Springer Company is considering the purchase of a new machine for $80,000.The machine would generate an annual cash flow before depreciation and taxes of $28,778 for five years.At the end of five years, the machine would have no salvage value.The company's cost of capital is 12 percent.The company uses straight-line depreciation with no mid-year convention and has a 40 percent tax rate. What is the net present value for the machine?

Question

Quizplus · Accepted Answer

To find the net present value (NPV), we need to discount the present value of the future cash flows to their present value using the company's cost of capital.

Step 1: Find the annual cash flows before depreciation and taxes.

$28,778

Step 2: Calculate the depreciation expense.

Since the company uses straight-line depreciation, the annual depreciation expense is calculated as:

Depreciation expense = (Purchase price - Salvage value) / Useful life
Depreciation expense = ($80,000 - $0) / 5
Depreciation expense = $16,000

Step 3: Calculate the annual cash flows after depreciation and taxes.

Cash flow after taxes = (cash flow before taxes - depreciation) x (1 - tax rate)
Cash flow after taxes = ($28,778 - $16,000) x (1 - 0.4)
Cash flow after taxes = $8,267

Step 4: Calculate the present value of each cash flow using the discounted cash flow formula.

PV = CF / (1 + r)^n

where:
PV = present value
CF = cash flow
r = discount rate (or cost of capital)
n = number of periods

Year 1: PV = $8,267 / (1 + 0.12)^1 = $7,383
Year 2: PV = $8,267 / (1 + 0.12)^2 = $6,601
Year 3: PV = $8,267 / (1 + 0.12)^3 = $5,893
Year 4: PV = $8,267 / (1 + 0.12)^4 = $5,249
Year 5: PV = $8,267 / (1 + 0.12)^5 = $4,663

Step 5: Calculate the net present value.

NPV = sum of present values of all cash flows - initial cost
NPV = ($7,383 + $6,601 + $5,893 + $5,249 + $4,663) - $80,000
NPV = $5,318

Therefore, the net present value for the machine is $5,318. The best choice is A) because it has the highest positive NPV, meaning the investment is expected to generate positive returns and is worth pursuing.

Springer Company Is Considering the Purchase of a New Machine