Question

Investors require a 7% rate of return on Mather Company's stock (i.e., r_s = 7%).

1. What is its value if the previous dividend was D₀ = $2.00 and investors expect dividends to grow at a constant annual rate of (1) -5%, (2) 0%, (3) 3%, or (4) 5%? Do not round intermediate calculations. Round your answers to the nearest cent.

   (1) $  

   (2) $  

   (3) $  

   (4) $  

2. 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?

   1. These results show that the formula makes sense if the required rate of return is equal to or greater than the expected growth rate.
   2. 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.
   3. 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.
   4. 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.
   5. These results show that the formula makes sense if the required rate of return is equal to or less than the expected growth rate.
   
   -Select-IIIIIIIVVItem 7
   
3. Is it reasonable to think that a constant growth stock could have g > r_s?
   
   1. It is not reasonable for a firm to grow even for a short period of time at a rate higher than its required return.
   2. It is not reasonable for a firm to grow indefinitely at a rate lower than its required return.
   3. It is not reasonable for a firm to grow indefinitely at a rate equal to its required return.
   4. It is not reasonable for a firm to grow indefinitely at a rate higher than its required return.
   5. It is reasonable for a firm to grow indefinitely at a rate higher than its required return.
   
   -Select-IIIIIIIVVItem 8
   

Answer 1

Part a)

The value of company's stock can be calculated with the use of following formula:

Value of Stock = Dividend*(1+Growth Rate)/(Required Rate of Return-Growth Rate) or D₀*(1+g)/(r_s-g)

____

1)

Here, D₀ = 2, g = -5% and r_s = 7%

Using these values in the above formula, we get,

Value of Stock = 2*(1+(-5%))/(7%-(-5%)) = $15.83

____

2)

Here, D₀ = 2, g = 0% and r_s = 7%

Using these values in the above formula, we get,

Value of Stock = 2*(1+0%)/(7%-0%) = $28.57

____

3)

Here, D₀ = 2, g = 3% and r_s = 7%

Using these values in the above formula, we get,

Value of Stock = 2*(1+3%)/(7%-3%) = $51.50

____

4)

Here, D₀ = 2, g = 5% and r_s = 7%

Using these values in the above formula, we get,

Value of Stock = 2*(1+5%)/(7%-5%) = $105

_____

Tabular Representation:

	Value of Stock
1)	$15.83
2)	$28.57
3)	$51.50
4)	$105

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Part b)

The value of company's stock can be calculated with the use of following formula:

Value of Stock = Dividend*(1+Growth Rate)/(Required Rate of Return-Growth Rate) or D₀*(1+g)/(r_s-g)

1)

Here, D₀ = 2, g = 8% and r_s = 8%

Using these values in the above formula, we get,

Value of Stock = 2*(1+8%)/(8%-8%) = Undefined or NA

_____

2)

Here, D₀ = 2, g = 12% and r_s = 8%

Using these values in the above formula, we get,

Value of Stock = 2*(1+12%)/(8%-12%) = -$56

_____

Tabular Representation:

	Value of Stock
1)	NA
2)	-$56

_____

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. (which is Option III)

_____

Explanation:

A company cannot continue to operate at a growth rate which is either equal to or higher than the required rate of return in the real world. If the growth rate exceeds the required rate of return, it is not possible to determine the accurate value of the company's stock because the calculation would provide a negative value for the stock price (as is the case when required return of 8% is less than the growth rate of 12%). Similarly, if the required rate of return is equal to the growth rate, the value of the stock cannot be determined (as is the case when required return of 8% is equal to the growth rate of 8%). A stock cannot have a negative or an undefined value. Therefore, Option III is correct.

_____

Part c)

It is not reasonable for a firm to grow indefinitely at a rate higher than its required return. (which is Option IV)

_____

Explanation:

A constant growth stock having a growth rate greater than the required rate of return for an indefinite period of time would have a negative value (as determined in Part b) till the time the required rate of return exceeds the growth rate. A company cannot continue to have a negative stock value for an indefinite period of time. Therefore,Option IV is correct.