Nu-Tek, Inc.is expecting a period of intense growth and has decided to retain more of its earnings to help ﬁnance that growth.As a result it is going to reduce its annual dividend by 10% a year for the Next three years.After that, it will maintain a constant dividend of €.70 a share.Last month, the Company paid €1.80 per share.What is the value of this equity if the required rate of return is 13%?

Question

Quizplus · Accepted Answer

First, we need to calculate the future dividends after the reductions for the next three years:

Year 1 dividend = €1.80 x 0.9 = €1.62
Year 2 dividend = €1.62 x 0.9 = €1.46
Year 3 dividend = €1.46 x 0.9 = €1.31

Starting Year 4, the dividend will remain constant at €0.70.

Next, we need to calculate the present value of the future dividends using the constant growth model:

PV = (D1 / (r - g)) + (D2 / (1 + r)^2) + (D3 / (1 + r)^3) + (D4 / (r - g)) x (1 / (1 + r)^3)

Where:
D1 = Year 1 dividend
D2 = Year 2 dividend
D3 = Year 3 dividend
D4 = Dividend from Year 4 onwards = €0.70
r = Required rate of return = 13%
g = Dividend growth rate = 0% (since the dividend will remain constant from Year 4 onwards)

Plugging in the numbers, we get:

PV = (1.62 / (0.13 - 0.1)) + (1.46 / (1 + 0.13)^2) + (1.31 / (1 + 0.13)^3) + (0.70 / (0.13 - 0)) x (1 / (1 + 0.13)^3)
PV = €4.27 + €1.90 + €1.53 + €2.52
PV = €10.22

Therefore, the value of the equity is €10.22. However, since the question asks for the value per share, we need to divide this by the number of shares outstanding. Since the number of shares outstanding is not given, we cannot calculate the value per share.