Answer to Question #194825 in Financial Math for yash

Question

Integrated Potato chips paid a $2 per share dividend yesterday. It is expected to grow steadily at the rate of 4% per year.

a.        What is expected dividend in each of next 3 years?

b.        If the discount rate of the stock is 12%. At what price will the stock sell if the forecasted price at the end of third year is $20?

c.        What is the expected price after 3 years if today it is selling for $15?

 

4.        A company paid dividend $12. Company is expected to grow the dividend at 10% per year for next 3 years and then at 6% per year forever. What is the price of stock at the end of third year if your discount rate is 14%?

 

Answer 1

(a)

$D_1=D_0\times(1+g)\\=\$2\times (1+0.04)\\=\$2.08$

Where:

Current dividend payment (D0) = $2

Growth rate (g) = 4% or 0.04

Calculating expected dividend in year 2 (D2):

$D_2=D_1\times (1+g)\\=\$2.08\times(1+0.04)\\=\$2.1632$

Where:

Dividend in year 1 (D1) = $2

Growth rate (g) = 4% or 0.04

Calculating expected dividend in year 3 (D3):

$D_3=D_2\times(1+g)\\=\$2.1632\times(1+0.04)\\=\$2.24976$

Where:

Dividend in year 2 (D2) = $2.1632

Growth rate (g) = 4% or 0.04

(b)

Calculating the current intrinsic value of the stock (P0):

$P_0=\frac{D_1}{(1+r)^1}+\frac{D_2}{(1+r)^2}+\frac{D_3}{(1+r)^3}+\frac{P_3}{(1+r)^3}$

$=\frac{\$2.08}{(1+0.12)^1}+\frac{\$2.1632}{(1+0.12)^2}+\frac{\$2.24973}{1+0.12)^3}+\frac{\$20}{(1+0.12)^3}$

$=\$19.2476$

Where:

Expected dividend in year 1 (D1) = $2.08

Expected dividend in year 1 (D2) = $2.1632

Expected dividend in year 1 (D3) = $2.24973

Expected stock price in year 3 (P3) = $20

Thus, the stock should be selling now at $19.25 (rounded off). 

(c)

Calculating the expected dividend in year 4 (D4):

$D_4=D_0\times(1+g)^n\\=\$2\times(1+0.04)^4\\=\$2.339717$

Where:

Current dividend payment (D0) = $2

Constant growth rate (g) = 4% or 0.04

Number of years (n) = 4

Calculating the expected stock price in year 3 (P3):

$P_3=\frac{D_4}{r-g}$

$=\frac{\$2.339717}{(0.12-0.04)}$

$=\$29.2464$

Where:

Expected dividend payment in year 4 (D4) = $2.339717

Discount rate (r) = 12% or 0.12

Constant growth rate (g) = 4% or 0.04

 

Thus, the expected stock price in year 3 is $29.25 (rounded off). 

4.

Cell reference:

The price of stock at the end of third year will be $199.64