A share you are interested in paid a dividend of €1 last month.The anticipated growth rate in dividends and earnings is 25% for the next 2 years before settling down to a constant 5% growth rate.The discount rate is 12%.Calculate the expected price of the share.
A)€15.38
B)€20.50
C)€21.04
D)€22.27
E)€26.14

Question

Quizplus · Accepted Answer

Step 1: Calculate the dividends for the next two years using the anticipated growth rate of 25%:

Year 1 dividend = €1 x 1.25 = €1.25
Year 2 dividend = €1.25 x 1.25 = €1.56

Step 2: Calculate the dividend for the following year assuming a constant growth rate of 5%:
Year 3 dividend = €1.56 x 1.05 = €1.64

Step 3: Calculate the present value of each dividend using the discount rate of 12%:
PV of Year 1 dividend = €1.25 / 1.12 = €1.12
PV of Year 2 dividend = €1.56 / (1.12 x 1.12) = €1.20
PV of Year 3 dividend = €1.64 / (1.12 x 1.12 x 1.12) = €1.29

Step 4: Calculate the present value of the share price at the end of Year 3 using the dividend discount model:
P3 = (D4 / (r - g)) = (€1.64 x 1.05) / (0.12 - 0.05) = €21.04

Step 5: Calculate the present value of the expected share price at the end of Year 3:

PV of P3 = €21.04 / (1.12 x 1.12 x 1.12) = €16.98

Step 6: Add the present values of all the dividends and the expected share price to get the expected price of the share today:

Expected share price = PV of Year 1 dividend + PV of Year 2 dividend + PV of Year 3 dividend + PV of P3
Expected share price = €1.12 + €1.20 + €1.29 + €16.98 = €20.59

The closest answer to €20.59 is C) €21.04.

A Share You Are Interested in Paid a Dividend of €1