Question

You wish to earn a return of 13% on each of two stocks, X and Y. Stock X is expected to pay a dividend of $3 in the upcoming year while Stock Y is expected to pay a dividend of $4 in the upcoming year. The expected growth rate of dividends for both stocks is 7%. The intrinsic value of stock X______

a. cannot be calculated without knowing the market rate of return
b. will be greater than the intrinsic value of stock Y
c. will be the same as the intrinsic value of stock Y
d. will be less than the intrinsic value of stock Y
e. none of the above is a correct answer.

Answer 1

Using the Gordon Growth Model, the intrinsic value of stock X is calculated to be $50, and the intrinsic value of stock Y is $66.67. Hence, the intrinsic value of stock X is less than that of stock Y.

Step-by-step explanation:

To determine the intrinsic value of stock X and stock Y, we can use the Gordon Growth Model (also known as the Dividend Discount Model). This model takes into account the expected dividend, the required rate of return, and the expected growth rate of dividends. The formula is:

Intrinsic Value = Expected Dividend per Share / (Required Rate of Return - Growth Rate)

For Stock X, the expected dividend is $3, the required rate of return is 13% and the expected growth rate is 7%. Thus, the intrinsic value can be calculated as follows:

Intrinsic Value of Stock X = $3 / (0.13 - 0.07) = $3 / 0.06 = $50

Similarly, the intrinsic value for Stock Y can be calculated using its expected dividend of $4, with the same required rate of return and growth rate.

Intrinsic Value of Stock Y = $4 / (0.13 - 0.07) = $4 / 0.06 = $66.67

Comparing the intrinsic values, we can see that the intrinsic value of Stock X will be less than the intrinsic value of stock Y. Therefore, the correct answer to the student's question is:

The intrinsic value of stock X will be less than the intrinsic value of stock Y.

Answer 2

Answer: D. will be less than the intrinsic value of stock Y

Step-by-step explanation:

Based on the information given above, the intrinsic value of Stock X will be calculated thus:

D1 = Dividend in next year = $3

g = growth rate = 7%

r = = 13%

Therefore, intrinsic value of Stock X will be:

= D1 / (r-g)

= 3 / (13% - 7%)

= 3/6%

= 3 / 0.06

= $50

Therefore, the intrinsic value of stock X is $50.

Intrinsic value of Stock Y will b calculated thus:

D1 = $4

g = 7%

r = 13%

Intrinsic value of Stock Y will be:

= D1 / (r-g)

= 4 / (13% - 7%)

= 4/6%

= 4 / 0.06

= 66.67

Intrinsic value of Stock Y is $66.67

Therefore, the intrinsic value of Stock X will be less than the intrinsic value of Stock Y