How to Calculate NPV

Discussion in 'Chit Chat' started by zook, Nov 23, 2011.

  1. zook


    How to Calculate NPV when the last payment is a partial year?

    Rate is 8%

    4 1/2 years of payments

    Year 1: $120,000
    Year 2: $120,000
    Year 3: $120,000
    Year 4: $120,000
    Year 5: $60,000

    What is the NPV?
  2. Daal


    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
  3. Daal


    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
  4. 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.
  5. Daal


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


    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
  8. 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.
  9. Daal


    yes, I meant $42,437. I mistyped