To know whether a purchase earns anything, you need two answers, not one: when the money comes back, and how much is left once the money has also paid for the time it was tied up. The first is the payback, and the second is the net present value (NPV). Two purchases of 300,000 that both pay back in two periods can land on opposite sides: at 12% a period, one loses 46,492 in value and the other adds 125,833.
At the end of this article you fill in a one-page decision sheet: the rate you accept and where it came from, the cash the purchase changes, a verdict on value and on cash, and a blank line to check the first year against your forecast.
Two purchases of 300,000 each show why one answer is not enough. The currency does not matter, and a period is whatever you count in, a year or a production cycle. Purchase A returns 150,000 in each of the first two periods and nothing after. Purchase B returns the same 150,000 twice and then 90,000 in each of three more periods. Both pay back in exactly two periods. If the money costs you 12% a period, A leaves you about 46,500 worse off than not buying at all, and B leaves you about 125,800 better off.
Same money in, same payback, and some 172,300 apart. Both cases can be checked in the payback, net present value (NPV) and internal rate of return (IRR) calculator.
A machinery dealer usually works out only the first answer, on the back of an envelope: price divided by what the machine saves in a year. Nobody is lying. From that sum you learn when the money comes back, which is worth knowing. What happens after that day is never part of it, and the whole gap between A and B comes from what happens after that day.
Why isn’t getting your money back the same as earning anything?
Payback is counted only up to the break-even point, the day the running total of cash gets back to zero, and that day is almost never the end of the investment. Purchase A handed back exactly 300,000 against 300,000 put in. Nothing was earned. Less than nothing, in fact: the 300,000 left the account on day one and came back spread over two periods, and money that arrives later buys less than money you already hold.
Aswath Damodaran, a finance professor at New York University who publishes his course material openly, writes that cash flows across time cannot be added up. They have to be brought to the same point in time before aggregation. Simple payback adds them up anyway, which is why it is so easy to do in your head.
| Cash flow by period | Payback | Net present value | Internal rate of return | |
|---|---|---|---|---|
| Purchase A | 150,000 · 150,000 · 0 · 0 · 0 | 2.0 periods | −46,492.35 | 0.0% |
| Purchase B | 150,000 · 150,000 · 90,000 · 90,000 · 90,000 | 2.0 periods | +125,832.92 | 30.2% |
Rurivia calculation from the two hypothetical cash flows above, made with the payback, net present value and internal rate of return calculator on this site.
The internal rate of return is, in Damodaran’s definition, the discount rate that sets the net present value equal to zero. Purchase A gives back exactly what it took and not a cent more, so the only rate at which it comes out even is 0%, and that zero is exact, not rounded. Every unit of the difference between A and B was earned after the break-even point, in periods that are not counted in the payback.
This is not a corner case built to make a point. It is the shape of most investments whose useful life runs longer than their payback. In a peer-reviewed Brazilian study of a blueberry orchard, Oliveira and four colleagues found that “The return time (discounted payback period) of the total initial investment occurred after 4.96 years” of a ten-year useful life. More than five of those ten years, the ones in which a planted orchard earns most, sit outside the payback figure.
Why can the rate you use flip the answer?
Change nothing on the farm and the answer can still flip. Take a third purchase of 300,000, Purchase C, that returns nothing in the first period and then 80,000, 120,000, 140,000 and 150,000. At 12% per period it creates 23,275.70. At 14% it creates 3,350.52, next to nothing on 300,000. At 16% it loses 14,930.34. The flows did not change; only the rate did.
| Rate per period | Net present value | Discounted payback |
|---|---|---|
| 8% | +68,838.63 | 4.3 periods |
| 10% | +45,033.56 | 4.5 periods |
| 12% | +23,275.70 | 4.7 periods |
| 14% | +3,350.52 | 5.0 periods |
| 16% | −14,930.34 | never breaks even |
The rate at which the answer turns from yes to no is 14.35% (the calculator rounds it to 14.4%), and that rate has a name: it is the internal rate of return of these flows. It is not a fourth figure sitting beside the others. It is this table read backwards. The guide to farm investment projects from the Food and Agriculture Organization of the United Nations (FAO) describes it the same way, as the highest discount rate a project can carry and still be worth doing, since a rise in the rate lowers the net present value.
So where does your rate come from? There is no universal one, and it goes by several names. Damodaran calls it the hurdle rate and ties it to the cost of capital, the FAO guide calls it the discount rate, and the blueberry study calls it the minimum attractive rate of return. Whatever the name, it is the lowest return you will accept from this money.
Three open studies of real farm decisions each chose a different rate and wrote down why. The blueberry orchard used 11% a year, tied to Brazil’s base interest rate, the SELIC, in the same period. Bravo Motiño, planning an organic cacao farm in a thesis at Zamorano, an agricultural university in Honduras, worked out an opportunity cost of 12.57% for the owners’ money and discounted at 15% anyway, a rate chosen to be more severe and conservative in the investment plan.
A goat milk system in north-eastern Brazil, costed by França and three colleagues at Embrapa, Brazil’s public agricultural research agency, set no rate of its own: the authors judged the two rates of return they found against a benchmark, calling them both very high, when 25% would already be a reasonable rate.
Eleven, fifteen, twenty-five. All three are defensible, and all three are choices. What makes a choice defensible is that its origin is written next to the number, with a date, so that next year somebody can ask whether the origin still holds.
For a farm, a workable rate is the higher of two figures, plus a premium for risk. The first is the interest on the loan that would pay for this purchase, taken from the loan contract or the lender’s offer as the full yearly cost with fees included, because money borrowed at 14% cannot be judged at 8%. If you have never added those fees up, there is a separate article on adding interest, fees and tax to your cost. The second is what the money earns where it sits now, if it is sitting somewhere.
Then add a premium when this project is riskier than the farm’s ordinary work, which Damodaran states as a first principle: The hurdle rate should be higher for riskier projects. In practice it often goes the other way: the risky project gets the low rate, because the low rate is the one that lets it pass.
One check catches a common mistake. Damodaran’s rule is that The cash flows on a project and the discount rate used should be defined in the same terms, and specifically that If the cash flows are nominal (real), the discount rate has to be nominal (real). In practice: if you wrote the flows in today’s money, without letting prices rise, the rate has to have inflation taken out of it too. Applying a bank rate that already carries inflation to flows that do not is the quickest way to reject a good investment while doing every step correctly.
Why do net present value and payback disagree?
They answer two different questions, and only one of them is about value. Payback is the time your cash stays out. Net present value is what is left once the money has come back and paid the rate you demanded. A farm needs both answers; the mistake is asking one figure for both.
Graham and Harvey, two finance professors who surveyed 392 chief financial officers of companies in the United States and Canada, sum up the case against payback in one line: “Payback ignores the time value of money and cash flows beyond the cutoff date; the cutoff is usually arbitrary”. The cutoff is the longest payback the buyer will accept, say three years. Discounted payback, which shrinks each period’s cash by your rate before adding it up, fixes the first of those three defects and leaves the other two.
In the same survey more than half the financial officers said they always or almost always used payback, and the authors found no link between using it and how much debt a company carried; those are corporations, not farms, so from the survey you learn who uses the method, not who should.
Fixing that one defect moves Purchase C by a whole period. Counted without discounting, it pays back in 3.7 periods; discounted at 12%, in 4.7. On a five-period investment, a fifth of the horizon separates two figures that many people treat as the same number. That gap is the cost of time.
The other two defects stay. Cash after the break-even point is still invisible, which is the whole contrast between A and B, and a three- or four-year cutoff is usually habit rather than a calculation.
None of this crosses payback off your sheet. It changes why it is there: you have a loan with a due date and a credit limit with a figure on it, and payback is the only one of the three figures you can hold against those two.
What is payback really about, and who needs it?
It is the time your cash stays exposed, and that matters to your lender before it matters to your profit. That is why it belongs on the sheet beside the other two.
The goat milk study is a clear case. França and colleagues found that recovering the extra investment in animals, shelter, fencing and forage would take 7.3 years. On its own that figure decides nothing. It becomes a decision against the loan the authors assumed: a subsidized ten-year term carrying zero charges, with the yearly installment taking 51.8% of the net margin, which the authors read as a comfortable position for the farmer and one the lending banks accept. Recovery in 7.3 years inside a ten-year term leaves room. The same 7.3 years inside a five-year term is the same investment on a farm in trouble.
A second cash figure matters more than the break-even point and is rarely written down: the deepest point, the moment the running cash is furthest in the red. For Purchase C it comes at the end of the first period, 300,000 in the red. Hold that figure against the credit limit the bank has actually approved for you, because that is the moment the farm either has the money or does not. If you do not yet know how much debt the farm can carry, checking whether your farm debt fits what it earns comes first. From a payback of 4.7 periods alone you cannot tell how deep the hole got on the way.
And the first break-even point is not always the last. A cost later on, a replanting, an engine, a year when the price collapses, can push the running cash back below zero. The payback figure is then still correct but no longer means what people take it to mean: it is the first time the cash got back to zero, not the end of the exposure. The calculator flags that case instead of printing a tidy number over it.
Read value and cash together and you get four answers, not two. Purchase C creates 23,275.70 of value at 12%, so it passes on value. On cash it is tight: 300,000 in the red at the end of the first period, and at the end of the fourth still 61,838.33 short of breaking even. If the periods are years and the loan runs four years, the last installment falls due before the money is back, and it gets paid out of some other activity.
- Value yes, cash yes: sign.
- Value yes, cash no: the investment is not bad, the financing is wrong. Renegotiate the term, not the price.
- Value no, cash yes: the money comes back fast only because the asset does not last long, so the dealer’s figure looks good and the purchase is still wrong. Sign it only when the money buys something other than a return, a legal requirement or a bottleneck that stops the whole harvest, and write that reason on the sheet.
- Value no, cash no: drop it.
The two answers in the middle are the ones that settle the year, and with a single figure you cannot see them.
When does the rate of return not exist, and when does it exist twice?
A project has exactly one net present value and can have several rates of return. Damodaran puts it flatly: A project can have only one NPV, whereas it can have more than one IRR. His example is a flow of 1,000 out, then 800, 1,000 and 1,300 in, then 2,200 out at the end: “This project has two internal rates of return. The first is 6.60%, whereas the second is 36.55%”.
That looks like a textbook curiosity until you notice what produces it: any investment that asks for money again partway through. Cash that goes out, comes in and goes out again is the ordinary shape of a long-lived farm asset, and that shape can carry two rates of return or none.
The calculator counts the sign changes and flags a flow of that shape, but you have to recognize the shape before you type it. Replanting a perennial crop, restoring a pasture in year six, the engine overhaul already in the plan, a new shed roof: each puts a second outflow into the flow. Leaving it out does make the second rate disappear, but then the rate belongs to an asset nobody maintains. Read the net present value instead, because there is only ever one.
That is the first limit of the rate of return. The second costs money more often: it is a percentage, and from a percentage alone you cannot tell how big anything is. Damodaran: The NPV is a dollar surplus value, whereas the IRR is a percentage measure of return, so the net present value runs larger for big projects and the rate of return runs higher for small ones. A repair that returns a high percentage on a small sum and an expansion that returns a lower percentage on a large one cannot be compared by percentage: what you need to know is which one leaves more money in the account, and that is an amount.
There is one case where the net present value on its own also ranks wrongly, and it is common on farms: one credit line and two purchases competing for it. Damodaran notes that “The problem with the NPV rule, when there is capital rationing, is that it is a dollar value. It measures success in absolute terms”, and the fix is to divide it by the initial investment.
In his example, a project creating 467,937 on 1,000,000 invested creates 0.47 of value per unit invested, and one creating 1,358,664 on 10,000,000 creates 0.14. The smaller one wins. When what is short is credit and not opportunities, rank by value per unit of credit tied up, not by the largest net present value.
The third limit matters most on a farm. Behind the rate of return is a quiet assumption: that cash coming back is reinvested at that same rate. Damodaran sets the two rules side by side: the net present value assumes reinvestment at the rate you set, while the internal rate of return rule assumes that intermediate cash flows on the project get reinvested at the IRR.
On a farm the cash that comes back in period two goes into the operating account and pays for diesel and wages; it earns nothing like the rate that came out of the calculator. A spectacular rate of return on a long project only holds on a farm that does not exist; the net present value at a rate you can defend holds on yours.
What do the three figures leave out?
All three are only as good as the flows you typed. If the list you typed is wrong, the answer is wrong to the last decimal.
How much that matters can be measured. Bravo Motiño tested the cacao plan against price and cost separately: the net present value reaches zero when variable costs rise by 177%, but already when the sale price falls by 58%. Costs would have to nearly triple; the price only has to fall by a little more than half. Dividing one by the other (our arithmetic, not the author’s), the price was about three times as dangerous as cost on that project, so the price is the figure to watch through the whole cycle.
The same test on Purchase C is blunter. Take 10% off every inflow, a mild bad year rather than a disaster, and the net present value goes from 23,275.70 to −9,051.87. The simple payback moves from 3.7 periods to 4.0. One figure barely moved and the other changed sides. That is also a reason to build each period’s cash from a budget of each activity, such as the margin you expect a crop to leave, rather than from a percentage applied to last year.
There is a risk none of these figures captures, and the authors of the goat milk study flag it themselves after finding a rate of return of 77%: they call the results worrying, because they depend entirely on the purchase guarantee and the subsidized prices of the federal milk program. A high rate of return that rests on a single buyer is only as good as that buyer, and none of the three figures has a place for it. Whoever writes the flows has to write beside them who each one depends on.
Projects of different length, when you can pick only one, cannot be compared directly. Damodaran: “The net present values of mutually exclusive projects with different lives cannot be compared, since there is a bias towards longer-life projects”. His fix is to replicate the shorter project until both horizons match, or convert each net present value into the equivalent annuity for that life, the even yearly amount that, over the project’s life and discounted at the same rate, is worth the same.
In his example a five-year project is worth 442 and a ten-year one 478; as yearly amounts at 12% they swap places, 122.62 a year against 84.60. On a farm this is the used tractor that lasts five years against the new one that lasts ten: comparing raw net present values favors the longer one for being longer, not better. For the same reason, do not pick the horizon that makes the number look best.
The blueberry study set its ten-year horizon on obsolescence, judging that after ten years much of the equipment may need replacing: an argument somebody else can check and reject. It is the same judgment you make when you write down how long a machine should last, before the decision rather than during it.
The flows must be incremental: only what changes because of this decision. Damodaran’s instruction fits on the office wall: Use cash flows rather than earnings. You cannot spend earnings. Depreciation is not a flow. Profit is not a flow. The whole activity’s result is not the flow either, because part of it would have happened without the purchase.
One outflow is still missing, the one that is never in the supplier’s quote and the most common surprise of the first year: the money tied up in the operation while it runs. Inputs bought ahead, animals being raised, stock waiting for a price, credit you gave the buyer. Damodaran calls it working capital and warns that “The failure to consider working capital in a capital budgeting project will overstate cash flows on that project and make it look more attractive than it really is”.
That money leaves at the start and comes back at the end, when the stock is sold, so it goes on your list twice: with a minus sign in the first period and a plus sign in the last. Count only the price of the equipment and you are valuing a cheaper investment than the one you are making.
The list is the difference between the farm with this decision and the farm without it, so the calculator compares against doing nothing, never against the alternative that would take the same money. Give that alternative its own line, and write down the figure that ruled it out while it is fresh, in a record of the options you decided against; six months later nobody remembers it.
Where to start
Two hours, with the supplier’s quote, the loan terms and last year’s actual figures on the table. One sheet of paper, one decision, a date at the bottom.
That last line is the only part of the sheet anyone can ever check. The rate was a choice, the horizon was a judgment, and no net present value will ever appear on a bank statement. The first period’s actual cash against what you forecast for it can be checked. Fill that line three years running and you will know whether your estimates run optimistic, and by how much, in your own currency on your own farm.
Two related decisions each have their own article. The first is a written investment plan, where you settle which purchases are on the list at all and what has to be true before you buy one; it carries no return figures. The second is the choice to rent the land or buy it, this same arithmetic run on the biggest purchase most farms ever make, where the horizon is a generation and the alternative is not doing nothing.
Other money decisions are in the finance section of this library, and the farm management page is about running the whole farm as a business, where the same habit pays: a decision nobody wrote down cannot be learned from, however well it turned out.