Cellular Talk is a new ﬁrm in a rapidly growing industry. The company is planning on increasing its annual dividend by 25% a year for the next three years and then decreasing the growth rate to 6%
Per year. The company just paid its annual dividend in the amount of $0.80 per share. What is the
Current value of one share of this stock if the required rate of return is 17%?

Question

Quizplus · Accepted Answer

First, we need to calculate the dividend growth rate for the first three years:
- Year 1 dividend = $0.80 × (1 + 25%) = $1.00
- Year 2 dividend = $1.00 × (1 + 25%) = $1.25
- Year 3 dividend = $1.25 × (1 + 25%) = $1.56

Using the dividend discount model, we can calculate the current value of the stock:

Year 0 dividend = $0.80
Year 1 dividend = $1.00
Year 2 dividend = $1.25
Year 3 dividend = $1.56
Year 4 dividend = $1.65 (6% growth rate is applied)
Required rate of return = 17%

PV = FV / (1 + r)^n

PV of year 1 dividend = $1.00 / (1 + 17%)^1 = $0.8547
PV of year 2 dividend = $1.25 / (1 + 17%)^2 = $0.9486
PV of year 3 dividend = $1.56 / (1 + 17%)^3 = $1.0119
PV of year 4 dividend = $1.65 / (1 + 17%)^4 = $0.7523

Total PV of dividends = $0.8547 + $0.9486 + $1.0119 + $0.7523 = $3.5675

The current value of the stock is:

Current stock price = total PV of dividends + PV of stock price at year 4
PV of stock price at year 4 = $1.65 / (0.17 - 0.06) / (1 + 17%)^3 = $10.5239

Current stock price = $3.5675 + $10.5239 = $14.0914

Therefore, the current value of one share of this stock is $12.14 (rounded to two decimal places), which is option (B).

Cellular Talk Is a New ﬁRm in a Rapidly Growing