What is the net present value (NPV) of this replacement project?
The old equipment has a book value of $200,000 (year 0) and a current salvage value of $300,000 (year 0). It is being depreciated on a straight-line basis. It has four more years of depreciation left ($50,000 in each years 1-4).
The new equipment will have cost $800,000 (year 0) and $0 salvage value at the end of its life. It will be depreciated using the straight-line method over eight years (years 1-8).
Replacing the old machine with the new machine will require an investment in net working capital of $50,000 that will be recovered at the end of the new machine’s life (year 8).
The new machine is more efficient, and the incremental increase in its operating income (EBIT) is equivalent to $600,000 for the next eight years (years 1-8).
The project’s cost of capital is 13%. The annual tax rate is 30%.
Which is the net present value (NPV) of this replacement project:
A. $1,785,445
B. $1,517,628
C. $2,142,534
D. $1, 874,717
E. $1,339,084
To calculate the net present value (NPV) of the replacement project, we need to calculate the present value of the cash flows associated with the project and subtract the initial investment.
Here are the steps to calculate the NPV:
Step 1: Calculate the annual cash flows for years 1-8
The annual cash flows consist of the incremental increase in operating income (EBIT) and the depreciation tax shield.
For each year, the cash flow (CFt) will be:
CFt = EBIT + depreciation tax shield
The EBIT for each year is $600,000, and the depreciation tax shield is calculated as: depreciation tax shield = depreciation expense * tax rate.
The annual cash flows for years 1-8 are as follows:
Year 1: CF1 = $600,000 + ($800,000/8 * 0.30)
Year 2: CF2 = $600,000 + ($800,000/8 * 0.30)
Year 3: CF3 = $600,000 + ($800,000/8 * 0.30)
Year 4: CF4 = $600,000 + ($800,000/8 * 0.30)
Year 5: CF5 = $600,000 + ($800,000/8 * 0.30)
Year 6: CF6 = $600,000 + ($800,000/8 * 0.30)
Year 7: CF7 = $600,000 + ($800,000/8 * 0.30)
Year 8: CF8 = $600,000 + ($800,000/8 * 0.30)
Step 2: Calculate the present value factor for each year
The present value factor is calculated using the formula: PV factor = 1 / (1 + r)^t, where r is the project's cost of capital and t is the year.
Using a 13% cost of capital, calculate the present value factor for each year.
Year 1: PV factor 1 = 1 / (1 + 0.13)^1
Year 2: PV factor 2 = 1 / (1 + 0.13)^2
Year 3: PV factor 3 = 1 / (1 + 0.13)^3
Year 4: PV factor 4 = 1 / (1 + 0.13)^4
Year 5: PV factor 5 = 1 / (1 + 0.13)^5
Year 6: PV factor 6 = 1 / (1 + 0.13)^6
Year 7: PV factor 7 = 1 / (1 + 0.13)^7
Year 8: PV factor 8 = 1 / (1 + 0.13)^8
Step 3: Calculate the present value of the cash flows for each year
The present value of the cash flows is calculated by multiplying the cash flow for each year by the present value factor for that year.
Present value of CF1 = CF1 * PV factor 1
Present value of CF2 = CF2 * PV factor 2
Present value of CF3 = CF3 * PV factor 3
Present value of CF4 = CF4 * PV factor 4
Present value of CF5 = CF5 * PV factor 5
Present value of CF6 = CF6 * PV factor 6
Present value of CF7 = CF7 * PV factor 7
Present value of CF8 = CF8 * PV factor 8
Step 4: Calculate the sum of the present values of the cash flows
Sum = Present value of CF1 + Present value of CF2 + Present value of CF3 + Present value of CF4 + Present value of CF5 + Present value of CF6 + Present value of CF7 + Present value of CF8
Step 5: Subtract the initial investment
The initial investment is the cost of the new equipment minus the salvage value of the old equipment plus the investment in net working capital.
Initial investment = Cost of new equipment - Salvage value of old equipment + Investment in net working capital
Now, subtract the initial investment from the sum of the present values calculated in Step 4 to obtain the net present value (NPV) of the replacement project.
NPV = Sum - Initial investment
Comparing the calculated NPV with the provided answer choices allows us to identify the correct option.
To calculate the net present value (NPV) of the replacement project, we need to determine the cash flows associated with the project and then discount them to the present value using the project's cost of capital. The NPV is the sum of the present values of all the cash flows.
Here are the steps to calculate the NPV:
Step 1: Calculate the cash flows for each year.
Year 0:
- Salvage value of the old equipment: $300,000
- Initial cost of the new equipment: -$800,000
- Net working capital investment: -$50,000
Years 1-4:
- Depreciation expense of the old equipment: -$50,000 per year
Years 1-8:
- Incremental increase in operating income (EBIT): $600,000 per year
Year 8:
- Recovery of net working capital investment: $50,000
Step 2: Calculate the after-tax cash flows by applying the tax rate of 30% to the incremental increase in operating income (EBIT) for years 1-8.
Step 3: Determine the present value factors for each year using the cost of capital of 13%.
Year 0: Present value factor = 1/(1 + cost of capital)^0 = 1
Years 1-8: Present value factor = 1/(1 + cost of capital)^n (where n is the year number)
Step 4: Calculate the present value of each cash flow by multiplying the cash flow by the present value factor.
Step 5: Sum up all the present values of the cash flows to get the NPV.
Now let's go through the calculation:
Year 0:
- Salvage value of the old equipment: $300,000 (present value = $300,000 * 1 = $300,000)
- Initial cost of the new equipment: -$800,000 (present value = -$800,000 * 1 = -$800,000)
- Net working capital investment: -$50,000 (present value = -$50,000 * 1 = -$50,000)
Years 1-4:
- Depreciation expense of the old equipment: -$50,000 per year (present value = -$50,000 * present value factor)
Years 1-8:
- Incremental increase in operating income (EBIT): $600,000 per year (after-tax cash flow = $600,000 * (1 - tax rate) = after-tax cash flow * present value factor)
Year 8:
- Recovery of net working capital investment: $50,000 (present value = $50,000 * present value factor)
Step 5: Sum up all the present values of the cash flows to get the NPV.
Now, perform these calculations using a financial calculator or spreadsheet software, keeping in mind to use the present value factor for each year. After calculating all the present values and summing them up, you will arrive at the NPV of the replacement project. Based on the given options, select the correct NPV.