Better Mousetraps has come out with an improved product, and the world
is beating a path to its door. As a result, the firm projects growth
of 20 percent per year for 4 years. By then, other firms will have
copycat technology, competition will drive down profit margins and the
sustainable growth rate will fall to 5 percent.
The most recent annual dividend was DIV0 = $1.00 per share.						
						
a. What are the expected values of DIV1, DIV2, DIV3, and DIV4?						
						
b. What is the expected stock price 4 years from now? The discount
rate is 10 percent.
						
c. What is the stock price today?						
						
d. Find the dividend yield, DIV1/P0.						
						
e. What will next year's stock price, P1, be?						
						
f. What is the expected rate of return to an investor who buys the
stock now and sells it in 1 year?

Hi!!

a. What are the expected values of dividends in years 1, 2, 3, and 4?

D(i+1) = Di*(1+Gi)^i  where Gi is the year i growth rate. 

D1 = 1.00 * (1+0.2) = 1.20

D2 = D1 * 1.2 = 1.44 ; 
D3 = 1.728 ; 
D4 = 2.0736

----------------------------------------------------------

b. What is the expected stock price 4 years from now? The discount
rate is 10 percent.

D5 = D4 * (1+0.05) = 2.18

P4 = D5/(k-g) = 2.18/(0.10 - 0.05) = 43.55

----------------------------------------------------------

c. What is the stock price today? 

"Stock Value = PV of Dividends"

P0 = D1/(1+k) + D2/(1+k)^2 + D3/(1+k)^3 + D4/(1+k)^4 + P4/(1+k)^4

P0 = 1.20/(1.10) + 1.44/(1.10)^2 + 1.73/(1.10)^3 + 2.07/(1.10)^4 + 43.55/(1.10)^4

P0 = 34.74

----------------------------------------------------------

d. Find the expected dividend yield. 

Dividend yield = D1/P0 = 1.20/34.74 = 0.0345 or 3.45%

-----------------------------------------------------------

e. What is the expected capital gains rate?

Capital Gains = k - Dividend Yield = 10 - 3.45 = 6.55%

------------------------------------------------------------

f. What is the expected rate of return to an investor who buys the
stock now and sells it in 1 year?

k = D1/P0 + G1 = 1.20/34.74 + 0.20 = 0.2345 = 23.45%

-------------------------------------------------------------

For references see the following documents:
"CHAPTER 9  Stocks and Their Valuation":
http://www.bilkent.edu.tr/~aydogan/man321/ffm909.ppt

"Chapter 5 Valuation Concepts ":
http://mgtclass.mgt.unm.edu/Schatzberg/326/Publisher's%20PowerPoint%20Slides/Chapter_05tt.ppt

---------------------------------------------------------------

I hope that this helps you. Feel free to request for further
assistance if you need it before rate this answer.

Regards.
livioflores-ga

---

Request for Answer Clarification by mj100-ga on 28 Jan 2005 09:18 PST

Thanks for the answers. I have been beating my head on how to compute
these figures. Could you explain how and why you came to the
conclusion? Thanks for the quick response. The answers are not as
important as understanding the reasoning.
Thanks

---

Clarification of Answer by livioflores-ga on 28 Jan 2005 20:12 PST

Hi!!

Almost the required explanations are in the document:
"CHAPTER 9  Stocks and Their Valuation":
http://www.bilkent.edu.tr/~aydogan/man321/ffm909.ppt


You can see this file using Microsoft PowerPoint or the free PowerPoint Viewer:
http://www.microsoft.com/downloads/details.aspx?FamilyId=428D5727-43AB-4F24-90B7-A94784AF71A4&displaylang=en

Download it from here:
http://download.microsoft.com/download/a/1/a/a1adc39b-9827-4c7a-890b-91396aed2b86/ppviewer.exe


All the results came from the use of the formulas given in definitions
or explanations on the mentioned document.
For example the stock price is defined as the present value of the
dividends, this is why I use the formula to find the present value of
the dividends plus the stock price at year 4, the same with all the
others problems.
I suggest you to take a look to the "CHAPTER 9  Stocks and Their
Valuation" document searching for each part of the problem topic
inside it. If you still experience some doubts or need further
assistance please tell me specifically what is your question and I
will try to answer you.
So please do not consider this answer ended, take your time to see the
theory and compare it with the problem and ask your questions.


PS: 
Other excellent source is:
"Chapter 8 Stock Valuation":
The explanations here are easy to follow and also has good examples.
http://www.mcgrawhill.ca/college/rossfund/olc/olc/graphics/rossfund3ff_s/ch08/slideshows/sld001.htm


Regards.
livioflores-ga