Question

eBook Problem Walk-Through Investors require an 8% rate of return on Mather Company's stock (i.e., rs = 8%). What is its value if the previous dividend was D0 = $4.00 and investors expect dividends to grow at a constant annual rate of (1) -3%, (2) 0%, (3) 3%, or (4) 7%? Do not round intermediate calculations. Round your answers to the nearest cent. (1) $   (2) $   (3) $   (4) $   Using data from part a, what would the Gordon (constant growth) model value be if the required rate of return was 8% and the expected growth rate was (1) 8% or (2) 12%? Round your answers to the nearest cent. If the value is undefined, enter N/A. (1) $   (2) $   Are these reasonable results? These results show that the formula does not make sense if the expected growth rate is equal to or less than the required rate of return. These results show that the formula does not make sense if the required rate of return is equal to or less than the expected growth rate. These results show that the formula does not make sense if the required rate of return is equal to or greater than the expected growth rate. These results show that the formula makes sense if the required rate of return is equal to or less than the expected growth rate. These results show that the formula makes sense if the required rate of return is equal to or greater than the expected growth rate. -Select-IIIIIIIVVItem 7 Is it reasonable to think that a constant growth stock could have g > rs? It is not reasonable for a firm to grow indefinitely at a rate higher than its required return. It is reasonable for a firm to grow indefinitely at a rate higher than its required return. It is not reasonable for a firm to grow even for a short period of time at a rate higher than its required return. It is not reasonable for a firm to grow indefinitely at a rate lower than its required return. It is not reasonable for a firm to grow indefinitely at a rate equal to its required return.

Answer 1

Answer (a)

P0 = D1 / (r - g) and

D1 = D0 * (1 + g)

(1) Value of Stock = 4 * (1 - 3%) / (8% + 3%) = $35.27

(2) Value of Stock = 4 * (1 + 0%) / (8% - 0%) = $50.00

(3) Value of Stock = 4 * (1 + 3%) / (8% - 3%) = $82.40

(4) Value of Stock = 4 * (1 + 7%) / (8% - 7%) = $428.00

Hence:

(1) $35.27

(2) $50.00  

(3) $82.40

(4) $428.00

Answer (b):

(1) g = 8%

Value of Stock = 4 * (1 + 8%) / (8% - 8%) = 4.32 / 0% = Undefined = N/A

(2) g = 12%

Value of Stock = 4 * (1 + 12%) / (8% - 12%) = 4.48 / -4% = -$112.00 (negative stock value which does not make sense)

Hence:

(1) N/A

(2) -$112.00 (negative stock value which does not make sense)

No, these are not reasonable results. Here required rate of return is equal to or less than expected growth rate.

II. These results show that the formula does not make sense if the required rate of return is equal to or less than the expected growth rate.

Answer (c):

Correct answer is:

I. It is not reasonable for a firm to grow indefinitely at a rate higher than its required return.

Explanation:

It is not reasonable to expect a firm to grow indefinitely at a rate higher than its required return.In case of new and emerging sector there could be g > r_s for a short period but in due course competition will come in and demand and supply factor will work.