Question

A company's stock pays an annual dividend that is expected to increase by 9% annually. The stock commands a market rate of return of 12% and sells for $60.50 a share. What is the expected amount of the next dividend to be paid on the stock?

Battery Co. will pay an annual dividend of $2.08 a share on its common stock next year. Last week, the company paid a dividend of $2.00 a share. The company adheres to a constant rate of growth dividend policy. What will one share of Super Light Battery’s common stock be worth ten years from now if the applicable discount rate is 9%?

Your company is a new firm in a rapidly growing industry. It is planning on increasing its annual dividend by 20% a year for the next four years and then decreasing the growth rate to 5% per year. If your company just paid its annual dividend in the amount of $1.00 per share, what is the current value of one share? Required rate of return is 9.00%

Billy & Sons pays no dividend at the present time. The company plans to start paying an annual dividend in the amount of $.30 a share for two years commencing two years from today. After that time, the company plans on paying a constant $.70 a share dividend indefinitely. Given a required return of 14%, what is the value of this stock?

Answer 1

Answer to Question 1:

Current Price, P0 = $60.50
Growth Rate, g = 9%
Rate of Return, r = 12%

Let expected dividend be D1

P0 = D1 / (r - g)
$60.50 = D1 / (0.12 - 0.09)
$60.50 = D1 / 0.03
D1 = $1.82

So, expected dividend be $1.82

Answer to Question 2:

D0 = $2.00
D1 = $2.08

Let growth rate be g%

D0 * (1 + g) = D1
$2.00 * (1 + g) = $2.08
1 + g = 1.04
g = 0.04 or 4.0%

Required Rate of return, r = 9%

D11 = D1 * (1 + g)^10
D11 = $2.08 * (1 + 0.04)^10
D11 = $3.0789

P10 = D11 / (r - g)
P10 = $3.0789 / (0.09 - 0.04)
P10 = $61.58

So, stock will worth $61.58 after 10 years

Answer 2

SOLUTION :

1.

Current price, P0 = 60.50 ($)

Rate of return, r = 12 % = 0.12

Dividend growth rate, g = 9 % = 0.09

Let $ D1 be the next year’s expected dividend.

Now,

D1 = (r - g) * P0

=> D1 = (0.12 - 0.09) * 60.50

=> D₁= 1.82 ($)

So, amount of the next year’s expected dividend = $1.82 (ANSWER).

2.

Dividend next year, D1  = 2.08 ($)

Last week, dividend paid, D0. = 2.00 ($) 

Discount rate = Rate of return, r = 9% = 0.09

Dividend growth rate, g = (D1 /D0) - 1 = (2.08/2.00) - 1 = 0.04 = 4%

Let the stock be currently worth P0 .

Now,

P₀ = D1 /(r - g)

= 2.08 / 0.09 - 0.04) 

= 41.60 ($)

P₁₀ = P0 * (1 + g)^10 

= 41.60 * (1 + 0.04)^10

= 61.58 ($)

3.

D0  = 1.00 ; D1  = 1.20 ; D2  = 1.44 ; D3  = 1.44*1.20 = 1.728 : 

D4  = 1.728*1.20 = 2.0736 ; D5  = 2.07336*1.05 = 2.17728

Discount rate, r = 9% = 0.09

=> 1 + r = 1 + 0.09 = 1.09 

Let current value of one share be P0.

So,

 P₀ = Sum ( Dn. / (1 +r)^n )  +(  D5 / (r - g))/(1+r)^4  (n = 1,2,3, 4)

= 1.20/1.09 + 1.44/1.09^2 + 1.728/1.09^3 + 2.0736/1.09^4 

+ ( 2.17728/(0.09 -0.05) ) / 1.09^4

= 43.68 ($)

So, current value of one share = $43.68   (ANSWER).

4.

Value of stock

= 0.30/1.14 + 0.30/1.14^2 + (0.70/0.14) / 1.14^2

= 4.34 ($)

Value of stock = 4.34 ($) (ANSWER).