internal rate of return

The equation is,
- 2, 500, 000 + 750, 000 v + 750, 000 v^2 + ... + 750, 000 v^6
where v = 1 / (1+r)
- 2, 500, 000 + 750, 000 v ( 1 + v + ... + v^5)
- 2, 500, 000 + 750, 000 v ( 1 - v^6 / 1 - v )
- 2, 500, 000 + 750, 000 1/r ( 1 - v^6)

When r is in fact equal to 11%, the above equation will equal to 672, 903.39, which is positive.
To make the equation equal to zero ( which is the definition of the IRR), we need a higher discount rate.
Lets try 20%.
At 20%, the equation is equal to -5, 867.41, which is negative.

Therefore, we know the IRR is somewhere between 11% and 20%

Using Linear Interpolation,
Let the required IRR be i,
we have,

i - 0.2 / 0.11 - 0.2 = 0 - ( - 5, 867.41) / 672, 903.39 - ( - 5, 867.41)
we get, i = 19.92%

Therefore, the required IRR is 19.9222024%

Check: Substitute it back to the equation, we will get zero.

Hope this helps.

2007-06-01 16:50:07 補充：
Note, it wont be exactly equal to zero in the checks, but it should be reasonable close to zero. Since there is rounding error in the calculations

2007-06-01 16:58:40 補充：
Although from calculator, the correct answer is 19.905%But this method give the answer quite accurate. Only drawback is the more decimal places u cut off for the values in the linear interpolation, the larger the error. so its quite sensitive to rounding in the number used in it.

By using financial calculator.

eg. Casio FC100,

-2500000 CFj
750000 CFj
6 Nj
IRR=19.905% //

Rate return 11% should be market return which is to compare with IRR. It is to prove the investment of 2500000 worthwhile.

2007-05-31 17:00:03 補充：
2500000 = 750000/(1 r)1 750000/(1 r)2 .... 750000/(1 r)6Without using financial calaulator, it is almost impossible to find out r from the above equation. Perhaps, *Try and Error method would be an effective way to get the answer.*Try and Error is to substitute figures to fit the equation.

2007-05-31 17:01:30 補充：
2500000 = 750000/(1+ r)1 750000/(1+ r)2 .... 750000/(1+r)6Without using financial calaulator, it is almost impossible to find out r from the above equation. Perhaps, *Try and Error method would be an effective way to get the answer.*Try and Error is to substitute figures to fit the equation.