# NPV calculation of past flows [closed]

I have a theoretical question concerning NPV calculation of financial products.

I know how to calculate it when future flows have to be estimated, but I am wondering how to calculate past flows. In fact, I am even wondering if it makes sense to calculate past flows for NPV of a financial product as it is generally used to estimate value of cashflows to be received/paid in the future.

Let me give you more context about this question: I am a programmer and I am working on a "NPV" function where the pricing date is a parameter, this date is used to discount the flows (this "NPV" function will price "as of" pricing date). It would be possible to use this npv function choosing a pricing date before trade booking but also in the middle of the trade "life" (for example, for an IR Swap, it would be possible to select a pricing date where some payments have already been done and some other still didn't occur).

I see several possibilities:

• force to select a pricing date before occurence of the first payment (if we consider NPV calculation only making sense to evaluate if it worths entering in a new deal or not)

• only take into account future flows of the trade

• estimate future flows and, for the past flows, retrieve the realized payments

This question will probably look abstract (and even weird!) for most of you. I am aware of it and sorry about that. Your feedbacks are welcomed.

Thanks and regards

In basic instruments, one can ignore the past fixings and price purely on the future cashflows. Hence the term Net Present Value.

With more exotic stuff such as range accruals, the past fixings are used to calculate the future payoff. In this case, to find the NPV at an intermediate date between the start date and expiry, you typically need to enter the fixings on the past reset dates. Past as in before the date of interest. Of course the date of interest might be in the future from your actual today so you don't really know what the fixings will be. A reasonable way to proceed (if it is purely for indicative purposes) is to get the estimated fixings via the interest rate curve of the reference rate (I am assuming you have an exotic interest rate instrument). Take care to use the forward starting rates from the curve.

• Hi Spinor8, thanks a lot for your feedback. I would have a complementary question: I bought a range accrual and I am in the middle of the deal life (I already received some flows), I would like now to estimate the value of the future flows. Can this value still be called NPV of the deal ? Or the concept of NPV would only make sense before buying this Range Accrual, so at the time of investment decision? Thanks. Dec 27, 2016 at 10:09
• Yes, I would call it NPV of the trade for today being XX-XX-20XX. We don't need to fixate on the range accrual. There's another way to look at your particular question. Say you've bought a simple 6 year vanilla swap, resets quarterly. After exactly 3 years, can we ask what the NPV is? Of course. It should be exactly the NPV of a brand new spot-starting (up to some trivial subtleties) 3 year swap. It has to match otherwise one would be able to arbitrage by selling the more expensive one and buying the cheap one since the economic terms on both instruments are exactly the same moving forward. Dec 27, 2016 at 12:03

The idea of considering past cash flows into an NPV calculation is rather adventurous, in my opinion. If an investor wants to invest money into a financial instrument that has already generated positive cash flows before making his investment (e.g. investing into a bond when some interest payment dates have already passed), the investor would not consider these cash flows into his calculation.

The concept of the NPV is intended to calculate the growth of an investor's wealth at time $t$, discounting all the cash flows attributable to an investment minus its costs. Since an investment can be understood as the process of buying the entitlement to receive future cash flows, it is not very intuitive to consider cash flows from the past.

I might be wrong, but that's my view on the subject. :)

• Hi Marcel, thanks for your answer. I fully agree with your view, I am more and more considering the first option (for NPV calculation, force to select a pricing date before occurence of the first payment), as NPV would be used to consider a new deal/investment/project where cashflows are still hypothetical. Dec 27, 2016 at 9:30
• A function calculating the realized value at any given date in a trade life is probably also useful but it will be something else, not NPV. Dec 27, 2016 at 9:38

Late to the party but I believe I have just figured this out.

Formula for present value of future cashflows is = cash flow ÷ ((1 + WACC)^(time period))

Formula for present value of past cashflows is = cash flow x ((1 + WACC)^(time period))

Or, combined into one formula, PV = cash flow x ((1 + WACC)^(time period))

where the time periods are positive going into the past and negative going into the future. 4yrs into the past is +ve 4 while 4yrs into the future is -ve 4. Time period of current year (or the year in which the investment is being evaluated) is Zero.

One scenario where you might need to consider past cashflows is when you need to compare the past performance of an investment against the risk free rate or other investments you could have made.

Scenario two is when you have already made cash injections into an investment going back a few years instead of one cash injection as the NPV formula demands. In this scenario, you will need to convert all past cashflows into their present values before adding them up for use in the NPV formula.