The General Residual Income Model
Dividends are a use of excess free cash flow available to equity holders. So it makes sense that the dividend amount and the residual income amount will be equal.
And that's what the __clean surplus relation__ represents. The clean surplus relation states that the increase (decrease) to book value during the period is the earnings net of dividends, apart from ownership transactions. Essentially, it's an extension of clean surplus accounting because income is assumed to reflect all changes in the book value of equity, other than ownership changes.
Say Lero Motors pays a total dividend of INR 108,000,000 and has the exact same residual income amount of INR 108 per share.
Why do you think this is a high probability?
Check out this equation again.
$$\displaystyle V_0 = B_0 + \sum^{\infty}_{t=1} \frac{E_t - rB_{t-1}}{(1+r)^t}$$
Where do you think ROE can be substituted?
No.
_B_0 represents the current book value.
Not quite.
This is the discount rate, so it doesn't deal with income.
Yes!
You can also show the term
$$\displaystyle E_t - rB_{t-1}$$
as
$$\displaystyle (ROE - r)B_{t-1}$$.
That's because return on equity is calculated as
$$\displaystyle \frac{EPS}{B_{0}PS}$$.
Or earnings per share divided by beginning book value per share, so it's the same as taking earnings per share less the required rate of return times the book value.
So the entire equation is
$$\displaystyle V_0 = B_0 + \sum^{\infty}_{t=1} \frac{(ROE - r)B_{t-1}}{(1+r)^t}$$.
So the key is to note that the residual income model can incorporate ROE under the assumption of clean surplus accounting.
Now, neither US GAAP or IFRS requires clean surplus accounting, so some items bypass the income statement and impact the equity value directly. So it's crucial to be able to estimate these differences and adjust net income to incorporate each difference.
To summarize:
[[summary]]
The equation for the clean surplus relation is
$$\displaystyle B_t = B_{t-1} + E_t - D_t$$.
And by rearranging the equation to solve for dividends, you can essentially solve for residual income.
$$\displaystyle D_t = E_t + B_{t-1} - B_t$$
When you substitute the dividend equation into the DDM model, you will arrive at the residual income model.
$$\displaystyle V_0 = B_0 + \sum^{\infty}_{t=1} \frac{E_t - rB_{t-1}}{(1+r)^t}$$
So, it's no surprise that similar assumptions in the model will lead to similar results.
No.
Dividends don't flow to all capital holders.
That's it!
Dividends flow to all capital holders, just like residual income
Dividends are a use of free cash flow available to equity holders
$$B_0$$
$$(1+r)^t$$
$$E_t - rB_{t-1}$$
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