Question

Olson Corp. plans to pay equal amount of dividend for the next 2 years; then increase it by 5% for year 3, and 10% thereafter. The current stock price is $48. The required return is 12%.

a)     What is the expected dividend at year 1?

b)     What is the expected dividend at year 4?

c) What is the price at t = 18?

please type the answer. not photo or excel thank you!

Answer 1

(a) Let the dividend in Year n be denoted by Dn

Let D1 = D
D2 = D
D3 = 1.05D
D4 = 1.05*1.10D

According to Gordon's Growth model,

P3 = D4/(r - g)

where, r = required return = 12% and g = 10%

=> P3 = 1.05*1.10D/(0.12 - 0.10) = 57.75D

Given, P0 = 48

=> P0 = D1/(1+r) + D2/(1+r)² + D3/(1+r)³ + P3/(1+r)³

=> 48 = D/1.12 + D/1.12² + 1.05D/1.12³ + 57.75D/1.12³

=> 48 = 43.54D

=> D = 1.10

Hence, expected dividend in Year 1 = D = $1.10

(b) Expected Dividend in Year 4 = D4 = 1.05*1.10D = 1.05*1.10*1.10 = 1.27

(c) Dividend Paid in Year 19 = D19 = 1.05*1.10^19-3D = 1.05*1.10¹⁶*1.10 =

Price of Stock in Year 18 = P18 = D19/(r - g) = 1.05*1.10¹⁶*1.10/(0.12 - 0.10) = $265.36