Vol 2 P204 Reading 10 EOC 13

As a Level III rookie, I got a little confused about the answer for return calculation.

It asks you to calculate the pretax return. According to the solution, first you have to convert the pretax salary into after-tax form: 80,000*(1-40%)=48,000, after incorporating annual living expense (74,000), we can get ongoing net expenses = 74,000-48,000=26,000 (PMT). N=18 FV=2,000,000 PV=1,235,000

Then we get after-tax return (I/Y)=4.427%, and finally convert it into pretax return = 4.427%/(1-40%)=7.38%. This solution seems straightforward.

I was wondering whether it makes sense that we convert the living expense instead of salary into pretax form firstly, say, 74,000/(1-40%)= 123,333, then calculate pretax PMT = 123,333-80,000=43,333, other inputs keep unchanged. Finally the calculated I/Y should also be in pretax form directly? The result is 5.59%, which is way different from the solution above.

Am I looking at it the wrong way?

I found the conversion between pretax return and after-tax return is quite confusing, especailly in the case of IRR form calculation. Shall we convert all inputs into the consistent tax basis with the asked return fisrtly or calculate after -ax return first, then convert it into pretax form?

Any input is highly appreciated!!

Your living expense cannot be pre-tax. It’s not tax-deductible. Like it or not, you have to pay your bills out of the after-tax money. If the govrnment taxed you on your net income (income - expenses) like it does for companies, then that would be different. Sadly, not the world we live in where I can legally deduct my bar bill…

Thanks a lot, 1recho! That helps:)