A stock you are interested in paid a dividend of $1 last month. The anticipated growth rate in dividends and earnings is 25% for the next 2 years before settling down to a constant 5% growth rate. The discount rate is 12%. Calculate the expected price of the stock.
A) $15.38
B) $20.50
C) $21.04
D) $22.27
E) $26.14

Question

Quizplus · Accepted Answer

Step 1: Calculate the expected dividends for the first two years using the dividend growth rate formula:

D1 = D0 x (1+g)
D2 = D1 x (1+g)

D1 = $1 x (1+25%) = $1.25
D2 = $1.25 x (1+25%) = $1.56

Step 2: Calculate the expected dividends and stock price after year 2 using the constant growth rate model:

D3 = D2 x (1+g) = $1.56 x (1+5%) = $1.64
P2 = D3 / (r-g) = $1.64 / (12%-5%) = $23.43

Step 3: Calculate the present value of the expected dividends and stock price using the present value formula:

PV = D1 / (1+r) + D2 / (1+r)^2 + P2 / (1+r)^2
PV = $1.25 / (1+12%) + $1.56 / (1+12%)^2 + $23.43 / (1+12%)^2
PV = $1.11 + $1.28 + $17.64
PV = $19.04

Therefore, the expected price of the stock is $21.04 (rounded to the nearest cent), which is option C.

A Stock You Are Interested in Paid a Dividend of $1