Question

23-Two stocks each pay a $1 dividend that is growing annually at 4 percent. Stock A's beta = 1.3; stock B's beta = 0.8.

a. Which stock is more volatile?

b. If Treasury bills yield 2 percent and you expect the market to rise by 8 percent, what is your risk-adjusted required return for each stock?

c. Using the dividend-growth model, what is the maximum price you would be willing to pay for each stock?

d. Why are their valuations different?

Answer 1

Given,

last dividend = $1

growth rate of dividend = g = 4% = 0.04

Stock A's beta = 1.3

Stock B's beta = 0.8

a) Beta is a measure of stock moment relative to the overall market.

If beta of a stock is more then it means it is more volatile than the overall market whereas in case of low beta then it is less volatile when compared to the overall market.

In the above given case, beta of stock A (1.3) is more than beta of stock B (0.8).

So, stock A is more volatile.

b) Risk adjusted Required rate of return can be calculated using the following formula,

Risk adjusted Required rate of return = Risk free rate + beta*(market return - risk free rate)

In case of stock A:

Risk free rate = T- bills yield = 2% = 0.02

market return = 8% = 0.08

beta of stock A = 1.3

Substituting these in the above formula,

  Required rate of return = Risk free rate + beta*(market return - risk free rate)

   = 0.02 + 1.3*(0.08 - 0.02)

   = 0.02 + 1.3*0.06

   = 0.02 + 0.078

= 0.098

= 9.8%

In case of stock B:

Risk free rate = T- bills yield = 2% = 0.02

market return = 8% = 0.08

beta of stock B = 0.8

Substituting these in the above formula,

  Required rate of return = Risk free rate + beta*(market return - risk free rate)

   = 0.02 + 0.8*(0.08 - 0.02)

   = 0.02 + 0.8*0.06

   = 0.02 + 0.048

= 0.068

= 6.8%

c) Price can be calculated using the following formula,

Price = last dividend(1+g)/(required rate of return - g)

  In case of stock A:

last dividend = $1

g = 4% = 0.04

Required rate = 9.8% = 0.098

Substituting these in the above formula, we get

Price of stock A = $1(1+0.04)/ (0.098-0.04)

= 1.14/ 0.058

= 17.93

Therefore, price of stock A = 17.93

In case of stock B:

last dividend = $1

g = 4% = 0.04

Required rate = 6.8% = 0.068

Substituting these in the above formula, we get

Price of stock B = $1(1+0.04)/ (0.068-0.04)

= 1.14/ 0.028

= 37.14

Therefore, price of stock B = 37.14

d) Valuations are different since the required rate of returns of the stock A and stock B are different.