# Single stage RI Model

what does the single stage RI model assume about what is happening to RI in the future, does it assume that RI is increasing at a constant rate g. like 1, 1.1, 1.21, 1.331

overtime, I think RI is assume to move towards zero as ROE moves toward the cost of equity. But the RI model does assume a constant growth rate in order to obtain the terminal value.

actually, there is no constant growth rate in its formula. The period RI is just discounted to present to obtain the value of the firm using RI model.

i am talking about the formula bo + (roe - r )*b0 divided by r-g this formula assumes ri is growing at g? because mathematically that is what it seems to be saying

RI is not growing at G It is the Net Income (Earnings) that is growing at g. ROE * B0 = NI. --> which grows at g… (ROE-R) is the excess of ROE over the Required rate of return. ROE*B0 = NI (Earnings) R*B0 = Return on Invested Capital. Since the NI grows at G -> the (R-G) factor is applied to the whole thing … to get the present value of the RI. Also from the formula - you would see that unlike in the DDM and the FCF models where the Terminal value is the biggest portion of value - here the B0 term (initial Book Value) is the biggest component of final value of Equity.

when u take some value at the top and divide it by r-g like d1 divided by r-g, fcfe divided by r-g, or in this case the value at the top is RI (1) divided by r-g, mathematically we r asuming what will be the pv of whatever is on top if it grows at g froever???

B0, NI and Div all grow at g. Does not mean that RI also grows at g. since there is a (ROE-r) on the numerator factor.

the complete figure in the numerator is a constant, and its value is equal to residual income in the first year. roe-r is constant and bo is constant. we can also subsititue residual income in year 1 for whatever is in the numerator and correctly solve the problem. just like the d1 in dividend discount model

cp are you getting what i am trying to say ? this formula can also be written as Ri in year 1 divided by r-g. and and what does the solution to this formula imply about the the growth rate of ri? just like what does the solution to the frmula d1 divided by r-g imply about the growth rate of d1=

Earnings grows at g. Do not agree that RI grows at g.

Agree with CP. g is for growth in Earnings. But, along with constant ‘growth in Earnings’ assumption, Single Stage RI model also assumes ‘Constant ROE’ for all future periods. Now, if we have a constant ROE for all future periods and that ROE is greater than r, our (ROE - r) remains constant. But (ROE - r) * B0 will grow, as Book Value grows each period due to increased retained earnings. Which means RI grows too at the same growth rate g. It is difficult for me to comprehend RI growing at a rate g indefinitely. It violates our readings in economics which say: supernormal profits cannot be sustained in long run. But, I guess single stage RI model is for exceptional companies (unregulated monopolies?), which can continue to earn supernormal profits continuously in long term.

^… or companies with continuous Product Differentiation ? …

RI has to grow at g since ROE is assumed to be constant.

In this case, RI is assumed to be growing at a constant rate. ROE - R is the equivalent of NI - R*BegB0 if you think about it.