Brodigan Corporation has provided the following information concerning a capital budgeting project. The expected life of the project and the equipment is three years, and the equipment has zero salvage value. The company uses straight-line depreciation on all equipment, and the depreciation expense on the equipment would be $150,000 per year. Assume cash flows occur at the end of the year except for the initial investments. The company takes income taxes into account in its capital budgeting. The net annual operating cash inflow is the difference between the incremental sales revenue and incremental cash operating expenses.
What is the net present value of the project?
Investment required in equipment: $450,000
Net annual operating cash inflow: $220,000
Tax rate: 30%
After-tax discount rate:12%
To calculate the net present value (NPV) of the project, we need to discount the cash flows to present value and then subtract the initial investment.
To find the present value of the net annual operating cash inflow, we can use the formula:
PV = CF / (1 + r)^n
Where PV is the present value, CF is the cash flow, r is the after-tax discount rate, and n is the number of years.
In this case, the net annual operating cash inflow is $220,000, the after-tax discount rate is 12%, and the project has a 3-year life.
Calculating the present value of the net annual operating cash inflow:
PV = $220,000 / (1 + 0.12)^3
PV = $220,000 / 1.404928
PV = $156,769.23
Next, we need to calculate the depreciation expense each year:
Depreciation expense = $150,000
The tax savings from the depreciation expense can be calculated as:
Tax savings = depreciation expense * tax rate
Tax savings = $150,000 * 0.30
Tax savings = $45,000
Now, we can calculate the after-tax cash flow each year:
Year 1:
After-tax cash flow = net operating cash inflow + tax savings
After-tax cash flow = $220,000 + $45,000
After-tax cash flow = $265,000
Year 2:
After-tax cash flow = net operating cash inflow + tax savings
After-tax cash flow = $220,000 + $45,000
After-tax cash flow = $265,000
Year 3:
After-tax cash flow = net operating cash inflow + tax savings
After-tax cash flow = $220,000 + $45,000
After-tax cash flow = $265,000
Now, we can calculate the net present value:
NPV = sum of present value of cash flows - initial investment
NPV = ($156,769.23 * 1) + ($156,769.23 * 1) + ($156,769.23 * 1) - $450,000
NPV = $470,307.69 - $450,000
NPV = $20,307.69
Therefore, the net present value of the project is $20,307.69.
To calculate the net present value (NPV) of the project, follow these steps:
Step 1: Calculate the after-tax cash inflows for each year.
Since the net annual operating cash inflow is given as $220,000, and the tax rate is 30%, the after-tax cash inflow for each year can be calculated as follows:
Year 1: $220,000 * (1 - 0.30) = $154,000
Year 2: $220,000 * (1 - 0.30) = $154,000
Year 3: $220,000 * (1 - 0.30) = $154,000
Step 2: Calculate the present value of the after-tax cash inflows.
Using the after-tax discount rate of 12%, we can calculate the present value of the after-tax cash inflows for each year using the formula:
PV = CF / (1 + r)^n
Where PV is the present value, CF is the cash flow, r is the discount rate, and n is the number of years.
Present value of Year 1 cash inflow: $154,000 / (1 + 0.12)^1 = $137,500
Present value of Year 2 cash inflow: $154,000 / (1 + 0.12)^2 = $122,159
Present value of Year 3 cash inflow: $154,000 / (1 + 0.12)^3 = $108,646
Step 3: Calculate the present value of investment.
Since the initial investment of $450,000 occurs at year 0, its present value is simply $450,000.
Step 4: Calculate the net present value (NPV).
The net present value (NPV) is the difference between the present value of cash inflows and the present value of the initial investment:
NPV = Present value of cash inflows - Present value of initial investment
NPV = ($137,500 + $122,159 + $108,646) - $450,000
NPV = $367,305 - $450,000
NPV = -$82,695
Therefore, the net present value (NPV) of the project is -$82,695.
To calculate the net present value (NPV) of the project, you will need to discount the project's cash flows to their present value and subtract the initial investment. Here are the steps to calculate the NPV:
1. Calculate the annual after-tax cash flows: To do this, subtract the annual depreciation expense ($150,000) from the net annual operating cash inflow ($220,000). In this case, the annual after-tax cash flow would be $220,000 - $150,000 = $70,000.
2. Calculate the present value factor: Using the after-tax discount rate of 12% and the project's expected life of three years, you can calculate the present value factor for each year. The formula for the present value factor is (1 + discount rate)^(-n), where n is the number of years.
For Year 1, the present value factor would be (1 + 0.12)^(-1) = 0.8929.
For Year 2, the present value factor would be (1 + 0.12)^(-2) = 0.7972.
For Year 3, the present value factor would be (1 + 0.12)^(-3) = 0.7118.
3. Calculate the discounted cash flow for each year: Multiply the annual after-tax cash flow by the respective present value factor for each year.
For Year 1, the discounted cash flow would be $70,000 * 0.8929 = $62,503.
For Year 2, the discounted cash flow would be $70,000 * 0.7972 = $55,805.
For Year 3, the discounted cash flow would be $70,000 * 0.7118 = $49,827.
4. Calculate the present value of the project: Add up all the discounted cash flows from step 3 to get the present value.
Present value = $62,503 + $55,805 + $49,827 = $168,135.
5. Calculate the net present value: Subtract the initial investment of $450,000 from the present value calculated in step 4.
Net present value = $168,135 - $450,000 = -$281,865.
Therefore, the net present value of the project is -$281,865.