Sorry, I had a "brain fart" before. I disagree with your NPV calculation, but only in terms of apples-to-apples comparisons. The fact is: because of the way that Excel NPV treats initial empty cells (v. zero), your use of NPV and FV in rows 30 and 31 is consistent.
And with that in mind, you are correct: your primary mistake is treating the annual income as "pmt" instead of "pv" in your use of FV in rows 5 through 28. That fails when the annual income varies.
I think the following
should work:
[TABLE="class: grid, width: 500"]
<tbody>[TR]
[TD]
Plan A, D5
[/TD]
[TD]
=FV($A$2,$B$4-B5,-C5,0,0)
[/TD]
[TD]
=D4+FV($A$2,$B$4-B4,0,-C5,0)
[/TD]
[/TR]
[TR]
[TD]
Plan B, F10
[/TD]
[TD]
=FV($A$2,$B$4-B5,-E10,0,0)
[/TD]
[TD]
=F9+FV($A$2,$B$4-B4,0,-E10,0)[/TD]
[/TR]
[TR]
[TD]
Plan C, H13
[/TD]
[TD]
=FV($A$2,$B$4-B5,-G13,0,0)
[/TD]
[TD]
=H12+FV($A$2,$B$4-B4,0,-G13,0)[/TD]
[/TR]
[TR]
[TD]
Plan D, J10
[/TD]
[TD]
=FV($A$2,$B$4-B5,-I10,0,0)
[/TD]
[TD]
=J9+FV($A$2,$B$4-B4,0,-I10,0)
[/TD]
[/TR]
</tbody>[/TABLE]
But that still
does not work for Plan D (varied annual income). Frankly, I don't know why (yet). Another "brain fart".
The following does work.
It mirrors your use of NPV and FV in 30 and 31, but based on NPV the way that __I__ believe it should be calculated. That is, we should always discount to age 61 for an apples-to-apples comparison; thus, we must always compound
that NPV over 25 years.
Aside.... By calculating the NPV in that manner, it is not necessary to calculate the FV. The better plan is the one with the larger NPV.
Enter the following into D5:
=IF(C5="", "", N(D4) + FV($A$2,$B$5,0,-PV($A$2,$B$4-$B5,0,-C5)))
Copy into D5:D28, F5:F28, H5:H28 and J5:J28.
The N() function avoids a
#VALUE error in columns where annual income does not start in row 5.
I choose the cash flow signs so that PV or FV is always positive.
For brevity, I omit the type=0 parameter, since that is the default.
PS.... The SUM in J29 is meaningless. It should be deleted.