High School

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 $312,612 and will last for 15 years. It will have no salvage value at the end of its useful life. Garrett estimates the new lathe will reduce raw materials scrap by $33,000 per year. He also believes the lathe will reduce energy costs by $5,000 per year. If he purchases the new lathe, he will be able to sell the old lathe for $6,306.

(a) Calculate the lathe’s internal rate of return.

(b) If Ayayai Enterprises uses a 7% hurdle rate, should Garrett purchase the lathe?

- Select an option: Yes / No

(c) Without doing any calculations, what do you know about the lathe’s net present value?

- Net present value will be: [Fill in the blank]

Answer :

(a) To calculate the internal rate of return, the net present value must first be determined.

The net present value (NPV) can be determined using the following formula NPV = PV of cash inflows – PV of cash out flows In this case, there is only one cash outflow and two cash inflows.Cash outflow: The purchase price of the new lathe = $312,612 Cash inflow 1 The annual reduction in scrap value = $33,000 Cash inflow 2: The annual energy cost savings = $5,000. Present value factor for an annuity of $1 per year for 15 years at 10% discount rate is 7.606$312,612 - (7.606 * $38,000) + (present value factor of $1 for 15 years at 10% discount rate * $6,306) = $-13,638.

The lathe's IRR is 15.01 percent (b) Since the lathe's IRR is 15.01%, which is greater than the hurdle rate of 7%, Garrett should purchase the lathe. (c) Without doing any calculations, we can infer that the lathe's net present value will be positive. This is due to the fact that the lathe's internal rate of return is greater than the hurdle rate.

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Explanation of lathe's Internal Rate of Return, Hurdle Rate Decision, and Net Present Value (NPV).

Lathe's Internal Rate of Return Calculation: Internal Rate of Return (IRR) is the discount rate that makes the net present value (NPV) of all cash flows from a particular project equal to zero. To calculate the lathe's IRR, you would need to set up the cash flows over the 15-year period and solve for the discount rate that makes the NPV zero.

Hurdle Rate Decision: If Ayayai Enterprises uses a 7% hurdle rate, you would compare the lathe's expected return (IRR) to the hurdle rate. If the IRR is higher than the hurdle rate, the purchase is advisable.

Net Present Value (NPV): Without specific calculations, a positive NPV indicates that the present value of cash inflows exceeds the present value of cash outflows, making the investment economically viable.