Valuation Question question, investment, following, finding

SkipE99

From CFAI, Reading 41 (FCF Vauations), EOC Q11. In Part A, FCFE(4) = 918.19, calcuated by using the FCFE = NI - (1-DR)(Net investment in operating assets). Then using this FCFE(4), V3 is calculated as V3 = FCFE4/r-g, where g=8% for N.I grwoth rate is used. My question is why can't we use the same g=8% in the following

FCFE(4) = FCFE(3)(1+g) = 124.27(1.08) = 134.21 in finding the terminal value V3?, since we are using g=8% in terminal value formula, this should also be reflected in numerator?

kickthatcfa

Year 4's NI grows 8%, but this has nothing to do with the constant 8% growth of FCFE going forward. The 8%s are co-incidental.

In Year 4 NI grows 8%, but Net Investment drops from $1,520.88m to $335.92m - from Year 4 on it will be 30% of NI (a smaller fraction than previously). This relation of the FCFE components, incidentally, is a necessary condition of future constant FCFE growth (because all parts of the equation will put on weight proportionally together).

To put it another way, because of the anticipated sudden drop in net investment, FCFE will grow a massive 639% in Year 4 ($124.27m to $918.19m), and is predicted to grow constantly at only 8% from then on! If you substitute Year 4's substantial FCFE with a puny 8% growth figure (on a false analogy with NI) you will be seriously understating the starting point of the constant growth, and your terminal value will be much too low.