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The equation to calculating the internal rate of return is a complex one, based primarily on the value of the initial investment:
(Yousaf)
In the case of the first investment project, the equation to calculating the IRR would be as follows:
130 = 25 / (1 + r) 1 + 35 / (1 + r) 2 + 45 / (1 + r) 3 + 50 / (1 + r) 4 + 55 / (1 + r) 5
For project B, the equation is:
85 = 40 / (1 + r) 1 + 35 / (1 + r) 2 + 30 / (1 + r) 3 + 10 / (1 + r) 4 + 5 / (1 + r) 5
Given the complexity of these formulas, the method used is that of estimating results and verifying until a correct solution is identified. "We use linear interpolation to estimate the actual rates of return for the four investment alternatives. Linear interpolation is a trial and error method of estimating actual rates of return when such rates are different from tables or calculators" (Yousaf).
For project A, an estimated internal rate of return of 9% would lead to the following:
130 = 25 / 1.09 + 35 / 1.18 + 45 / 1.29 + 50 / 1.41 + 55 / 1.53 130 = 158.89, which is false, meaning then that the IRR for project A is larger than 9%. Considering an IRR of 11%:
130 = 25 / 1.11 + 35 / 1.23 + 45 / 1.36 + 50 / 1.51 + 55 / 1.68 130 = 149.91, which is also false, requiring the need for an even larger estimation. For an IRR of 15%:
130 = 25 / 1.15 + 35 / 1.32 + 45 / 1.52 + 50 / 1.75 + 55 / 2.01 130 = 133.79; this result is the closest one, meaning then that the estimated IRR for project investment A is of 15.5%
For project B, the estimative calculations commence at a value of the internal return rate of 10%:
85 = 40 / 1.1 + 35 / 1.21 + 30 / 1.33 + 10 / 1.46 + 5 / 1.6 85 = 97.82, which is clearly false, meaning as such that the IRR is larger. For an estimated...
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