“When residual income is expected to persist at its current level forever, the persistence factor is highest”

What does this mean? Isn’t this just saying Ri / (1+r), where RI is static over time, or is it saying that RI is growing enough to more than offset the discount in the denominator? I took this to mean that RI isn’t growing so the presistence factor isn’t the highest it could possibly be.

If you recall the formula RI/(1+r-w), if the persistence factor is at its highest then the persistence factor w is equal to 1. And we are left with the formula for a perpetuity which is RI/r. RI is consitently growing at it’s current level.

if the persistence factor is at its highest, w = 1. The formula then is RI / (1+r-w). w will fall between 0 & 1. If it at its highest, the formula becomes RI / ( 1 + r -1 ), or, simply RI / r. If the persistence factor is 1, then abnormal profits are expected to be maintained in perpetuity (very unlikely).