a two stage problem

What type of problem is this?
A preferred stock will pay an annual dividend of $12 per share in perpetuity beginning 8 years from now. What is one share of this stock worth today if the market requires a return of 9.5 percent?

This is a zero growth problem

Key Words:

• Annual dividend

• Perpetuity

How do you solve a zero growth problem like this?

A preferred stock will pay an annual dividend of $12 per share in perpetuity beginning 8 years from now. What is one share of this stock worth today if the market requires a return of 9.5 percent?

You use this formula:

Pt = D / R

Perpetuity year 8:

P7 = 12 / .095

P7 = 126.32

Perpetuity year 0

P0 = Pt / ( 1 + R ) ^ t

P0 = 126.32 / 1.085 ^ 7

= $66.92

There are two formulas for zero growth problems:

1. Pt = D / R

2. P0 = Pt / ( 1 + R ) ^ t

What type of problem is this?

A firm paid an annual dividend of $2.62 on its common stock yesterday. This dividend increases at an average rate of 3.8 percent per year. The stock is currently selling for $28.12 per share. What is the market rate of return?

A dividend growth rate problem

How do you solve a problem like this?

A firm paid an annual dividend of $2.62 on its common stock yesterday. This dividend increases at an average rate of 3.8 percent per year. The stock is currently selling for $28.12 per share. What is the market rate of return?

YESTERDAY means $2.62 is D0

D1 formula = D1 ​= D0 ​× (1+g)

D1 = $2.62 x (1.038) 

D1 = 2.719

Now we take this:

P0 = D1 / R - g 

We are solving for R here, so rearrange that hoe

R = D1 / P0 + g 

R = $2.719 / 28.12 + .038 

R = .0966927454 + .038

R = .1346 or 13.7%

For dividend growth rate problems

You need

D1

You plug that into

P0 = D1 / R - g 

Tricky growth rate problem

The next dividend for the Gordon Growth Company will be $4 per share. Investors require a 16 percent return on companies such as Gordon. Gordon’s dividend increases by 6 percent every year. Based on the dividend growth model, what is the value of Gordon’s stock today? What is the value in 4 years?

The tricky thing here is that the next dividend, (D1), is given as $4, so we won’t multiply this by (1 + g). With this in mind, the price per share is given by:

P0 = D1 / (R - g)

= $4 / (.16 - .06)

=$4 / .10

=.40

Because we already have the dividend in one year, we know that the dividend in four years is equal to D1 x ( 1 + g ) = $4 x 1.06 ^ 3 = $4.764

So the price in four years is:

P4 = D4 x (1 + g) / (R - g)

=$4.764 x 1.06 / (.16 - .06)

= $5.05 / .10

=$50.50

Notice in this example that P4 is equal to P0 x (1 + g) ^4

P4 = $50.50 = $40 x 1.06 ^ 4 = P0 x (1 + g)  ^ 4

To see why this is so, notice first that: 

P4 = D5 / (R - g)

However, D5 is just equal to D1 x (1 + g) ^ 4 so we can write P4 as follows:

P4 = D1 x (1 + g) ^ 4 / ( R - g)

= [D1 / (R - g)] x (1 + g) ^4

= P0 x (1 + g) ^ 4

What type of problem is this

The dividends paid by a rapidly growing firm are expected to increase by 8 percent annually for the next three years, with the growth rate falling off to a constant 3 percent thereafter. The required return is 14 percent. The company just paid its annual dividend of $3.64 per share. What is the current share price?"

“Dividends paid by…” is a two stage problem

How do you solve

“The dividends paid by a rapidly growing firm are expected to increase by 8 percent annually for the next three years, with the growth rate falling off to a constant 3 percent thereafter. The required return is 14 percent. The company just paid its annual dividend of $3.64 per share. What is the current share price?"

Step 1

p3 = [3.64 (1.08³) (1.03) / (.14 - .08)

P3 = 42.94

P0 = [3.64 (1.08 ) / (.14 - .08) ] [ 1 - ( 1.08 / 1.14) ^ 3 ] + 42.92 / 1.14 ^ 3

P0 = 38.97

What type of problem is this?

A firm is paying an annual dividend of $1.78 to common stockholders every other year. The last dividend was paid last year. The firm will continue this policy until two more dividend payments have been paid. Three years after the last normal dividend payment, the company plans to pay a final liquidating dividend of $32 per share. What is the current market value of this stock if the required return is 14.7 percent?

“A firm is paying an annual…” is a zero growth problem

How do you solve this?

A firm is paying an annual dividend of $1.78 to common stockholders every other year. The last dividend was paid last year. The firm will continue this policy until two more dividend payments have been paid. Three years after the last normal dividend payment, the company plans to pay a final liquidating dividend of $32 per share. What is the current market value of this stock if the required return is 14.7 percent?

Last year = year -1

P0 = $1.78 / 1.147

• + $1.78 / 1.147³

• + $32 / 1.147^6

• = $16.78

When using the two-stage dividend growth model:

g1 can be greater than R1

How do you solve this?

A preferred stock sells for $63.60 per share and provides a return of 8.40 percent. What is the amount of the dividend per share?

P0 = D / R

D = P0 x R

D = 63.60 x .840

ANSWER = $5.34

Answer this

Suppose the paradise prototyping company has a policy of paying $10 per share dividend every year. If this policy is to be continued indefinitely, what is the value of a share of stock if the required return is 20 percent?

D / R = P0

$10 / .20 = $50 per share

Stocks can have _______ growth rates.

negative

Solve this

A stock currently sells for $54.80 per share. The market required return is 14.2 percent while the company maintains a constant 3 percent growth rate in dividends. What was the most recent annual dividend per share paid on this stock?

Dividend growth rate:

P0 = D1 / R - g

The next dividend is 

D1 = D0 x (1 + g)

The formula for most recent dividend is 

D0 = P0 x ( R - g ) / 1 + g 

D0 = $54.80 x ( .142 - .03) / 1 + .03 

D0 = $54.80 x .112 / 1.03

D0 = 6.1376 / 1.03

D0 = 5.96 (ROUNDED)

An investor owns 30 shares of stock of a firm and wants to win a seat on the board of directors. The firm has a total of 100 shares of stock outstanding. Each share receives one vote. At present, the company is voting to elect three new directors. Given this information, which one of the following statements must be true?

If cumulative voting applies, the investor is assured one seat on the board.

Solve this:

A firm has an EPS of $2.56, a benchmark PE of 12.1, and an earnings growth rate of 1.9 percent. What is the target share price 4 years from now?

P4=$2.56 (1.0194)(12.1) P4= $2.56 (1.0194) (12.1)

P4=$33.40 P4=$33.40

Financial calculator solution:

N = 4, I = 1.9, PV = −2.56(12.1), PMT = 0, Solve for FV = 33.40

How do you solve this?

A stock currently sells for $64 per share and the required return is 12 percent. The total return is evenly divided between the capital gains yield and the dividend yield. What is the current dividend per share if it's the company's policy to always maintain a constant growth rate in its dividends?

Use the growth rate model:

P0 = D1 / R - g

“Total return is evenly split between dividend yield and capital gains yield.”

So R is .12 / 2

D1 / P0 = dividend yield

D1 = P0 x dividend yield = 64 x .06 = 3.84

D0 = 3.84 / 1.06

D0 = $3.62

A firm paid $3.60 as an annual dividend to stockholders this morning. Future dividends are projected at $3.80, $4.10, and $4.25 over the next three years, respectively. Beginning four years from now, the dividend is expected to increase by 3.25 percent annually. What is one share of this stock worth today at a discount rate of 12.5 percent?

D0 = 3.60

D1 = 3.80

D2 = 4.10

D3 = 4.25

P3 = 4.25 ( 1.0325) / (.125 - .0325)

P3 = 47.44

P0 = 3.80 /