Recovering Cash Flows from a Target Net Present Value

Summary

The document asks how to infer a sequence of uneven cash flows when the net present value is fixed. It proposes parameters such as the number of periods, discount rate, inflation or indexation, and weights that allocate cash flows across periods. The question is framed as a numerical problem because the cash-flow amounts are linked by a chosen weighting scheme.

It also distinguishes the present value of future receipts from net present value, which includes the initial outlay. The example describes an initial investment followed by intermediate receipts tied to that investment and a resale value at the end. No formula, algorithm, package recommendation, worked solution, or empirical evidence is provided, so the document identifies a modeling problem rather than resolving it. Any calculation would depend on how the weights and links between cash flows are defined, and a fixed NPV alone does not uniquely determine a cash-flow path.

Key ideas

• A fixed net present value does not by itself specify a unique sequence of cash flows.
• A model would need assumptions about the discount rate, timing, inflation, and allocation weights.
• Net present value includes the initial investment as well as discounted future cash flows.
• The document poses the inverse cash-flow problem but does not provide a solution.

Tags

# Discounted-cash-flow-analysis: Is it possible to calculate the the flow of cash given a certain fixed net present value?


# Discounted-cash-flow-analysis: Is it possible to calculate the the flow of cash given a certain fixed net present value?












Is it possible to calculate the flow of cash in each period given a certain fixed net present value?

I would like to be able to apply a certain weighting that can be applied to the cash flows of each period e.g. 90% will be paid back in the last period, 1/(number of periods-1) in all other preceding periods.

For example, parameters could be: number of periods of the cash flow, discount rate, indexation/inflation, certain weighting that can be applied to the cash flows of each period, etc.

What formula should I start from? Or is there a R/Python/... package that can calculate this for me?

So I want to calculate the uneven cash flows CF 1-n, which has to be done numerically I guess.

he thing is that I also need to calculate net present value, not just present value. So e.g. in the initial period there is a negative value of e.g. -100, and at the end it is assumed it can be resold for e.g. +95. Or based on some formula that relates the 100 to the 95 which can be complex. And all the in between cash flows are dependent on the 100 too, e.g. if they were discounted; they would each equal 1/(number of periods-2) of the initial cashflow

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.