The Internal Rate of Return is the interest rate (i.e., the discount rate) at which the present value of expected cash inflows from a project equals the present value of expected cash outflows. The present value of expected cash inflows for an annuity consisting of equal payments is the annual amount multiplied by the factor for the Present Value of an Annuity using the appropriate discount rate and term. The present value of an annuity of $175,000 at 10% for 4 years is $175,000 × 3.170, or $554,750. $554,750 is not equal to the initial investment amount of $500,000, so the IRR cannot be 10%.
The Internal Rate of Return is the interest rate (i.e., the discount rate) at which the present value of expected cash inflows from a project equals the present value of expected cash outflows. The present value of expected cash inflows for an annuity consisting of equal payments is the annual amount multiplied by the factor for the Present Value of an Annuity using the appropriate discount rate and term. The present value of an annuity of $175,000 at 40% for 4 years is $175,000× 1.84923, or $323,615. $323,615 is not equal to the initial investment amount of $500,000, so the IRR cannot be 40%. Note: The factor for calculating the present value of an annuity at a discount rate of 40% is not available in most factor tables. However, the factor can be calculated using the following formula: (1 + i)n? 1 ——————— i(1 + i)n (1 + .40) 4 ? 1 2.8416 ——————— = ———— .4(1 + .40)4 1.5366 = 1.84923
The Internal Rate of Return is the interest rate (i.e., the discount rate) at which the present value of expected cash inflows from a project equals the present value of expected cash outflows. The present value of expected cash inflows for an annuity consisting of equal payments is the annual amount multiplied by the factor for the Present Value of an Annuity using the appropriate discount rate and term. Therefore, solving the equation 175,000X = 500,000 for the value of X will result in the present value factor for the relevant annuity. Once we have the factor, we can look across the 4-year line on the factor table to locate the closest factor or factors and get the rate, which will be the IRR. 175,000X = 500,000 X = 2.85714 Looking across the 4-Year line on the table for Present Value of an Annuity, we find factors of 2.914 for a 14% discount rate and 2.798 for a 16% discount rate. 2.85714 is in between those two factors. Therefore, the IRR is approximately 15%.
This is $175,000 divided by $500,000. The Internal Rate of Return is the interest rate (i.e., the discount rate) at which the present value of expected cash inflows from a project equals the present value of expected cash outflows. Therefore, present value concepts need to be used to answer this question.
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