Derivation of Fundamental Determinants of Residual Income

H

harrygo

New member
Joined
Apr 2, 2016
Messages
0
Reaction score
0
When reading this topic, I had a hard time deriving at the equation provided below. Can somebody help explain the process? Thanks.
Assuming the Gordon (constant growth) DDM and the sustainable growth rate equation, g = b × ROE,
P0 ROE - g
— = ————
B0 r - g
 
Thanks. And yes, I did, but got stuck.
Cannot figure out why, D0 * (1 + g)
——————- = ROE - g
B0
 
Gordon formula:
Po = Do*(1+g) / (r - g)
I will make the earnings appear:
Po = Eo*(1-b)*(1+g) / (r-g) ….. “b” is the retention ratio, so (1-b) is the payout ratio. Do=Eo*(1-b)
Note ROE = E1 / B = Eo*(1+g) / B. Hence:
Po / B = ROE*(1-b) / (r-g)
Remember that ROE x b = g ….. The sustainable growth rate (g) is the retention ratio per ROE
Po / B = [ ROE - ROE*b ] / (r-g)
Po / B = [ ROE - g ] / (r-g)
Hope this helps!
 
nitish3861 wrote:
Derivation——>
P0 = D0(1+g)/r-g
P0/B0 = D0/B0(1+g)
Click to expand...
Sorry, but Do/Bo is nothing useful in this case. If you want to arrive at ROE, you need E1 / Bo like I stated above.
 
Derivation——>
P0 = D0(1+g)/r-g
D0/B0(1+g)
P0/B0 = ——————
r-g
= D1/E1 *1/ROE/(r-g) as D0 *(1+g) = D1 & B0= E1/ROE
= (1-b) *ROE/r-g as D1/E1 =1-b Dividend payout ratio
=ROE-ROEb/r-g
=ROE-ROE*g/ROE as b=g/ROE
=ROE-g/r-g
 
You must log in or register to reply here.
Back
Top