# Residual Income

Page, 316, book 4, Schweser: Karuba Manufacturing has a book value of \$15 per share and is expected to earn \$3/share indefinitely. The company does not reinvest any of its earnings. Karuba’s required rate of return is 10%. What is the value of Karuba stock according to the residual income model? If you notice when drawing out the residual income diagram for each year, since EPS stays the same at \$3/share, and thus BV increases \$3 every year, by year 5 residual income=0. (Year 1:1.5, Year 2: 1.2, Year 3: .9, Year 4: .3, Year 5, 0). So the residual income factor does not equal 1 because the residual income is 0 by year 5. Why do they use 1 as the residual income factor?

well, there is no growth. so the PV of the residual incomes - is simply 1.50/.1. - I relate the persistence factor to terminal value. - Note: that its indefinite than your W(persistence) = 1. - so (1+R-W) - or (1+.10-1) = .10 Its more like an annuity problem with fancy launguage. so the pv of the residual incomes = 15 — plus your book value = \$30. This question is a trick though, you don’t even need to the calcs if you remember that the div discount model and the RI model will yield the same value. Another Q off that one, under what circumstance will your RI model equal your book value? Rellison, I actually brought this book to work today, this one has an obscene amount formulas - trying to commit them to memory now so I can concentrate on the theory easier.

Infinitesun Wrote: ------------------------------------------------------- > This question is a trick though, you don’t even > need to the calcs if you remember that the div > discount model and the RI model will yield the > same value. Bingo - that’s the way I did and chose C, since both matching columns were C only

hehe but Swaption, isn’t persistance factor the GROWTH of residual income? Since residual income is shrinking, why is the factor equal to 1? I am not saying you’re wrong, I don’t get it. I have no problem with other residual income model problems…

‘is expected to earn \$3/share indefinitely’ So PV(RI) calculation basically become a perpetuity calculation. RI = NI - EQ RI = 3 - BV*r RI = 3 - 15*0.10 = 1.5 PV(RI) = 1.5/0.10 = 15 Value = Bv0 + PV(RI) = 15 + 15 = 30 I don’t understand why you are complicating it more with persistent factors??

persistence factor is more of a fade than a growth. - its the level that Residual income is expected to decline. The higher level of competitive advantage a firm has, than the higher the p factor (W). Think of the economics from lev 1, eventually economic profit declines to…? - Residual Income is by definition your economic profit.

oh I was using the wrong formula for calculating RI, and I mistook earnings growth in infinite for RI growth is infinite.