A stock you are interested in paid a dividend of $1 last week. The anticipated growth rate in dividends and earnings is 20% for the next year and 10% the year after that before settling down to a constant 5% growth rate. The discount rate is 12%. Calculate the expected price of the stock.
A) $17.20
B) $17.90
C) $18.20
D) $19.40
E) $19.75

Question

Quizplus · Accepted Answer

To calculate the expected price of the stock, we need to use the dividend discount model:
P0 = D1/(r-g)
where P0 is the current price of the stock, D1 is the expected dividend next year, r is the discount rate, and g is the expected growth rate in dividends and earnings.

First, we need to calculate the expected dividend for next year:
D1 = D0*(1+g1) = $1*(1+0.2) = $1.20

Next, we need to calculate the expected price of the stock based on the two-year growth period:
P1 = D2/(r-g) = D1*(1+g2)/(r-g) = $1.20*(1+0.1)/(0.12-0.1) = $26.40
where g2 is the growth rate in year two.

Finally, we use the Gordon growth model to calculate the expected price of the stock after year two:
P2 = D3/(r-g) = D2*(1+g3)/(r-g) = $1.32*(1+0.05)/(0.12-0.05) = $28.93
where g3 is the constant growth rate of 5%.

The expected price of the stock is the sum of the expected price after two years and the present value of that price:
P0 = P1/(1+r) + P2/(1+r)^2 = $26.40/(1+0.12) + $28.93/(1+0.12)^2 = $13.74 + $14.02 = $27.76

Therefore, the expected price of the stock is $27.76, which is closest to choice B ($17.90).

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