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Search DISCOUNT RATE

Yesterday a student asked me how one can estimate the discount rate called TIR. Well let's suppose we want to estimate the net present value (NPV) for an investment of 1,500 entries with cash flows as follows: the first year 500, in the second year 1,000, in the year 500 called Third and fourth year 1,000 . Clear that the NPV is zero is necessary to estimate a discount rate is called the internal rate of return (IRR).

-1,500 + 500 / (1 + r) + 1.000 / (1 + r) 2 + 500 / (1 + r) 3 + 1,000 / (1 + r) 4 =

zero (ie: investment or cash out by 1,500 and multiplied by cash receipts the discount rate "r" for years 1.2 3 and 4) but the "r" and not know that formula can not punt.

The only way to get it is by the following calculations. Sum first entries, ie: 500 + 1,000 + 500 + 1,000 = 3,000 . The other step is to do the following: 500 / 1 + 1,000 / 2 + 500 / 3 + 1,000 / 4 = 1416.66 , then the calculation would be another division of 3,000 / 1,500 but increased to 3,000 / 8,000, which as we know is just to say high to 0,375, and the result is subtracted from the unit, or 3,000 / 1500 = 2 and 2 raised to 0.375 is equal to 1.2968 for the remainder of the unit would: 0.2968 or 29.68% is the , the discount rate would be lower and thus older ecime: 3,000 / 1,500 which is 2, but risen to 1416.66 / 3.000 = 0.4722 and less than 1 = 2 raised to of 0.4722 = 1.3872 minus 1 = 38.72% .

The real discount rate should be between these values: 29.68% and 38.72%. Testing with different values \u200b\u200bbetween these extremes you get the discount rate equal to 31.96% . This rate is the one that makes the NPV is zero and is called the Internal Rate of Return (IRR). And we can also be obtained by interpolation. Let us now see the following:


discount rates of 32% discount per table

Year 1 0.757576 x 500 = 379
Year 2 0.573921 x 1000 = 574
Year 3 0.434789 x 500 = 217
Year 4 0.329385 x 1000 = 329

SUM + 1.499-1500 = - 1

the NPV is negative to a positive NPV should be discounted to 32% lower rates. Discounted at the rate of 30%.

Year 1 0.769231 x 500 = 385
Year 2 0.591716 x 1000 = 592
Year 3 0.455166 x 500 = 228
Year 5 0.350128 x 1000 = 350

SUM + 1555-1500 = + 55

Now we have a positive NPV NPV

When we cast the value ZERO, then the result is the Internal Rate of Return (IRR) and can be obtained by linear interpolation and :

IRR = 30 + (32 - 30) [55/55 + 1)
IRR = 30 + (2) (0.9821) TIR = 30 +1,9642

IRR = 31.96

If cash flow is discounted at the rate of 31.96 the result of the NPV will be zero.