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# 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

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?

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. ### PointOne

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. ### PointOne

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

8. ### PointOne

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

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