Net present value, internal rate and payback
Your data
A negative line is money going out in that period, which is how a project with a mid life overhaul or a closing cost gets written. Those are exactly the cases where the internal rate stops behaving.
Results
What the project is worth today at your rate
—
| Rate at which the project is worth exactly nothing | — |
| Periods until the money comes back | — |
| The same, counting each return at your rate | — |
| Times the cash flow changes sign | — |
What the project is worth at other rates
| Rate | Worth today |
|---|
A spreadsheet answers this with a single internal rate because it starts from a guess and stops at the first rate it lands on. It does not tell you the others exist. Here the whole range is swept for sign changes before anything is reported, which is why a cash flow like minus one hundred, plus two hundred and thirty, minus one hundred and thirty two comes back with both ten and twenty per cent.
The internal rate also says nothing about size. Ten per cent of a large project and fifty per cent of a small one are not comparable as rates, and the amount above the table is the one that adds up across projects.
How do I work out the present value of a project?
Bring every amount back to today by dividing it by one plus your rate, raised to the period it lands in, and add them all up, counting the money that goes out as negative.
The rate to use is the one you would earn on that money elsewhere. That is why this page calls it the rate you would earn elsewhere rather than a magic constant: change it and the answer changes, which is the point.
Can a project have more than one internal rate of return?
Yes, and it happens more often than the textbooks suggest. The cash flow minus one hundred, plus two hundred and thirty, minus one hundred and thirty two is worth exactly nothing at ten per cent and also exactly nothing at twenty per cent.
You can check that by hand: writing x for one over one plus the rate, the whole thing becomes a quadratic, and a quadratic has two roots. The rule behind it is that the number of rates cannot exceed the number of times the cash flow changes sign, which this page counts for you.
Why does my spreadsheet only show one of them?
Because its function starts from a guess and stops at the first rate it lands on. Change the guess and it can return the other one, without a word of warning either time.
This page sweeps the whole range from minus ninety nine per cent upward looking for places where the value crosses zero, and reports every one it finds. That is slower and it is the only way to know how many there are.
So which number should I decide with?
The amount, not the rate. When there is more than one internal rate, comparing the internal rate against your own rate stops meaning anything, because there is no single internal rate to compare.
The rate also says nothing about size: ten per cent of a large project and fifty per cent of a small one cannot be added, ranked or spent. The present value can.
Reactions
0
0 Comments
Be the first to comment