Present and Future Worth of Irregular Project Cash Flows
Summary
The document considers a project with irregular income and expenditure at year-end, a stated annual compounding rate, and a valuation date. It describes valuing each cash flow separately: discount past or future amounts to the present for present worth, or compound each amount forward to the target date for future worth. It also asks whether spreadsheet functions such as NPV and FV can simplify the calculations, and presents an accepted answer that refers to spreadsheet calculations and manual future-value computation.
A key caveat is that timing conventions matter when using spreadsheet functions: standard NPV generally treats the first listed cash flow as occurring one period from the valuation point, so a cash flow at time zero may need separate handling. The answer also says cash flows before the present date are sunk costs for a forward-looking decision at that date. The document offers no displayed spreadsheet formulas or numerical results, so it does not fully show or verify the calculations; its main lesson is the discounting and compounding framework.
Key ideas
- Present worth is found by discounting each cash flow to the valuation date using its time distance and the stated rate.
- Future worth is found by compounding each cash flow forward to the selected future date.
- Cash flow timing must be aligned with spreadsheet function conventions when calculating net present value.
- Past cash flows are sunk costs when evaluating a decision made at the present date.
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Full text
# Financial Analysis of Project Cash Flows: Present and Future Worth Calculations
# Financial Analysis of Project Cash Flows: Present and Future Worth Calculations
Update We use all the transactions from 2010 to 2033, . You need to find the equivalent value of each transaction based on the number of compounded interests.
Consider the following income and expenditure of a project over past years and expected in future years. The income and expenditures happen on the last day of each year. The present time is at the end of 2024. The interest rate of 12% compounded annually.
| Year | Cash Flow (CF) |
| 2010 | -6453 |
| 2011 | 2300 |
| 2012 | |
| 2013 | 8200 |
| 2014 | |
| 2015 | 810 |
| 2016 | -4100 |
| 2017 | |
| 2018 | |
| 2019 | 1200 |
| 2020 | 1890 |
| 2021 | |
| 2022 | |
| 2023 | -6342 |
| 2024 | |
| 2025 | 1900 |
| 2026 | |
| 2027 | |
| 2028 | 1500 |
| 2029 | -850 |
| 2030 | |
| 2031 | 1230 |
| 2032 | -710 |
| 2033 | 1000 |
1-Plot the Cash Flow
2- Using excel formulas, calculate the present worth of the project.
3-Using excel formulas, calculate future worth of the project at the end of year 2033.
#### 1. Present Worth (PW) Calculation
The formula for Present Worth (PV) for each year is:
$$ PV = \frac{CF}{(1 + i)^n} $$
Where:
- ( CF ) = Cash Flow in a given year
- ( $i = 0.12$ ) (Interest rate)
- ($ n$ ) = Number of years from the base year (2010)
#### 2. Future Worth (FW) Calculation
The formula for Future Worth (FV) for each year is:
$$ FV = CF \times (1 + i)^{(2033 - n)} $$
Where:
- ( CF ) = Cash Flow in a given year
- ( i = 0.12 ) (Interest rate)
- ( n ) = Year of transaction
- ( 2033- n ) = Number of years to the end of 2033
Is this the right method for solving this problem? Is there a simpler approach? Can it be solved using Excel functions? e.g.
Present worth `= NPV (i%, second_cell:last_cell) + first_cell`
Future worth `=FV(i%, n, A, P)` ?
## Answer by phdstudent (score 1, accepted)
https://quant.stackexchange.com/a/81675
Here's the solution to your question in excel. Unsure if the FV formula can be used so I just compute the future value manually. Two pictures below one with the values and the other one with the formulas. Again this is probably to basic for quant.stackexchange. You can safely ignore all the cashflows before 2024 since those are sunk costs.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.