Question

Consider a firm that has just paid a dividend of $2. An analyst expects dividends to grow at a rate of 8% per year for the next five years. After that dividends are expected to grow at a normal rate of 5% per year. Assume that the appropriate discount rate is 7%. The price of the stock today (P0) is:______.A. $136.29.
B. $133.03.
C. $120.33.
D. $123.43.
E. $126.60.

Answer 1

Answer:

C. $120.33

Explanation:

Div₀ = 2

Div₁ = 2.16

Div₂ = 2.333

Div₃ = 2.519

Div₄ = 2.721

Div₅ = 2.939

Div₆ = 3.09

we must first find the terminal value for year 5 (when growth rate stabilize)

P₅ = 3.09 / (7% - 5%) = $154.28

now we must discount all the future dividends + terminal value:

P₀ = 2.16/1.07 + 2.333/1.07² + 2.519/1.07³ + 2.721/1.07⁴ + 2.939/1.07⁵ + 154.28/1.07⁵ = 2.02 + 2.04 + 2.06 + 2.08 + 2.10 + 110 = $120.30 ≈ $120.33 (assuming a slight rounding error)