First, let’s calculate the present value of the cash inflows: Annual environmental cost savings: $450,000 Next, let’s calculate the present value of the cash outflows . . . . . .
First, let’s calculate the present value of the cash inflows:
Annual environmental cost savings: $450,000
Next, let’s calculate the present value of the cash outflows:
Initial equipment cost: $1,100,000
Annual cash operating expenses: $260,000
Major overhaul cost at the end of the fifth year: $110,000
Salvage value of the equipment at the end of the seventh year: $96,000
Increase in working capital at the beginning: $130,000
Given the discount rate of 12%, we’ll refer to the present value tables to find the discount factor for each year.
Using the present value tables for a discount rate of 12%:
For 7 years: The discount factor is 0.403. (From Table A-1: Present Value of $1)
For 5 years: The discount factor is 0.567. (From Table A-1: Present Value of $1)
Now, let’s compute the present value of each cash flow:
Present value of annual environmental cost savings: $450,000 × 0.403 = $181,350 (rounded to the nearest dollar)
Present value of initial equipment cost: $1,100,000 × 1 = $1,100,000
Present value of annual cash operating expenses (annuity): $260,000 × (1 – 0.403) × (1/0.12) = $682,114 (rounded to the nearest dollar)
Present value of major overhaul cost: $110,000 × 0.567 = $62,370 (rounded to the nearest dollar)
Present value of salvage value of the equipment: $96,000 × 0.403 = $38,688 (rounded to the nearest dollar)
Present value of increase in working capital: $130,000 × 0.403 = $52,390 (rounded to the nearest dollar)
Now, let’s sum up the present values of all cash flows:
Total present value of inflows = $181,350
Total present value of outflows = $1,100,000 + $682,114 + $62,370 + $38,688 + $52,390 = $1,935,562 (rounded to the nearest dollar)
Finally, let’s compute the NPV:
NPV = Total present value of inflows – Total present value of outflows
NPV = $181,350 – $1,935,562 ≈ -$1,754,212
Therefore, the NPV of the project is approximately -$1,754,212.
Determine Discount Rate: The discount rate given in the question is 12%. This rate is used to discount future cash flows to their present values, considering the time value of money.
Calculate Discount Factors: Using the present value tables, we found the discount factors corresponding to the project’s duration. For 7 years, the discount factor is 0.403, and for 5 years, it is 0.567. These factors represent the present value of $1 received in each respective year at a 12% discount rate.
Compute Present Values: We multiplied each cash flow by its corresponding discount factor to calculate its present value. For example, the present value of the annual environmental cost savings was calculated by multiplying $450,000 by the discount factor for 7 years.
Sum Present Values: We summed up the present values of all cash inflows and outflows separately to get the total present value of inflows and outflows.
Calculate NPV: Finally, we subtracted the total present value of outflows from the total present value of inflows to get the NPV. A negative NPV indicates that the project’s costs outweigh its benefits, while a positive NPV indicates that the project is profitable.
In this case, the NPV is approximately -$1,754,212, indicating that the project is expected to result in a significant loss when considering the time value of money at a 12% discount rate.
Follow-up question
Student
The answer does not seem correct. Can you verify the solution again?
Tutor
Let’s double-check the calculations:
Present value of annual environmental cost savings:
$450,000 × 0.403 = $181,350 (rounded to the nearest dollar)
Present value of initial equipment cost:
$1,100,000 × 1 = $1,100,000
Present value of annual cash operating expenses (annuity):
$260,000 × ((1 – 1) / 0.12) × 0.567 = $1,357,600 (rounded to the nearest dollar)
Present value of major overhaul cost:
$110,000 × 0.567 = $62,370 (rounded to the nearest dollar)
Present value of salvage value of the equipment:
$96,000 × 0.403 = $38,688 (rounded to the nearest dollar)
Present value of increase in working capital:
$130,000 × 0.403 = $52,390 (rounded to the nearest dollar)
Now, let’s sum up the present values of all cash flows:
Total present value of inflows = $181,350
Total present value of outflows = $1,100,000 + $1,357,600 + $62,370 + $38,688 + $52,390 = $2,611,048 (rounded to the nearest dollar)
Now let’s recalculate the NPV:
NPV = Total present value of inflows – Total present value of outflows
NPV = $181,350 – $2,611,048 ≈ -$2,429,698
After recalculating, the NPV of the project is approximately -$2,429,698. It appears there was an error in the calculation of the present value of annual cash operating expenses. The annuity formula was incorrectly applied.
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