Calculating NPV for future cash inflows
When calculating the NPV, is there anything I need to do in between the project start date outlay (Nov 2017), and the first cash inflow (July 2019). Do I need to discount the cashflow to the present, and if so, how? Yes, you need to discount every cash flow to the present time, not just the first one.   When discounting cash flows, the appropriate discount rate needs to represent the opportunity cost of the initial cash outlay.  Meaning if you were to use that money for something else, what rate of return would you expect? You could be safe and assume only a risk-free return (like 2-3%) or use the average rate of return of other investments (e.g. 10-15%). Another common approach is to use your cost of capital if you're raising funds for the project, or would instead have use the funds to pay off existing debt. Once you find a relevant discount rate, then just discount each cash flow by dividing them by e^rt, where r is the annualized discount rate (e.g. 0.10 for 10%) and t is the decimal number of years between now and the cash flow (e.g. 1.5 for 18 months)
The short answer is you'd be much better off paying up front in this case.  The present value of $2,500 plus 12 $500 monthly payments is $8,128 at a 12% discount rate, which is much higher then the $6,000 you could pay now. The long answer is how you get that present value.  How can I use time value of money to find the present value of money if I choose to go with option A? First of all, I'd question your discount rate.  A 12% discount rate means that you can safely reinvest the money that you're not spending today at a 12% annual (1% monthly) rate, which seems very high.  Normally for short-term spending decisions you'd use a risk-free rate, which would be closer to 1%-2%. However, to discount at 1% monthly you'd just divide each monthly payment by 1 plus the discount rate raised to the power of the number of periods until each payment. So the total is which is $8,127.54 You could also use the NPV function in Excel. It seems like to get an accurate answer the calculation of the interest rate should take into account compounding period as well? Correct, and in the example above the compounding is assumed to be monthly since that's the periodicity of the cash flows. You could calculate it with a different compounding period but it gets much more complicated and probably wouldn't make a significant difference. The discount rate does take compounding into effect, meaning if you saved the $5,628 (the PV of $8,128 minus the $2,500 initial payment), you'd earn 1% interest on $5,628 the first month, $5,128 plus that interest the second month, etc. **Using your Time Value of Money functions on your calculator**   N = 3x2 = 6   PV = -914   PMT = (.16 x 1000)/2 = 80   FV = 1000    Compute I/Y  Or     **Step by step calculations**   1) Compute the PV of **(FV of Bond)**1000 in **(3x2)**6 periods at **(16%/2)**8% with no payments   2) Compute the PV of an Annuity of **(.16/2x1000)**$80 payments over **(3x2)**6 periods with an interest rate of **(16%/2)**8% and 0 Future Value   3) Combine the values from Steps 1 and 2 "I got $3394.83 The first problem with this is that it is backwards.  The NPV (Net Present Value) of three future payments of $997 has to be less than the nominal value.  The nominal value is simple:  $2991.   First step, convert the 8% annual return from the stock market to a monthly return.  Everyone else assumed that the 8% is a monthly return, but that is clearly absurd.  The correct way to do this would be to solve for m in  But we often approximate this by dividing 8% by 12, which would be .67%.  Either way, you divide each payment by the number of months of compounding.   Sum those up using m equal to about .64% (I left the calculated value in memory and used that rather than the rounded value) and you get about $2952.92 which is smaller than $2991.   Obviously $2952.92 is much larger than $2495 and you should not do this.  If the three payments were $842.39 instead, then it would about break even.   Note that this neglects risk.  In a three month period, the stock market is as likely to fall short of an annualized 8% return as to beat it.  This would make more sense if your alternative was to pay off some of your mortgage immediately and take the payments or yp pay a lump sum now and increase future mortgage payments.  Then your return would be safer.   Someone noted in a comment that we would normally base the NPV on the interest rate of the payments.  That's for calculating the NPV to the one making the loan.  Here, we want to calculate the NPV for the borrower.  So the question is what the borrower would do with the money if making payments and not the lump sum.   The question assumes that the borrower would invest in the stock market, which is a risky option and not normally advisable.  I suggest a mortgage based alternative.  If the borrower is going to stuff the money under the mattress until needed, then the answer is simple.  The nominal value of $2991 is also the NPV, as mattresses don't pay interest.  Similarly, many banks don't pay interest on checking these days.  So for someone facing a real decision like this, I'd almost always recommend paying the lump sum and getting it over with.  Even if the payments are ""same as cash"" with no premium charged." Both are correct depending on what you are really trying to evaluate. If you only want to understand how that particular investment you were taking money in and out of did by itself than you would ignore the cash.  You might use this if you were thinking of replacing that particular investment with another but keeping the in/out strategy. If you want to understand how the whole investment strategy worked (both the in/out motion and the choice of investment) than you would definitely want to include the cash component as that is necessary for the strategy and would be your final return if you implemented that strategy. As a side note, neither IRR or CAGR are not great ways to judge investment strategies as they have some odd timing issues and they don't take into account risk. O boy you can take an entire on this. Here are the basics. Project future cash flows on a series of underlying assumptions such as growth rate and risk free rate. You then have to adjust top line items such as depreciation and come up with FCF. Then discount everything back with a terminal value. Set your xirr formula to a very tall column, leaving lots of empty rows for future additions. In column C, instead of hardcoding the value, use a formula that tests if it's the current bottom entry, like this: =IF(ISBLANK(A7),-C6, C6) If the next row has no date entered (yet), then this is the latest value, and make it negative. Now, to digress a bit, there are several ways to measure returns. I feel XIRR is good for individual positions, like holding a stock, maybe buying more via DRIP, etc. For the whole portfolio it stinks. XIRR is greatly affected by timing of cash flows. Steady deposits and no withdrawals dramatically skew the return lower. And the opposite is true for steady withdrawals. I prefer to use TWRR (aka TWIRR). Time Weighted Rate of Return. The word 'time' is confusing, because it's the opposite. TWRR is agnostic to timing of cashflows. I have a sample Excel spreadsheet that you're welcome to steal from: http://moosiefinance.com/static/models/spreadsheets.html (it's the top entry in the list). Some people prefer XIRR. TWRR allows an apples-to-apples comparison with indexes and funds. Imagine twin brothers. They both invest in the exact same ideas, but the amount of cash deployed into these ideas is different, solely because one brother gets his salary bonus annually, in January, and the other brother gets no bonus, but has a higher bi-weekly salary to compensate. With TWRR, their percent returns will be identical. With XIRR they will be very different. TWRR separates out investing acumen from the happenstance timing of when you get your money to deposit, and when you retire, when you choose to take withdrawals. Something to think about, if you like. You might find this website interesting, too: http://www.dailyvest.com/ If you mean the internal rate of return, then the quarterly rate of return which would make the net present value of these cash flows to be zero is 8.0535% (found by goal seek in Excel), or an equivalent compound annual rate of 36.3186% p.a. The net present value of the cash flows is: 10,000 + 4,000/(1+r) - 2,000/(1+r)^2 - 15,125/(1+r)^3, where r is the quarterly rate. If instead you mean Modified Dietz return, then the net gain over the period is: End value - start value - net flow = 15,125 - 10,000 - (4,000 - 2,000) = 3,125 The weighted average capital invested over the period is: 1 x 10,000 + 2/3 x 4,000 - 1/3 x 2,000 = 12,000 so the Modified Dietz return is 3,125 / 12,000 = 26.0417%, or 1.260417^(1/3)-1 = 8.0201% per quarter, or an equivalent compound annual rate of 1.260417^(4/3)-1 = 36.1504%. You are using an inappropriate formula, because we know for a fact that the flows take place at the beginning/end of the period. Instead, you should be combining the returns for the quarters (which have in fact been provided in the question). To calculate this, first calculate the growth factor over each quarter, then  link them geometrically to get the overall growth factor. Subtracting 1 gives you the overall return for the 3-quarter period. Then convert the result to a quarterly rate of return. Growth factor in 2012 Q4 is 11,000/10,000 = 1.1 Growth factor in 2013 Q1 is 15,750/15,000 = 1.05 Growth factor in 2013 Q2 is 15,125/13,750 = 1.1 Overall growth factor is 1.1 x 1.05 x 1.1 = 1.2705 Return for the whole period is 27.05% Quarterly rate of return is 1.2705^(1/3)-1 = 8.3074% Equivalent annual rate of return is 1.2705^(4/3)-1 = 37.6046% ========= I'd recommend you to refer to Wikipedia. Illustrating with a shorter example:  Suppose I deposit 1,000 USD. Every year I deposit another 100 USD. I want to know how much money will be on that savings account in 4 years.  The long-hand calculation is Expressed with a summation  And using the formula derived from the summation (as shown by DJohnM) So for 20 years Note in year 20 (or year 4 in the shorter example) the final $100 deposit does not have any time to accrue interest before the valuation of the account. "When you're calculating the cash flows used to compute an IRR, with regard to the expenses used to calculate those cash flows:  Do you assume that expenses are going to be higher than they would be today, by using an assumed inflation rate?   Or is everything (all cash flows) assumed to be in today's dollars, and you account for inflation's effect on your actual returns at ""the end"" by subtracting off the inflation rate from the IRR?" What you are looking here is the cost of capital, because that is what you are effectively giving up in order to invest in those loans. In a discounted cash-flow, it would be the *i* in the denominator (1+*i*). For instance, instead of purchasing those loans you could have lent your money at the risk-free rate (not 100% true, but typical assumption), and therefore you are taking a slight risk in those loans for a higher return.  There are several ways to compute that number, the one most often used would be the rate if the bank were to lend that money. In this way, it would be the Fed Funds rate plus some additional risk premium. The solution is x = 8.92. This assumes that Chuck's six years of deposits start from today, so that the first deposit accumulates 10 years of gain, i.e. 20*(1 + 0.1)^10.  The second deposit gains nine years' interest: 20*(1 + 0.1)^9 and so on ...    If you want to do this calculation using the formula for an annuity due, i.e. http://www.financeformulas.net/Future-Value-of-Annuity-Due.html  where  (formula by induction) you have to bear in mind this is for the whole time span (k = 1 to n), so for just the first six years you need to calculate for all ten years then subtract another annuity calculation for the last four years.  So the full calculation is:  As you can see it's not very neat, because the standard formula is for a whole time span.  You could make it a little tidier by using a formula for k = m to n instead, i.e.  So the calculation becomes  which can be done with simple arithmetic (and doesn't actually need a solver). The preparation for starting up of the company has lasted already more than 2 years. Let's say the company starts officially in January next year. So, in January 2014... 8 million USD is invested to purchase the equipments and the company will start selling their prdocuts right away. Imagine the company will be selling the same amount of products each year at the same price for 5 years. After 5 years it will sell the equipments for 6 million USD and cease to exist. The depreciation of  equipments is divided into those 5 years. So, each year the depreciation of equipments is 400.000 USD. In despite of this, the company will make 500.000 USD per year as a profit before tax.  So, the equipments are bought in Januardy 2014 (first month of the existence of the company) and sold in December 2018 (last month of the existence of the company). This is the NPV that I calculated. Is it correct? I feel like IRR is the tool you want to use for this, then you can look at your output and determine if it's higher than what your discount rate is likely to be.  Similarly, you can just do a traditional NPV analysis and then examine the sensitivity by changing the discount rate. If you're safely in profitable territory then you're probably fine despite not knowing the discount rate. The MWRR that you showed in your post is calculated incorrectly. The formula that you use... ($15,750 - $15,000 - $4,000) / ($15,000 + 0.5 x $4,000) Translates into a form of the DIETZ formula of (EMV-BMV-C)/(BMV + .5 x C) The BMV is the STARTING balance. And as a matter of fact, the starting balance was NOT 15,000. It was IN FACT 11,000. See, the starting value for a month MUST BE the ending value of the prior month. So the BMV of 11,000 would give you the correct answer. Because if you added 4,000 at the start of the month (on day 1), it would have to have been ADDED to the 11,000 of the PRIOR month's ENDING value. Make sense? That would also mean that the addition of 4000 to the 11000 would imply that you started day 1 with 11,000. Make sense? Summary: When doing the calculations, you may use the ending value on the last day of the month to get your EMV. BUT YOU MAY NOT take the ending value on day 1 to get the BMV. That simply can not make sense since you already added a bunch of money during the day. Think about it. Davie The short answer is that you would want to use the net inflow or net outflow, aka profit or loss.   In my experience, you've got a couple different uses for IRR and that may be driving the confusion.  Pretty much the same formula, but just coming at it from different angles.   Thinking about a stock or mutual fund investment, you could project a scenario with an up-front investment (net outflow) in the first period and then positive returns (dividends, then final sale proceeds, each a net inflow) in subsequent periods.  This is a model that more closely follows some of the logic you laid out. Thinking about a business project or investment, you tend to see more complicated and less smooth cashflows.  For example, you may have a large up-front capital expenditure in the first period, then have net profit (revenue less ongoing maintenance expense), then another large capital outlay, and so on.   In both cases you would want to base your analysis on the net inflow or net outflow in each period.  It just depends on the complexity of the cashflows trend as to whether you see a straightforward example (initial payment, then ongoing net inflows), or a less straightforward example with both inflows and outflows.   One other thing to note - you would only want to include those costs that are applicable to the project.  So you would not want to include the cost of overhead that would exist even if you did not undertake the project.