Just paid a $1.60 annual dividend on each share. It is planning on increasing its dividend by 16 percent a year for the next 4 years. The corporation will then decrease the growth rate to a rate of 6 percent per year, and keep it that way indefinitely. The required rate of return is 7.10 percent. Calculate the current value of one share of this corporation's stock.

$200.17

Explanation:

Step 1: Calculation of dividend for the next 4 years

To do this, we use the following formula:

Dt = Do × (1 + g) (1)

Wheree;

Dt = next year dividend

Do = current year dividend

g = dividend growth rate = 16% = 0.16

We employ equation (1) as follows:

For Year 1:

D1 = ?

Do = $1.60

g = 0.16

Therefore,

D1 = $1.60 × (1 + 0.16) = $1.60 × 1.16 = $1.8560

For Year 2:

D2 = ?

Do = D1 = $1.8560

g = 0.16

Therefore,

D2 = $1.8650 × (1 + 0.16) = $1.850 × 1.16 = $2.1530

For Year 3:

D3 = ?

Do = D2 = $2.1530

g = 0.16

Therefore,

D3 = $2.1530 × (1 + 0.16) = $2.1530 × 1.16 = $2.4974  

For Year 4:

D3 = ?

Do = D3 = $2.4974

g = 0.16

Therefore,

D4 = $2.4974 × (1 + 0.16) = $2.4974 × 1.16 = $2.8970

Step 2: Calculation of the value of one share of this corporation's stock in fourth year.

To do this, we employ the following dividend growth model use in calculating stock price as follows:

Stock price = D4 ÷ (r - ng)   (2)

Where;

D4 = $2.8970 (as calculated in Step 1 above)

r = required rate of return = 7.10% = 0.0710

ng = new dividend growth rate = 6% = 0.06

We can therefore substitute as follows:

Stock price in 4th year = $2.8970 ÷ (0.0710 - 0.060)

                                      = $2.8970 ÷ 0.110

Stock price in 4th year = $263.37.

Therefore, the value of one share of this corporation's stock in 4th year is $263.37.

Step 3: Calculation of the current or present value of one share of this corporation's stock.

To do this, we use the PV formula as follows:

Current or present value = $263.37 ÷ (1 + 0.0710)^4

                                          = $263.37 ÷ (1.0710)^4

                                           = $263.37 ÷ 1.3157

Current or present value = $200.17

Therefore, the current value of one share of this corporation's stock is $200.17.

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