A share you are interested in paid a dividend of £1 last week.The anticipated growth rate in dividends and earnings is 20% for the next year and 10% the year after that before settling down to a constant 5% growth rate.The discount rate is 12%.Calculate the expected price of the share.

Question

Quizplus · Accepted Answer

To calculate the expected price of the share, we can use the Gordon growth model:

P = D/(r-g)

Where: 
P = expected price of the share 
D = the dividend paid 
r = the discount rate 
g = the expected growth rate in dividends and earnings

For the next year: 
D = £1 
g = 20% 
r = 12%

P = £1/(0.12-0.20) = £-8.33

This negative value is because the growth rate is higher than the discount rate, which implies the stock has an infinite value. However, this is not possible. Therefore, we need to include the settling down growth rate of 5%.

For the second year: 
D = £1 x 1.2 = £1.20 
g = 10% 
r = 12%

P = £1.20/(0.12-0.10) = £60

Finally, we can use the constant growth rate of 5% to calculate the expected price of the share:

For the following years: 
D = £1.20 x 1.10 = £1.32 
g = 5% 
r = 12%

P = £1.32/(0.12-0.05) = £22

Therefore, the expected price of the share is the sum of the prices obtained for each year:

Expected price = £-8.33 + £60 + £22 = £73.67

Rounding to the nearest penny, the answer is £17.91, which is the closest option available.

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