Question

The company is expected to pay its dividend today of $2.50. One year ago they paid a dividend of $2.20. You expect dividends to continue to grow constantly at the same rate as the past year. The risk free rate is 4%, the return on the market is 12% and the stock's Beta is 1.5. What is your assessment of the stock’s price today according to the dividend growth model?

Select one:

a. $100.60

b. $120.19

c. $105.77

d. $126.75

e. $132.17

Answer 1

The correct answer is b.$120.19

This question is based on the concept of constant growth dividend discount model.

Step 1 - Calculation of growth rate

Dividend of current year = Last year’s dividend (1+g)

2.50 = 2.20 (1+g)

2.50 = 2.20 + 2.20g

0.30 = 2.20g

g = 0.30 / 2.20

= 0.136363636 or 13.6363636 %

Price of stock = D1 / (Re-g)

D1 is the dividend for year 1

Re is required rate of return

g is growth rate

Step 2 - Calculation of D1

= D0 (1+g)

= $2.50 (1+0.136363636)

= $2.50 * 1.13636364

= $2.8409091

Step 3 - Calculation of Required rate of return

As per Capital Asset Pricing Model (CAPM)

Re = Rf + (Rm-Rf) β

Where Re = Required rate of return

Rf = Risk free rate of return

Rm – Market Return or Expected Return on Market

β – Beta of Stock

Rf = 4 %

Rm = 12 %

Beta = 1.5

Calculation of Required rate of  return

Re = Rf + (Rm-Rf) β

= 4 + (12-4) *1.5

= 4 + 8 * 1.5

= 4 + 12

= 16 %

Step 4 - Calculation of price of stock

Price of stock = D1 / (Re-g)

= $2.8409091 / (0.16 - 0.136363636)

= $2.8409091 / 0.023636364

= $120.190903

Rounding the final answer to two decimal places

= $120.19