Javascript IRR (Internal rate of return) Formula Accuracy

Question

I'm using a IRR function in javascript to create calculation a that is done in excel using its own IRR function. The problem is mine is little off and I have no idea why. Here's the code below.

var IRRval = [];

IRRval.push(-financed);
for (i = 0; i < period; i++) {
    IRRval.push(rental);
}

var IRR = IRRCalc(IRRval, 0.001) * 0.01;

function IRRCalc(CArray, guest) {
    inc = 0.000001;
    do {
        guest += inc;
        NPV = 0;
        for (var j=0; j < CArray.length; j++) {
            NPV += CArray[j] / Math.pow((1 + guest), j);
        }
    } while (NPV > 0);
    return guest * 100;
}

Now if you use these figures:

Period 24

Financed 22000

Rental 1017.5000

My Result is: 0.008523000000000175

Excel Result is: 0.008522918

OR

Period 42

Financed 218000

Rental 5917.1429

My Result is: 0.006247000000000489

Excel Result is: 0.00624616

The Excel function is called: =IRR(T12:T73,0.01) T12-T73 is the same figures I'm using.

Any help would be much appreciated, Thanks Jason

UPDATE

I've solved it by changing the values below. But now the performance is too slow. Any ideas on how to improve this?

IRRCalc(IRRval, 0.001)

//to

IRRCalc(IRRval, 0.0001)

inc = 0.000001;

//to

inc = 0.00000001;

Not a good way to program an IRR function, you are going through the domain of the function and finding it's value over the range. For a good number of cash flows, your code will never come to a halt as NPV will never be below or at zero. — , Mar 02 '13 at 01:33
@AbrahamA Thanks for your comment. If you have the time I'd love to see how it should be done correctly. — dciso, Mar 04 '13 at 15:07
@dciso Have a look at tadJS JavaScript financial functions library at https://github.com/FinancialEngineer/tadJS — , Feb 10 '14 at 06:11

score 12 · Answer 1 · answered Oct 24 '13 at 07:59

12

We modified the code to achieve performance and accuracy. Try this:

function IRRCalc(CArray) {

  min = 0.0;
  max = 1.0;
  do {
    guest = (min + max) / 2;
    NPV = 0;
    for (var j=0; j<CArray.length; j++) {
          NPV += CArray[j]/Math.pow((1+guest),j);
    }
    if (NPV > 0) {
      min = guest;
    }
    else {
      max = guest;
    }
  } while(Math.abs(NPV) > 0.000001);
  return guest * 100;
}

answered Oct 24 '13 at 07:59

Zohaib

496
7
21

Zohaib, Thanks for your code, its working like a charm when we giving more terms like 20 or 25 years, but its hanged when giving terms like 3 05 5. can you help on this? – Giridaran Regunathan Feb 13 '14 at 08:22
@GiridaranRegunathan - you need to add a counter and exit after a certain number of iterations without resolution (the method fails and you have an undefined result). The actual value depends on your accuracy requirements, but we use 100000 for some non-critical path code. – Edward Jul 23 '14 at 21:48
2

if you want to reproduce Excels IRR function that also returns negative values, setting min = -1.0; works for me. – schudel Aug 27 '15 at 08:36
@Zohaib just trying to come up with a good way of exiting after a certain number of iterations and returning `undefined`. my attempt is below which I though you might be able to help me with. – HattrickNZ Dec 20 '15 at 22:47
How does this work for anyone? By itself there are errors thrown for min, max guest and NPV being undefined. Where does guest (guess) get incremented? – Altimus Prime Jun 29 '17 at 14:36

whitneyit · Accepted Answer · 2013-02-26T12:52:40.050

10

After a quick skim read through your code, the error seems to be related to floating point precision error. More information can be found here: http://ajaxian.com/archives/crock-on-floating-points-in-javascript

In older javascript engines, if you did 0.3 + 0.3 you get something like 0.600000000001

Though most javascript engines today return 0.6, under the hood, the problem remains. Adding floats together causes unexpected results. So in your case the

inc = 0.000001;
guest += inc;

seems to me, to be the problem.

A way to solve this would be to use whole numbers. So instead of 0.000001 you would use 1 and instead of 0.001 you would use 1000. Then divide your return result by 100000

edited Feb 26 '13 at 12:52

answered Feb 26 '13 at 12:36

whitneyit

1,226
8
17

Thanks for your reply. I tried using whole numbers only to get 8523000. Same level of accuracy. – dciso Feb 26 '13 at 13:20
The / Math.pow() in NPV could be the next culprit. Either way, you probably won't be able to solve it there. – whitneyit Feb 26 '13 at 13:23
I have tested more than 5 IRR library, non of them are correct until I found this. Thank you so much!!!! – jasonfungsing Nov 22 '16 at 03:21

score 2 · Answer 3 · edited Jun 15 '22 at 01:32

2

Try this.

function NPV(discountRate, cashFlow){
    var npv = 0;
    for(var t = 0; t < cashFlow.length; t++) {
        npv += cashFlow[t] / Math.pow((1+ discountRate),t);
    }
    return npv;
}


function IRR(cashFlow,guess){
    guess = guess ? guess : 0.1;
    var npv;
    do
    {
        npv = NPV(guess,cashFlow);
        guess+= 0.001;

    }
    while(npv > 0)

    return guess;
}

edited Jun 15 '22 at 01:32

Mohamed Sayed

491
7
10

answered May 27 '13 at 17:50

Zulfugar Ismayilzadeh

2,643
3
16
26

What if the guess is too high? Your function will never decrease it. – Jakob Alexander Eichler Nov 13 '19 at 17:51

score 1 · Answer 4 · answered Feb 26 '13 at 14:44

1

It's a floating point issue to be sure. You're going to want to use a library like BigDecimal.js to handle your values. It's really the only way to avoid this issue.

answered Feb 26 '13 at 14:44

Ben Lesh

107,825
47
247
232

HattrickNZ · Answer 5 · 2015-12-20T22:50:55.443

I would like to build on from @Zohaib Answer, but what I would like to do is show undefined where appropriate. The best I can do is get it to equal to zero. I am using this simple dataset irr_arr=[-100, 100, 100, 100, 100,100]. I would appreciate some advice.

//IRRCALC funtion that handles irr going to infinity 

function IRRCalc_test(CArray) {

  min = 0.0;
  max = 1.0;
  c=0;
  do {
    guest = (min + max) / 2;
    NPV = 0;
    for (var j=0; j<CArray.length; j++) {
          NPV += CArray[j]/Math.pow((1+guest),j);
    }
    if (NPV > 0) {
      min = guest;
      c++; 
    }
    else {
      max = guest;
      c++;
    }

    if(c>=15){ return guest*100; }
  } while(Math.abs(NPV) > 0.000001);
  return guest*100;
}


// some testing 

irr_arr=[-100, 100, 100, 100, 100,100]
irr_res_arr_expected=[0,0,61.8,83.93,92.76,96.6]
for(i=1;i<=irr_arr.length;i++){
console.log("irr_arr - ",irr_arr.slice(0,i));
console.log("IRRCalc - ",IRRCalc(irr_arr.slice(0,i)))
//console.log("irr_expected - ", irr_res_arr_expected[i-1])
//if(IRRCalc(irr_arr.slice(0,i))===parseFloat(irr_res_arr_expected[i-1]).toFixed(2)){console.log(i,"- TRUE")} else {console.log(i,"- FALSE")}
}

this is the output

irr_arr -  [-100]
IRRCalc -  0.00      <<<<<<<<<<<<<<<<<<<------- this should be 'undefined' and not 'zero'
irr_arr -  [-100, 100]
IRRCalc -  0.00
irr_arr -  [-100, 100, 100]
IRRCalc -  61.80
irr_arr -  [-100, 100, 100, 100]
IRRCalc -  83.93
irr_arr -  [-100, 100, 100, 100, 100]
IRRCalc -  92.76
irr_arr -  [-100, 100, 100, 100, 100, 100]
IRRCalc -  96.60

here is the excel of what I am trying to produce

score 0 · Answer 6 · answered Feb 21 '16 at 12:10

0

Don't set your min IRR to 0. That is what bounds your answer. Try allowing it to go negative. Also don't try to calc an IRR on one number.

answered Feb 21 '16 at 12:10

Set F

1

score 0 · Answer 7 · answered Sep 14 '20 at 16:03

This might be a better way of writing the calculation. This allows the code to calculate instances of negative IRR or IRR above 100%.

        var IRRval = [];

        IRRval.push(-financed);
            for (i = 0; i < period; i++) {
            IRRval.push(rental);
        }
        var IRR = IRRCalc(IRRval, 0.001) * 0.01;

        function IRRCalc(CArray) {
            var r = 0
            min = -1.0;
            max = 10000.0;
            do {
                guest = (min + max) / 2;
                NPV = 0;
                for (var j = 0; j < CArray.length; j++) {
                    NPV += CArray[j] / Math.pow((1 + guest), j);
                }
                if (NPV > 0) {
                    min = guest;
                }
                else {
                    max = guest;
                }
                r++
            } while (r < 100);
            return guest * 100
        }

score 0 · Answer 8 · answered Jun 15 '23 at 12:29

Here is an optimized cote to calculate IRR

This starts incrementing in 1 and if the algo reaches negative it change signal and divide increment by 10, now it decrements in 0.1 and now if it goes to positive change signal again divides by 10,and now it increments again in 0.01, it goes on till react temp between -100 and 100, wuat guarants a precise IRR.

function tirCalc(amounts, investment) {
    // This algorithm goes up and down till reach zero.
    let tir = 0.0;
    let result = false;
    let dividend = 100;
    let actualSignal = 1; //positive, means tir is increasing

    if (investment > 0) investment *= -1;
    do {
        let temp = 0;
        //Calculate tir based on the formula
        for (let i = 0; i < amounts.length; i++) {
            temp += amounts[i] / Math.pow(1 + tir, i + 1);
        }
        temp += investment;

        //Checks if tir is zero, zero is the expected result
        if (temp < 100 && temp > -100) {
            result = true;
            break;
        }

        //During calculation this code change the sum direction and rate changing the signal and dividend size to reduce the increment
        if ((temp < -100 && actualSignal > 0) || (temp > 100 && actualSignal < 0)) {
            actualSignal *= -1;
            dividend /= 10;
        }
        if (actualSignal > 0) {
            tir += dividend / 100;
        }
        if (actualSignal < 0) {
            tir -= dividend / 100;
        }
    } while (result === false);
    return (tir * 100).toFixed(2);
}

Javascript IRR (Internal rate of return) Formula Accuracy

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