Discounted payback period:

Year Project A Discount rate $15\%$ PV of cash flows Cummulative cash flows Project B PV of cash flows Cummulative cash flows

$1$ $$450000\mathrm{.}8696$ $$39132$ $$39132$ $$24000$ $$20870$ $$20870$

$2$ $$650000\mathrm{.}7561$ $$49146$ $$88278$ $$22000$ $$16634$ $$37504$

$3$ $$650000\mathrm{.}6575$ $$42738$ $$131016$ $$19500$ $$12821$ $$50325$

$4$ $$4400000\mathrm{.}5718$ $$251592$ $$382608$ $$14600$ $$8348$ $$58673$

Total PV cash flows $$382608$ $$58673$

Initial investment $($$$350000)($$$50000)$

NPV $$32608$ $$8673$

Discounted payback period :

Project A $=3+0\mathrm{.}87$

$=3\mathrm{.}87$ years

Project B $=2+0\mathrm{.}97$

$=2\mathrm{.}97$ years.

NPV:

Project A $=$ $$32608$

Project B $=$ $$8673$

Profitability index $=$ PV of cash inflows $/$ PV of cash outflows

Project A $=$ $$382608/$ $$350000$

$=1\mathrm{.}09$

Project B $=$ $$58673/$ $$50000$

$=1\mathrm{.}17.$

Why do you not start the discounted payback period from $0?$ Wouldn't the cumulative cash flows be different resulting in a different payback period?