Question

Lohn Corporation is expected to pay the following dividends over the next four years: $14, $10, $9, and $4.50. Afterward, the company pledges to maintain a constant 4 percent growth rate in dividends forever. If the required return on the stock is 10 percent, what is the current share price

Answer 1

Answer:

Current share price is $59.88

Explanation:

First calculate present value of all four years dividend

Year  Calculations     PV

1.        14 x (1.10)^-1     $12.73  

2.       10 x (1.10)^-2   $8.26

3.       9 x (1.10)^-3     $6.76

4.       4.5 x (1.10)^-4  $3.07

As the Dividend in fifth year will grow for indefinite period of time, This is the perpetuity payment. The value of share can be determined  by calculating the present value of perpetuity payment.

Dividend in the fifth year = $4.5 x ( 1 + 4% ) = $4.68

The formula for the present value of perpetuity is as follow

Present value of perpetuity = Dividend / Required Rate of return

Value of Stock = Dividend / Required Rate of return

Value of Stock = $4.68 / 10%

Value of Stock  = $46.8

This the value in fifth year calculate it present value

Today's value = $46.8 x ( 1 + 10% )^-5 = $29.06

Now add the all present values

Total Present value = $12.73 + $8.26 + $6.76 + $3.07 + $29.06 = $59.88