Basic NPV: No Salvage Value or Taxes
Carrie Rushing is considering the purchase of a new production machine that costs $120,000. She has been told to expect decreased annual operating expenses of $40,000 for four years. At the end of the fourth year, the machine will have no salvage value and will be scrapped.
Required:
What is the net present value of the machine if Carrie's cost of capital is 9 percent? Use the time value of money charts for your calculations. Round to the nearest dollar. (Ignore income taxes.)
To calculate the net present value (NPV) of the machine, we need to discount the expected cash flows to their present value and then sum them up. Here's how to calculate it step by step:
Step 1: Determine the cash flows.
In this case, the annual operating expense savings of $40,000 is a cash flow that will be received for four years. Since there is no salvage value at the end, we do not consider any cash flows beyond the fourth year.
Year 1: $40,000
Year 2: $40,000
Year 3: $40,000
Year 4: $40,000
Step 2: Determine the discount rate.
The discount rate, also known as the cost of capital, is given as 9 percent. This rate is used to discount future cash flows to their present value.
Step 3: Calculate the present value of each cash flow.
To calculate the present value, we use the formula: PV = CF / (1 + r)^n
Where:
PV = Present Value
CF = Cash Flow
r = Discount Rate
n = Number of years
Year 1 PV = $40,000 / (1 + 0.09)^1 = $36,697 (rounded to the nearest dollar)
Year 2 PV = $40,000 / (1 + 0.09)^2 = $33,691 (rounded to the nearest dollar)
Year 3 PV = $40,000 / (1 + 0.09)^3 = $30,884 (rounded to the nearest dollar)
Year 4 PV = $40,000 / (1 + 0.09)^4 = $28,266 (rounded to the nearest dollar)
Step 4: Calculate the NPV.
The NPV is the sum of the present values of all cash flows discounted to the present.
NPV = Year 1 PV + Year 2 PV + Year 3 PV + Year 4 PV
= $36,697 + $33,691 + $30,884 + $28,266
= $129,538 (rounded to the nearest dollar)
Therefore, the net present value of the machine, considering Carrie's cost of capital of 9 percent, is $129,538.