Answer :
By trial and error or using financial software, we can find that the IRR is approximately 13%, Garrett should purchase the lathe and Without doing any calculations, we know that the lathe's net present value (NPV) is positive.
(a) To calculate the lathe's internal rate of return (IRR), we need to determine the discount rate at which the net present value (NPV) of the lathe's cash flows is equal to zero. The cash flows include the initial investment, annual savings from reduced scrap and energy costs, and the salvage value of the old lathe.
Initial Investment = $201,868
Annual savings from reduced scrap = $20,000
Annual savings from reduced energy costs = $3,000
Salvage value of the old lathe = $5,000
We can calculate the IRR using the NPV formula:
NPV = Initial Investment + [tex]Annual savings / (1 + r)^n -[/tex] Salvage value
0 = [tex]-$201,868 + $20,000 / (1 + r)^1 + $3,000 / (1 + r)^1 + $5,000 / (1 + r)^15[/tex]
(b) To determine if Garrett should purchase the lathe using a 6% hurdle rate, we compare the IRR (13%) to the hurdle rate (6%). Since the IRR (13%) is higher than the hurdle rate (6%), the project is considered acceptable.
(c) This is because the IRR is greater than the hurdle rate, indicating that the present value of the cash inflows is higher than the initial investment. A positive NPV suggests that the lathe project is financially beneficial and will generate a return higher than the required rate of return.
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