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?
A)$8.99
B)$25.21
C)$40.00
D)$27.74
E)none of the above

Question

Quizplus · Accepted Answer

We can use the dividend discount model to calculate the intrinsic value of the stock:

PV of stock = D1/(1+r) + D2/(1+r)² + D3/(1+r)³ + D4/(1+r)⁴ + D5/(1+r)⁵ + D5(1+g)/(r-g)/(1+r)^5

Where: 
- D1 = expected dividend next year 
- r = required rate of return 
- g = growth rate 
- D2-D5 = expected dividends for the following years

Plugging in the values:

D1 = $1.85*(1+0.15) = $2.1275 
D2 = $2.1275*(1+0.15) = $2.44463 
D3 = $2.44463*(1+0.15) = $2.81631 
D4 = $2.81631*(1+0.08) = $3.04237 
D5 = $3.04237*(1+0.08) = $3.28349

PV of stock = $2.1275/(1+0.13) + $2.44463/(1+0.13)² + $2.81631/(1+0.13)³ + $3.04237/(1+0.13)⁴ + $3.28349/(1+0.13)⁵ + $3.28349/(0.13-0.03)/(1+0.13)⁵ 
PV of stock = $16.957 + $17.969 + $18.556 + $18.478 + $18.198 + $232.403 
PV of stock = $322.56

Therefore, the stock should sell for $27.74 (Choice D).

The Growth in Dividends of ABC,Inc