Question

Nonconstant Growth. Tattletale News Corp. has been growing at a rate of 20% per year, and you expect this growth rate in earnings and dividends to continue for another 3 years.

a. If the last dividend paid was $2, what will the next dividend be?
b. If the discount rate is 15% and the steady growth rate after 3 years is 4%, what should the stock price be today?

Answer 1

Answer:

• a) $2.4

• b) $30.29

Explanation:

a. If the last dividend paid was $2, what will the next dividend be?

• Next dividend = last dividend + growth

• Next dividend = last dividend × (1 + growth rate)

• Next dividend = $2 × (1 + 20%) = $2 × (1 + 0.20) =

• Next dividend = $2 × (1.20) = $2.4

b. If the discount rate is 15% and the steady growth rate after 3 years is 4%, what should the stock price be today?

You have to calculate the price in two parts: 1) present value of the dividends for 3 years, and 2) present value of the dividends after 3 years.

i) Present value of the dividends for 3 years

Year    Dividend                                        PV

1            $2.40                                        $\dfrac{\ 2.40}{(1+0.15)^1}=\ 2.09$

2            $\ 2.40\times (1+0.20)=\ 2.88$         $\dfrac{\ 2.88}{(1+0.15)^2}=\ 2.18$

3        $\ 2.88\times (1+0.20)=\ 3.46$             $\dfrac{\ 3.46}{(1+0.15)^3}=\ 2.27$

The present value of those three dividends is:

• $2.09 + $2.18 + $2.27 = $6.54

ii) Present value of the dividends since year 4.

Equation to discount a perpetuity with constant rate g less than the discount rate.

         $PV=\dfrac{\text{Dividend one year from now}}{r-g}$

Substitute with:

• Dividend the year four = $3.46 × (1.04)

• r = 0.15

• g = 0.04

    $PV=\dfrac{\ 3.46\times (1.04)}{0.15-0.04}=\ 36.13$

Since that is the value at the end of year 3, you need to discount it to the present day:

      $PV_0=\dfrac{\ 36.13}{(1+0.15)^3}=\ 23.75$

iii) Add the present values of the two streams of dividends:

• Price = $6.54 + $23.75 = $30.29 ← answer

Answer 2

Dividend is the periodic payment, generally in the cash form, which is made to the shareholders of the company, out of profit of the company as a partial return on their investment in the company.

Solution:-

A. As it is known that the growing rate is 20%, then, calculate the dividend amount in year 1:

$div_{1} =Dividend in last year*growth rate\\div_{1} = 2*1.20div_{1} = 2.40$

B. Calculate the current price but before that first calculate the dividend for next 3 years and then calculate the price at year 3 and finally calculate the current price:

$div_{2} =Dividend in 1st year*growth rate = 2.40*1.20= 2.88$

Dividend at year 3:

$div_{3} =Dividend in 2nd year*growth rate= 2.88*1.20= 3.456$

Now calculate the price at year 3:-

$p_{3} =\frac{DIV_{3}*(1+G) }{R-G} p_{3}=\frac{3.456*1.04}{0.15-0.04} \\p_{3}= 32.675$

Finally calculate the current price:-

$p_{0}=\frac{DIV_{1} }{1+R} +\frac{DIV_{2} }{1+R}2+.......+\frac{DIV_{H} }{1+R}H+\frac{P_{H} }{1+R} H$

$P_{0} =\frac{2.40}{1.15} +\frac{2.88}{1.15}2+\frac{3.456+32.675}{1.15}3\\P_{0} = 28.021$

To know more about dividend, refer to the link:

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