Final answer:
To calculate the Internal Rate of Return (IRR) for an investment in a turbo powered machine tool gadget, one must find the discount rate that results in a net present value (NPV) of zero for cash flows of $2,000 in the first year and $4,000 in the second year, with an initial cost of $4,000. The calculation can be complex and requires a financial calculator or spreadsheet software.
Step-by-step explanation:
To determine the Internal Rate of Return (IRR) on an investment of a turbo powered machine tool gadget that costs $4,000 and generates $2,000 in the first year and $4,000 in the second year, you will need to find the discount rate that makes the net present value (NPV) of the cash flows equal to zero. The IRR is a financial metric used to evaluate the profitability of investments, expressed as a percentage. It is found by iteratively trying different discount rates until the NPV is zero.
The NPV formula is NPV = C0 + C1/(1+r) + C2/(1+r)^2 + ... + Cn/(1+r)^n, where C0 is the initial investment cost, C1 to Cn are the cash inflows in each period, r is the discount rate, and n is the number of periods. You plug the known values into the formula and solve for r:
0 = -$4,000 + $2,000/(1+IRR) + $4,000/(1+IRR)^2
This requires either the use of a financial calculator, spreadsheet software capable of solving for IRR, or iterative numerical methods since there's no algebraic solution for IRR in most cases.
In this scenario, the exact IRR value was not provided, so you would need to use one of the above methods to find the IRR that makes the NPV of this investment zero, which is not possible to calculate within the context of this platform.