How to Calculate NPV when the last payment is a partial year? Rate is 8% 4 1/2 years of payments Example: Year 1: $120,000 Year 2: $120,000 Year 3: $120,000 Year 4: $120,000 Year 5: $60,000 What is the NPV?

I arrived at the number $439,855. First calculated the NPV of the first 4 payments. Then calculated the last one alone with a "n" of 4.5 using an HP12c, then added them I'm not 100% this is correct

Seems that the result was slightly off. $439,892.19 seems correct I wasn't using compound interest for the 6 month odd period. The hp12c weirdly has simple interest as default

I get $439,860 using the following discount factors (divisors?) for each period: 1: 1.08 2: 1.08^2 3: 1.08^3 4: 1.08^4 4.5: 1.08^4 x 1.04 And applying the discount to each cash flow respectively assuming payment is made at the end of each period. i.e. don't pay more than $439,860 today for that cash stream if you require 8% p.a.

Isn't this formula essentially using simple interest instead of compound interest for that 6 month period?

You mean we should apply (1.08)^0.5 to the final period = 1.0392 rather than 1.04? Yes that makes sense too. Interested to hear what is the standard practice for loans, bonds etc.

FV = PV(1+i)^n 60,000 = x(1 + 0,08)^4.5 x = $49,498.50 adding to the PV of the other cashflows results in the 2nd reply answer I gave

Can't see how you get that. Formula looks right but not the result. I think you mean $42,437, right? Which is what my second response above gives, i.e. the discount factor for the final 60,000 is 1.41386 using compound interest versus 1.41491 using simple interest ($31 or so difference). I suspect simple interest would normally be applied in practice and await to hear from the pros with baited breath.