Please provide me with a formula for the following: 

Both Stock A and Stock B have a discount rate of 15 percent

                         Stock A                Stock B

Return on equity           15%                     10%
Earings per share          2.00                    1.50
Dividends per share        1.00                    1.00

Need formulas for the following:

a. What are the dividend payout ratios for each firm?
b. What are teh expected dividend growth rates for each firm?
c. What is the proper stock price for each firm?

Hi baseball!!


a. What are the dividend payout ratios for each firm?

The formula to answer this is:

DPR = DPS / EPS 

where:
DPR = dividend payout ratio
DPS = dividends per share
EPS = earnings per share



b. What are the expected dividend growth rates for each firm?

growth rate (g) = ROE * Retention rate

where 
ROE = return on equity
Retention rate = 1 - DPR, then:

g = ROE * (1-DPR) =
  


c. What is the proper stock price for each firm?

Given a growth rate g, the expected dividend in year i from now is:
Di = D0*(1+g)^i     (D0 is the current dividend per share, DPS)         
and 
D_(i+1) = Di*(1+g)

If Pi is the price at year i from now and r is the rate of return of
the stock, then:
Pi = D_(i+1) / (r-g)

Note that in this notation P0 is the current stock price, then:
P0 = D1 / (r-g) 


Now we can solve this part:
Use the growth rate (g) found at the b) part of the problem, then
calculate the current stock prices P0:

D1 = D0*(1+g) = DPS*(1+g)

REplacing in the P0 formula you get this new one:
P0 = DPS*(1+g) / (r-g)  ---> use this formula to get the results.

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

I hope that this helps you. Feel free to request for a clarification
if you need it.

Regards,
livioflores-ga

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Request for Answer Clarification by baseball2-ga on 31 Jul 2005 15:00 PDT

Thanks Livioflores! I am still a bit confused with the final portion
of your answer.  Actually, I gave you one wrong bit of information. I
neglected to tell you the discount rate would rise to 12% therfore
that is why I asked if 67.52 is the correct amount for the stock in
one year. I am not sure that I followed your last part of your answer.
However, this is how I figured the following (if you tell me if I am
going in the right direction that would be grteat)

Divendend yeild 67.53-66.67 / 66.67 = 1.29

Capital gain 67.52+ 66.67/ 66.67 =  2.01

Expected rate of return = 67.52 - 66.67/ 66.67 = 13%

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Request for Answer Clarification by baseball2-ga on 31 Jul 2005 15:06 PDT

Please ignore the first clarification to this question. I posted it to
the wrong question. Let me start over. I aunderstand a and b. I am
still a bit confused on c.

I startecd to calculate as such Stock A

Stock A 2.00 x ( 1 + 19.95)= 42.90 (this is my answer in b)

Stock b 1.00 x ( 1+ 10.00) = 11.00


And than I get stuck. Could you help?

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Clarification of Answer by livioflores-ga on 31 Jul 2005 17:19 PDT

Hi!!

Well, i do not understand what are you asking, but fo r a better
understand I will do all the calculations for stock A:

- dividend payout ratios:
DPR_A = DPS_A / EPS_A =
      = 1.00 / 2.00 =
      = 0.50  (or 50%)

- expected dividend growth rates:
g_A = ROE_A * (1-DPR_A) =
    = 0.15 * (1-0.50) =
    = 0.075  (or 7.5%)

- stock price:
P0_A = DPS_A*(1+g_A)/(r-g_A) =
     = 1.00*(1+0.075)/(0.15-0.075) =
     = 1.075 / 0.075 =
     = 14.33

You must do the same calculations for stock B and you will get:
DPR_B = 0.6667 = 66.67%
g_B = 0.0333 = 3.33%
P0_B = 8.85


I hope that this clarify the answer.

Regards,
livioflores-ga

Sorry if I was not clear. But, this is what I was seeking for
clarification. Thank you!