Question

Johnson, Inc. has made a commitment to pay the following dividends over the next four years: $7, $13, $18, and $3.25. At the end of this four year period, the firn has further commited to grow the dividend indefinitiely at a constant 5 percent growth rate. If you require a return on this stock of 8.4 percent, what is the current share price? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

Answer:

The current share price will be "$106.70".

Explanation:

Given over the stock of Johnson Inc,  

Expected dividends averaging 4 years,

D1 = $7  

D2 = $13

D3 = $18

D4 = $3.25

Rate of growing, g = 5%

Return required, rs = 8.4%

Thus, stock value for year four using just a constant dividend growth framework has been:

⇒  $P4=\frac{D4\times (1+g)}{rs-g}$

on putting the values in the above formula, we get

⇒       $=\frac{3.25\times 1.05}{0.084-0.05}$

⇒       $= 100.37$

The current share price would seem to be a total amount of PV of future dividends as well as a discount of P4 at rs:

⇒ $P0=\frac{D1}{(1+rs)}+\frac{D2}{(1+rs)^2}+\frac{D3}{(1+rs)^3}+\frac{D4}{(1+rs)^4}$

On putting values, we get

⇒      $=\frac{7}{1.084} +\frac{13}{1.084^2} +\frac{18}{1.084^3} +\frac{3.25}{1.084^4}$

⇒      $=106.70$