Garrett Boone, Ayayai Enterprises' vice president of operations, needs to replace an automatic lathe on the production line. The model he is considering has a sales price of $201,868 and will last for 15 years with no salvage value at the end of its useful life. Garrett estimates the new lathe will reduce raw materials scrap by $20,000 per year and reduce energy costs by $3,000 per year. If he purchases the new lathe, he will be able to sell the old lathe for $5,000.

(a) Calculate the lathe's internal rate of return. (Round your answer to 0 decimal places, e.g., 25\%.)
Internal rate of return: _%

(b) If Ayayai Enterprises uses a 6\% hurdle rate, should Garrett purchase the lathe?

(c) Without doing any calculations, what do you know about the lathe's net present value?
Net present value will be _.

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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