PHPExcel based function RATE() returning NAN()

Question

I have this code: http://pastebin.com/Sd9WKZFr

When i call something like rate(60, -6000, 120000) it returns me a NAN result, but the same function on MS Excel returns me 0,04678.... I have the same problem trying -5000, -4000, -3000 and -2000.

When i debug the code, i see that about the 8/9 iteration, the line number 29 begins to return a NAN result, making all of other results to turn NAN too.

BUT, when i call something like rate(60, -1000, 120000) it returns me a float -0.02044..., exactly the same result of MS Excel.

I have already tryed to convert all of math calculations into BCMath functions, but this way the results of -6000 is wrong (-1.0427... instead of 0,04678...) but using -1000 the result is correct, matching excel's result.

Is there a way to make it work correctly?

Thanks in advance for any useful sight about that.

Answer 1

I'll need to do some tests to ensure that there's no adverse effects in other situations; but the following looks as though it might fix this problem, and certainly calculates the correct rate value for your arguments RATE(60, -6000, 120000) stabilises at 0.046781916422493 in iteration 15.

define('FINANCIAL_MAX_ITERATIONS', 128); 
define('FINANCIAL_PRECISION', 1.0e-08); 


function RATE($nper, $pmt, $pv, $fv = 0.0, $type = 0, $guess = 0.1) { 

    $rate = $guess; 
    if (abs($rate) < FINANCIAL_PRECISION) { 
        $y = $pv * (1 + $nper * $rate) + $pmt * (1 + $rate * $type) * $nper + $fv; 
    } else { 
        $f = exp($nper * log(1 + $rate)); 
        $y = $pv * $f + $pmt * (1 / $rate + $type) * ($f - 1) + $fv; 
    } 
    $y0 = $pv + $pmt * $nper + $fv; 
    $y1 = $pv * $f + $pmt * (1 / $rate + $type) * ($f - 1) + $fv; 

    // find root by secant method 
    $i  = $x0 = 0.0; 
    $x1 = $rate; 
    while ((abs($y0 - $y1) > FINANCIAL_PRECISION) && ($i < FINANCIAL_MAX_ITERATIONS)) { 
        $rate = ($y1 * $x0 - $y0 * $x1) / ($y1 - $y0); 
        $x0 = $x1; 
        $x1 = $rate;
        if (($nper * abs($pmt)) > ($pv - $fv))
            $x1 = abs($x1);

        if (abs($rate) < FINANCIAL_PRECISION) { 
            $y = $pv * (1 + $nper * $rate) + $pmt * (1 + $rate * $type) * $nper + $fv; 
        } else { 
            $f = exp($nper * log(1 + $rate)); 
            $y = $pv * $f + $pmt * (1 / $rate + $type) * ($f - 1) + $fv; 
        } 

        $y0 = $y1; 
        $y1 = $y; 
        ++$i; 
    } 
    return $rate; 
}   //  function RATE() 

Answer 2

I would not suggest using Secant method to find internal rate of return as it consumes more time than other preferred iterative methods such as Newton Raphson method. From the code it seems setting a maximum of 128 iterations is a waste of time

Using Newton Raphson method to find RATE with either of the two TVM equations takes only 3 iterations

TVM Eq. 1: PV(1+i)^N + PMT(1+i*type)[(1+i)^N -1]/i + FV = 0

f(i) = 0 + -6000 * (1 + i * 0) [(1+i)^60 - 1)]/i + 120000 * (1+i)^60

f'(i) = (-6000 * ( 60 * i * (1 + i)^(59+0) - (1 + i)^60) + 1) / (i * i)) + 60 * 120000 * (1+0.05)^59

i0 = 0.05
f(i1) = 120000
f'(i1) = 42430046.1459
i1 = 0.05 - 120000/42430046.1459 = 0.0471718154728
Error Bound = 0.0471718154728 - 0.05 = 0.002828 > 0.000001

i1 = 0.0471718154728
f(i2) = 12884.8972
f'(i2) = 33595275.7358
i2 = 0.0471718154728 - 12884.8972/33595275.7358 = 0.0467882824629
Error Bound = 0.0467882824629 - 0.0471718154728 = 0.000384 > 0.000001

i2 = 0.0467882824629
f(i3) = 206.9714
f'(i3) = 32520602.801
i3 = 0.0467882824629 - 206.9714/32520602.801 = 0.0467819181458
Error Bound = 0.0467819181458 - 0.0467882824629 = 6.0E-6 > 0.000001

i3 = 0.0467819181458
f(i4) = 0.056
f'(i4) = 32503002.4159
i4 = 0.0467819181458 - 0.056/32503002.4159 = 0.0467819164225
Error Bound = 0.0467819164225 - 0.0467819181458 = 0 < 0.000001
IRR = 4.68%


TVM Eq. 2: PV + PMT(1+i*type)[1-{(1+i)^-N}]/i + FV(1+i)^-N = 0

f(i) = 120000 + -6000 * (1 + i * 0) [1 - (1+i)^-60)]/i + 0 * (1+i)^-60

f'(i) = (--6000 * (1+i)^-60 * ((1+i)^60 - 60 * i - 1) /(i*i)) + (0 * -60 * (1+i)^(-60-1))

i0 = 0.05
f(i1) = 6424.2628
f'(i1) = 1886058.972
i1 = 0.05 - 6424.2628/1886058.972 = 0.0465938165535
Error Bound = 0.0465938165535 - 0.05 = 0.003406 > 0.000001

i1 = 0.0465938165535
f(i2) = -394.592
f'(i2) = 2081246.2069
i2 = 0.0465938165535 - -394.592/2081246.2069 = 0.046783410646
Error Bound = 0.046783410646 - 0.0465938165535 = 0.00019 > 0.000001

i2 = 0.046783410646
f(i3) = 3.1258
f'(i3) = 2069722.0554
i3 = 0.046783410646 - 3.1258/2069722.0554 = 0.0467819004105
Error Bound = 0.0467819004105 - 0.046783410646 = 2.0E-6 > 0.000001

i3 = 0.0467819004105
f(i4) = -0.0335
f'(i4) = 2069813.5309
i4 = 0.0467819004105 - -0.0335/2069813.5309 = 0.0467819165937
Error Bound = 0.0467819165937 - 0.0467819004105 = 0 < 0.000001
IRR = 4.68%