What's 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
Please refer to your later post, which I saw first.
Sra
To calculate the net present value (NPV) of the replacement project, we need to find the present value of the cash flows associated with the project and subtract the initial investment.
Here are the steps to calculate the NPV:
1. Calculate the present value of the cash flows from the new equipment:
- The incremental increase in operating income (EBIT) is $600,000 per year for eight years.
- We need to discount these cash flows at the project's cost of capital, which is 13%.
Using the formula for the present value of an annuity, we can calculate the present value of these cash flows:
PV = CF * (1 - (1 + r)^(-n)) / r
Where:
PV = Present Value
CF = Cash Flow per period
r = Discount rate
n = Number of periods
Plugging in the values:
PV = $600,000 * (1 - (1 + 0.13)^(-8)) / 0.13
PV = $3,825,882.93
2. Calculate the present value of the salvage value of the old equipment:
- The old equipment has a current salvage value of $300,000.
- We need to discount this cash flow to year 0 (the present) using the same discount rate:
PV = CF / (1 + r)^n
Plugging in the values:
PV = $300,000 / (1 + 0.13)^0
PV = $300,000
3. Calculate the present value of the salvage value of the net working capital:
- The net working capital of $50,000 will be recovered at the end of year 8, so we need to discount it back to year 0 using the same discount rate.
PV = CF / (1 + r)^n
Plugging in the values:
PV = $50,000 / (1 + 0.13)^8
PV = $19,754.57
4. Calculate the total present value of the cash flows:
- Add the present values calculated in steps 1, 2, and 3:
Total PV = PV of cash flows from new equipment + PV of salvage value of old equipment + PV of salvage value of net working capital
Total PV = $3,825,882.93 + $300,000 + $19,754.57
Total PV = $4,145,637.50
5. Calculate the net present value (NPV):
- Subtract the initial investment of $800,000 (cost of the new equipment) from the total present value:
NPV = Total PV - Initial Investment
NPV = $4,145,637.50 - $800,000
NPV = $3,345,637.50
Therefore, the net present value (NPV) of this replacement project is $3,345,637.50.
None of the given options match the calculated NPV, so there might be an error in the calculations or an incorrect answer provided.