Question

You have the opportunity to buy a stock that just paid a dividend (D₀) of $2.00. After doing some research, you have forecasted the following growth rates for the firm’s dividends:

g₁ = -40%            g₂ = 0%               g₃ = 50%             g₄ = 25%              g_5-infinity = 3%      

In addition, you estimate that the required return for this stock should be 8%. Show your work.

1. Calculate the forecasted dividends for years 1 through 5
2. Calculate the forecasted stock price for year 4 (which represents the value of all dividends in years 5 through infinity as of four years from today)
3. Calculate the value of the stock today

Hand written or in a word document please

Answer 1

Question A:

g₁ = -40%           

g₂ = 0%              

g₃ = 50%            

g₄ = 25%             

g_5-infinity = 3%

r = required return = 8%

D0 = $2.00

D1 = D0 * (1+g1) = $2.00 * (1+-40%) = $1.20

D2 = D1 * (1+g2) = $1.20 * (1+0%) = $1.20

D3 = D2 * (1+g3) = $1.20 * (1+50%) = $1.80

D4 = D3 * (1+g4) = $1.80 * (1+25%) = $2.25

D5 = D4 * (1+g5) = $2.25 * (1+3%) = $2.3175

Question 2:

Stock Value at year 4 = D5 / (r - g5)

Horizon Value = $2.3175 / (8%-3%)

= $46.35

Stock Value at the end of year 4 is $46.35

Question 3:

Current Stock Price = [D1 / (1+r)^1] + [D2 / (1+r)^2] + [D3 / (1+r)^3] + [D4 / (1+r)^4] + [Horizon Value / (1+r)^4]

= [$1.20 / (1+8%)^1] + [$1.20 / (1+8%)^2] + [$1.8 / (1+8%)^3] + [$2.25 /(1+8%)^4] + [$2.3175 / (1+8%)^4]

= [$1.20 / 1.08] + [$1.20 / 1.1664] + [$1.8 / 1.259712] + [$2.25 /1.360489] + [$2.3175 / 1.360489]

= $1.11111111 + $1.028806584 + $1.428898034 + $1.653817169 + $34.06863368

= $39.29126658

Therefore, Value of stock today is $39.29