Question

- A stock expects to pay a year-end dividend of $2.50 a share (i.e., D₁ = $2.50); assume that last year’s dividend has already been paid). The dividend is expected to decline 5 percent a year, forever (i.e., g = -5%). The company’s expected and required rate of return is 12 percent. What is the current market price per share of this stock?

- The expected rate of return on the common stock of Northwest Corporation is 10 percent. The stock’s dividend is expected to grow at a constant rate of 6 percent a year. The stock currently sells for $55 a share. What is the next expected dividend per share (i.e., D₁) on this stock?

-  A share of preferred stock pays a quarterly dividend of $1.50. If the price of this preferred stock is currently $40, what is the nominal annual rate of return?

- Harper Manufacturing has realized the following annual sales dollar amounts:

                                             2016:                                                   $12,500,000

                                    2017:                                                   $16,000,000

                                    2018:                                                   $18,000,000

               Calculate the arithmetic average annual growth rate in sales dollars that Harper Manufacturing realized during the 2016 through 2018 time-frame.

Answer 1

1. The simplest dividend discount model, known as the Gordon Growth Model (GGM)'s formula is:

P = D1 / { Re - g }  

where : P = Current Market Price ,

D1 = Expected Dividend to be paid

Re = Required Rate / Expected Rate of Return

g = Constant Growth Rate.

Thus in the given data , D1 = 2.50 , g = -5% , Re = 12%%

From the above particulars, Price = 2.50 / {12% - (-5%)} = $ 14.7059

2.

The simplest dividend discount model, known as the Gordon Growth Model (GGM)'s formula is:

P = D1 / {Re - g }  

where : P = Current Market Price ,

D1 = Expected Dividend to be paid

Re = Required Rate / Expected Rate of Return

g = Constant Growth Rate.

Thus in the given data , Re = 10% , g= 6% , Current Price ( P) = $ 55, D1 = ?

From the above particulars :

$ 55 = D1 / { 10% - 6% }

D1 = $ 55 * { 10% - 6% }

D1 = $ 55 * 4% = $ 2.20

3.

There is a concept of Nominal Return and Real Return. In Nominal Return only the incremental amount is taken into consideration and divided by the original investment value to get the Return %.

And in case of Real Return , Inflation effect is to be taken into consideration.

Thus from the above particulars , Incremental Dividend = Quarterly Dividend = $ 1.50

That implies Annual Dividend = Quarterly Dividend * No. of Quarters ( $ 1.50 * 4 Quarters ) = $ 6.00

Current Price = $ 40.00

Thus Nominal Rate of Reurn = Annual Dividend / Current Price * 100

= $ 6.00 / $ 40.00 *100 = 15%

Thus , the Nominal Annual Rate of Return tantamounts to 15%.

4.

Arithmetic Average Annual Growth Rate (AAGR) implies average of the growth rates from year to year that is distinct from the Compounded Annual Growth Rate ( CAGR ) in the fact that compounding effect is not to be taken into cosideration.

Thus from 2016 to 2017 growth rate amounts to : {$ 1,60,00,000 - $ 1,25,00,000} / $ 1,25,00,000

= 28%

Thus from 2017 to 2018 growth rate amounts to : { $ 1,80,00,000 - $ 1,60,00,000 } / $ 1,60,00,000

= 12.5 %

Arithmetic average in Sales Dollars is computed as : {Sum of Growth Rates} / Number of years (n)

where Sum of Growth Rates = 28 +12.5 = 40.50%

Number of Years = from 2016 - 2017 = 1 year

from 2017- 2018 = 1 year  

2 years

Thus the Arithmetic Average Annual Growth Rate tantamounts to : {40.50 %} / 2 years

= 20.25 %