How to Calculate NPV

[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?

 

[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

 

[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

 

[PointOne]

Quote from 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?

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.

 

[Daal]

Quote from PointOne:


4.5: 1.08^4 x 1.04

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

 

[PointOne]

Quote from Daal:

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.

 

[Daal]

Quote from 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.

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

 

[PointOne]

Quote from 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

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.

 

[Daal]

Quote from 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.

yes, I meant $42,437. I mistyped