# Schweser Live Mock PM Q32

I have a question on the Live/In Person mock about residual income (Q32).

To calculate share price under the first assumption that ROE and payout ratio remain constant over time, they use equation (1) rather than equation (2) - see below.

(1) B + [(ROE-r)*B / r-g]

(2) B + [(ROE-r)*B / 1+r+w], where w = persistence factor.

I thought that a constant ROE, leads to constant residual income into the future with w=1.

In what situations do you use equation (1) vs equation (2) when solving for residual income? Thanks in advance!

Sorry correction on equation 2:

(2) B + [(ROE-r)*B / 1+r-w], where w = persistence factor.

You need the assumption that ROE and payout ratio remain constant to know what g is, primarily.

Persistance factor is the degree of “stickiness”, for lack of a better word, of residual income.

If persistance factor = 1, then you are assuming residual income will continue indefinitaly.

As it gets closer to 0, you are basically saying that you dont expect the value of residual income to persist for very long into the future (ie, if it equals 0, you are only expecting residual income in the next period only).

Unless you are given a persistance factor, I dont think you can calculate it.

I understand how persistence factor is used, I am just wondering in what circumstances you would use each of the two methods to calculate continuing residual income?

You would use 2 in situations where you are making an assumption that the residual income will not continue forever (ROE will eventually fall to the level of R), whereas in the first case you are assuming that RI will indefinitely be there.

I don’t agree. I believe that number 2 can be used in cases where residual income will continue forever. As you yourself mentioned "If persistance factor = 1, then you are assuming residual income will continue indefinitaly. "

There must be some other difference between the two versions…?

You are correct, - what I should have said was that the LEVEL of RI will continually be there in the first formula… One of the problems with Residual Income is the forecasting ability is tough(er) - the first level assumes ROE - g * B will produce the same Residual Income # as a percentage of equity indefinitely. If you are using the same R, the second version will always product a lower valuation - the persistance factor is there to say, Residual Income will continue, but we think there’s going to be a runoff factor.

With equation 2, the min of the denominator is limited by r, and residual income is limited to the present value of the RI next year. Whereas in the first formula r - g will always be less than r and produce a higher value - unless g is zero in which case either the firm pays out all \$ as dividends or doesnt earn NI, and Residual Income will be zero regardless. So, to forecast, the analyst can either forecast Book Value of Equity into the future (tough with clean surplus violations) or add some other discount factor in to de-risk the residual income valuation.

Perhaps someone else will have something to add?