I'm staring at this formula (its from The Portable MBA in Finance and Accounting) and although I get the concept really well, my math never advanced to subscripts. I am unable to figure several things out about this formula.

If we can start here, the author defines the variables as

"where Ks is the cost of equity, Ko is the cost of capital for an all-equity firm, Kb is the cost of debt, B is the value of the firm?s debt, and S is the value of the firm?s equity."

If Ko is the cost of capital for an *all equity firm* would the equation not HAVE TO BE (example, assuming 12% cost of equity)

Ks(12%) = 12% + (0%/100%) * (12%-0%)

Because it's 100% equity?? I don't get it!

Also, if I leave that misunderstanding behind and try to calculate as if the firm does have debt ...

Example:

12% + (20%/80%) * (12%-8.4%) = 12.9% <-- which should be 12.0%!

12% = Ko

8.4% = Kb

20% = value of debt (in %)

80% value of equity (in %)

Again, I never learned subscripts, so it's possible I'm completely ignoring some part of this that I shouldn't be. I've read a lot on subscripts (looking to solve/understand this equation), but I just can't make the stuff I'm reading relate to this.