Financial Analysis of Machine Replacement Decision: Evaluating Profitability and NPV”

QUESTION

One year​ ago, your company purchased a machine used in manufacturing for $115,000. You have learned that a new machine is available that offers many​ advantages; you can purchase it for $140,000 today. It will be depreciated on a​ straight-line basis over 10​ years, after which it has no salvage value. You expect that the new machine will contribute EBITDA​ (earnings before​ interest, taxes,​ depreciation, and​ amortization) of $50,000 per year for the next 10 years. The current machine is expected to produce EBITDA of $23,000 per year. The current machine is being depreciated on a​ straight-line basis over a useful life of 11​ years, after which it will have no salvage​ value, so depreciation expense for the current machine is $10,455 per year. All other expenses of the two machines are identical. The market value today of the current machine is $ 50,000. Your​ company’s tax rate is 30%​, and the opportunity cost of capital for this type of equipment is 11 %. Is it profitable to replace the​ year-old machine?

The NPV of the replacement is: $

The steps to solve this problem are as​ follows:

1. Calculate the change in EBITDA as a result of the replacement.

2. Calculate the change in depreciation expense as a result of the replacement.

3. Calculate the change in FCF in years 1 through 10 from replacing the machine.

4. Calculate the capital gain​ (or loss) as a result of selling the current machine.

5. Calculate the tax savings​ (or cost) as a result of selling the current machine.

6. Calculate the Year 0 Free Cash Flow.

7. Calculate the NPV of the FCF from replacing the machine.

To calculate the NPV of the​ replacement, use the following​ formula:

NPV of replacement equals Year 0 Free Cash Flow plus Present value of the annual incremental cash flows

We can also compute this result using a spreadsheet.

ANSWER

Replacing the year-old machine involves a series of financial calculations to determine whether it is a profitable decision for your company. The Net Present Value (NPV) method is a commonly used financial tool to assess the profitability of such investments. Let’s break down the steps and calculate the NPV of the replacement:

Step 1: Calculate the Change in EBITDA

First, calculate the change in EBITDA as a result of the replacement. EBITDA is expected to increase from $23,000 per year to $50,000 per year, so the change is:

Change in EBITDA = New EBITDA – Current EBITDA Change in EBITDA = $50,000 – $23,000 = $27,000 per year

Step 2: Calculate the Change in Depreciation Expense

Next, calculate the change in depreciation expense as a result of the replacement. The new machine will be depreciated over 10 years, whereas the current machine is being depreciated over 11 years. So, the change in depreciation expense is:

Change in Depreciation Expense = (Depreciation of Current Machine – Depreciation of New Machine) * Tax Rate

Change in Depreciation Expense = ($10,455 – $140,000 / 10) * 0.30 Change in Depreciation Expense = ($10,455 – $14,000) * 0.30 Change in Depreciation Expense = (-$3,545) * 0.30 Change in Depreciation Expense = -$1,063.50 per year

Step 3: Calculate the Change in Free Cash Flow (FCF) from Year 1 to 10

Now, calculate the change in FCF in years 1 through 10 from replacing the machine. To do this, we need to consider the change in EBITDA and the change in depreciation expense.

Change in FCF per year = Change in EBITDA – Change in Depreciation Expense Change in FCF per year = $27,000 – (-$1,063.50) Change in FCF per year = $28,063.50

Step 4: Calculate the Capital Gain or Loss from Selling the Current Machine

The market value today of the current machine is $50,000, and it was purchased for $115,000. Therefore, the capital gain or loss is:

Capital Gain/Loss = Market Value – Purchase Price Capital Gain/Loss = $50,000 – $115,000 Capital Gain/Loss = -$65,000 (a loss)

Step 5: Calculate the Tax Savings or Cost from Selling the Current Machine

The capital loss can provide tax savings, given the tax rate is 30%. So, calculate the tax savings:

Tax Savings = Capital Loss * Tax Rate Tax Savings = (-$65,000) * 0.30 Tax Savings = -$19,500

Step 6: Calculate the Year 0 Free Cash Flow

Year 0 Free Cash Flow is essentially the cash flow at the beginning of the investment. It includes the capital loss and the tax savings:

Year 0 Free Cash Flow = Capital Loss + Tax Savings Year 0 Free Cash Flow = (-$65,000) + (-$19,500) Year 0 Free Cash Flow = -$84,500

Step 7: Calculate the NPV of the Replacement

Now, we can calculate the NPV of the replacement using the formula:

NPV of replacement = Year 0 Free Cash Flow + Present value of the annual incremental cash flows

We need to calculate the present value of the change in FCF from year 1 to 10. The opportunity cost of capital is 11%, so we’ll discount each year’s cash flow accordingly.

NPV of replacement = -$84,500 + Σ [Change in FCF / (1 + 0.11)^t] for t = 1 to 10

Calculating the NPV using a spreadsheet or financial calculator, we find:

NPV of replacement ≈ -$84,500 + $189,192.16 ≈ $104,692.16

Therefore, the NPV of the replacement is approximately $104,692.16. A positive NPV suggests that replacing the year-old machine is a profitable decision for your company, taking into account the increase in EBITDA, the change in depreciation expenses, the capital loss, and the tax savings. It indicates that the investment is expected to generate a positive return above the opportunity cost of capital.