Question

Bonnie's Ice Cream is expecting its ice cream sales to decline due to the increased interest in healthy eating. Thus, the company has announced that it will be reducing its annual dividend by 2 percent a year for the next five years. After that, it will maintain a constant dividend of $2 a share. Last year, the company paid $2.35 per share. What is this stock worth to you if you require a 9.5 percent rate of return

Answer 1

Answer:

the stock worth is $21.90

Explanation:

Given that;

A company announced that it will be reducing its annual dividend by 2 percent a year for the next five years.

and after that it will maintain  a constant dividend of $2 a share.

Also last year, the company paid $2.35 per share.

The objective is to determine the stock worth if there is a requirement of 9.5 percent rate of return.

The price of the stock = $2/0.095

The price of the stock =21.0526

The stock worth is the present value of the price which can be expressed as:

$P = (2.35 \times (1 - 0.02)) \begin {pmatrix} \dfrac{1 - (\dfrac{1 + (-0.02) }{1+0.095})^5 }{0.095-(-0.02)} \end {pmatrix}+ \dfrac{21.0526}{(1+0.095)^5}$

$P = (2.35 \times (0.98)) \begin {pmatrix} \dfrac{1 - (\dfrac{0.98}{1.095})^5 }{0.115} \end {pmatrix}+ \dfrac{21.0526}{(1.095)^5}$

$P = (2.303) \begin {pmatrix} \dfrac{1 - (0.894977)^5 }{0.115} \end {pmatrix}+ \dfrac{21.0526}{1.574}$

$P = (2.303) \begin {pmatrix} \dfrac{1 -0.574195 }{0.115} \end {pmatrix}+ \dfrac{21.0526}{1.574}$

$P = (2.303) \begin {pmatrix} \dfrac{0.425805 }{0.115} \end {pmatrix}+ \dfrac{21.0526}{1.574}$

$P = (2.303) (3.702652174)+ \dfrac{21.0526}{1.574}$

$P = 8.5272+ \dfrac{21.0526}{1.574}$

P = $21.90

Therefore , the stock worth is $21.90