The Robert Phillips Co.currently pays no dividend.The company is anticipating dividends of €0,€0,€0,€.10,€.20,and €.30 over the next 6 years,respectively.After that,the company anticipates increasing the dividend by 4% annually.The first step in computing the value of this equity today,is to compute the value of the share when it reaches constant growth in year:

Question

Quizplus · Accepted Answer

To compute the value of the equity today, we need to use the dividend discount model. The formula for the present value of a stock with constant growth is:

PV = D / (r - g)

Where:
PV = present value
D = dividend in the next period (year)
r = required rate of return
g = growth rate

We know that the company will start paying dividends in year 3, so we need to find the value of the stock in year 6 when it reaches constant growth. This is because the dividend amount in year 6 is the first dividend that will be paid with constant growth.

So, we need to find the dividend in year 6 first:

D6 = D5 * (1 + g) = €0.30 * (1 + 0.04) = €0.312

Now, we can compute the value of the stock in year 6:

PV6 = D6 / (r - g) = €0.312 / (r - 0.04)

We don't know the required rate of return (r) yet, so we need to use the dividend growth model to find it. The formula is:

r = (D1 / P0) + g

Where:
D1 = next year's dividend (year 1)
P0 = current price of the stock

We are given that the current dividend is zero, so we can skip to year 1:

D1 = €0.10
P0 = ?
g = 0.04

r = (€0.10 / P0) + 0.04

We can assume a reasonable growth rate for r of, say, 10%. Then:

0.1 / P0 + 0.04 = 0.1

0.1 / P0 = 0.06

P0 = 0.1 / 0.06 = €1.67

Now, we can find the required rate of return:

r = (€0.10 / €1.67) + 0.04 = 0.10

So, we can plug this into the equation for PV6:

PV6 = €0.312 / (0.10 - 0.04) = €5.20

Therefore, the value of the share when it reaches constant growth is €5.20 in year 6. The correct answer is D.