Nucore Company is thinking of purchasing a new candy-wrapping machine at a cost of
$370,000. The machine should save the company approximately $70,000 in operating costs
per year over its estimated useful life of 10 years. The salvage value at the end of 10 years is expected
to be $15,000. (Ignore income tax effects.)
Required:
1. What is the machine’s payback period?
2. Compute the net present value of the machine if the cost of capital is 12%.
3. What is the expected internal rate of return for this machine?
1. To calculate the payback period of the candy-wrapping machine, we need to determine how long it will take for the savings from operating costs to recover the initial investment.
The annual savings from operating costs is $70,000, and the initial investment is $370,000. To find the payback period, we divide the initial investment by the annual savings:
Payback Period = Initial Investment / Annual Savings
Payback Period = $370,000 / $70,000
Payback Period = 5.29 years
Therefore, the payback period for the candy-wrapping machine is approximately 5.29 years.
2. To compute the net present value (NPV) of the machine, we need to discount the cash flows (savings and salvage value) back to the present value using the cost of capital (12%).
First, let's calculate the present value (PV) of the annual savings. We can use the formula:
PV = CF / (1 + r)^n
where CF is the cash flow, r is the discount rate (cost of capital), and n is the period.
PV of annual savings = $70,000 / (1 + 0.12)^1 + $70,000 / (1 + 0.12)^2 + ... + $70,000 / (1 + 0.12)^10
Next, let's calculate the present value of the salvage value at the end of 10 years:
PV of salvage value = $15,000 / (1 + 0.12)^10
Now, let's calculate the NPV by subtracting the initial investment from the discounted cash flows:
NPV = PV of annual savings + PV of salvage value - Initial Investment
NPV = PV of annual savings - $370,000 + PV of salvage value
Compute the values using a financial calculator or spreadsheet software to get the net present value.
3. To find the expected internal rate of return (IRR) for the machine, we need to determine the discount rate that makes the NPV zero. In other words, we need to find the rate at which the present value of cash inflows equals the initial investment.
Using the same formula as in the previous step, we need to find the discount rate (r) that makes the NPV zero:
NPV = 0 = PV of annual savings - Initial Investment + PV of salvage value
Solve for the discount rate by trial and error, adjusting the rate until the NPV becomes zero. This rate will be the expected internal rate of return for the machine.
Alternatively, you can use a financial calculator or spreadsheet software to calculate the IRR automatically by inputting the cash flows and initial investment.