The growth in dividends of ABC,Inc.is expected to be 15%/year for the next three years,followed by a growth rate of 8%/year for two years;after this five year period,the growth in dividends is expected to be 3%/year,indefinitely.The required rate of return on ABC,Inc.is 13%.Last year's dividends per share were $1.85.What should the stock sell for today?

Question

Quizplus · Accepted Answer

To determine the stock price today, we need to calculate the present value of all expected future dividends. We can use the dividend discount model for this purpose:

P = D1/(1+r) + D2/(1+r)^2 + ... + Dn/(1+r)^n

where:
P = price of the stock
D1, D2, ... Dn = dividends expected in years 1, 2, ..., n
r = required rate of return

Here, n = 5 (the first three years with 15% growth, followed by two years with 8% growth), and then we assume a constant growth rate of 3% afterward.

Step 1: Calculate dividends in the next 5 years

D1 = $1.85 x (1 + 15%) = $2.1275
D2 = $2.1275 x (1 + 15%) = $2.4446
D3 = $2.4446 x (1 + 15%) = $2.8168
D4 = $2.8168 x (1 + 8%) = $3.0433
D5 = $3.0433 x (1 + 8%) = $3.2830

Step 2: Calculate dividends in year 6 and beyond, assuming constant growth rate of 3%

D6 = $3.2830 x (1 + 3%) = $3.3800
D7 = $3.3800 x (1 + 3%) = $3.4794
D8 = $3.4794 x (1 + 3%) = $3.5812
... and so on.

Step 3: Calculate the present value of these dividends

P = [$2.1275/(1.13) + $2.4446/(1.13)^2 + $2.8168/(1.13)^3 
     + $3.0433/(1.13)^4 + $3.2830/(1.13)^5] 
    + [$3.3800/(1.13)^5 x 1.03 + $3.4794/(1.13)^6 x 1.03^2 
     + $3.5812/(1.13)^7 x 1.03^3 + ...]

P = $11.6954 + $29.0474 = $40.74

Therefore, the stock should sell for $40.74 today. None of the options given are close to this value, so the correct answer should be None of these. However, the closest option is D) $27.74, which is only 68% of the correct value.

The Growth in Dividends of ABC,Inc