Thomson Media is considering some new equipment whose data are shown below. The equipment has a 3 year tax life and would be fully depreciated by the straight line method over 3 years but it would have a positve pre-tax salvage value at the end of year 3, when the project would be closed down. Also, some new working capital would be required, but it would be recovered at the end of the project's life. Revenues and other operating costs are expected to be constant over the project's 3 year life. What is the project's NPV?

WACC = 10%
Net investment in fixed assets (depreciable basis) = $70,000
Required new working capital = $10,000
Straight line depr rate = 33.333%
Sales revenues each year = $75,000
Operating costs (excl depr) each year = $30,000
Expected pretax salvage value = $5,000
Tax rate = 35%

23,005

To calculate the project's NPV, we need to determine the cash flows associated with the project over its 3-year life.

1. Calculate annual depreciation expense:
The depreciable basis is $70,000, and the straight-line depreciation rate is 33.333%. Therefore, the annual depreciation expense is ($70,000 * 33.333%) = $23,333.33.

2. Calculate annual operating cash flow:
The operating cash flow for each year is the difference between the sales revenue and the operating costs (excluding depreciation). So, for each year, the operating cash flow is ($75,000 - $30,000) = $45,000.

3. Calculate the salvage value:
At the end of Year 3, the project has a pre-tax salvage value of $5,000. However, we need to adjust it for taxes. Since the tax rate is 35%, the after-tax salvage value is ($5,000 * (1 - 35%)) = $3,250.

4. Determine the year-by-year cash flows:
Year 0: Initial investment in fixed assets and working capital is ($70,000 + $10,000) = $80,000. This is an outflow of cash.

Year 1: Cash inflow from operating cash flow is $45,000. There is no tax expense in Year 1 since the depreciation expense fully offsets the taxable income.

Year 2: Cash inflow from operating cash flow is $45,000. Again, there is no tax expense due to the fully depreciated assets.

Year 3: Cash inflow from operating cash flow is $45,000. The salvage value of $3,250 is also a cash inflow.

5. Calculate the NPV:
Using the WACC of 10%, we can discount each cash flow to its present value and sum them to calculate the NPV. The formula for present value is as follows:

PV = Cash Flow / (1 + WACC)^n, where n is the year of the cash flow.

NPV = Year 0 Cash Flow + Year 1 PV + Year 2 PV + Year 3 PV

Year 0 Cash Flow: -$80,000
Year 1 PV: $45,000 / (1 + 10%)^1
Year 2 PV: $45,000 / (1 + 10%)^2
Year 3 PV: ($45,000 + $3,250) / (1 + 10%)^3

Calculate each of these values and sum them to determine the project's NPV.

To calculate the project's NPV, we need to consider the cash flows generated by the project and discount them back to the present value using the weighted average cost of capital (WACC).

First, let's calculate the annual depreciation expense. The depreciable basis is the net investment in fixed assets, which is given as $70,000. The straight-line depreciation rate is 33.333% per year over 3 years, so the annual depreciation expense would be:

Annual depreciation expense = depreciable basis * straight-line depreciation rate
Annual depreciation expense = $70,000 * 33.333%
Annual depreciation expense = $23,332.10

Now, let's calculate the annual cash flows generated by the project. The net cash flow for each year is the difference between the revenue and the total operating costs (excluding depreciation):

Net cash flow = Revenue - Operating costs (excluding depreciation)
Net cash flow = $75,000 - $30,000
Net cash flow = $45,000

Since this net cash flow remains constant over the project's 3-year life, the total cash flow for each year would be $45,000.

In year 3, when the project is closed down, there is also a salvage value. The salvage value is the amount received from selling the equipment at the end of its 3-year tax life. The pretax salvage value is given as $5,000. To calculate the after-tax salvage value, we need to consider the tax rate of 35%. The after-tax salvage value would be:

After-tax salvage value = pretax salvage value * (1 - tax rate)
After-tax salvage value = $5,000 * (1 - 35%)
After-tax salvage value = $3,250

Now, let's calculate the project's NPV. We will discount each cash flow back to the present value using the WACC of 10%. The formula for calculating NPV is:

NPV = (Net cash flow / (1 + WACC)^n) + (Salvage value / (1 + WACC)^n)

Where n is the year of the cash flow.

Year 0 (Initial investment):
Cash flow = Initial investment = -$70,000 (negative sign indicates cash outflow)

Year 1, 2, 3:
Cash flow = Net cash flow = $45,000

Year 3 (with salvage value):
Cash flow = Net cash flow + After-tax salvage value = $45,000 + $3,250

Now, let's calculate the present value of each cash flow:

PV = Cash flow / (1 + WACC)^n

Year 0:
PV at Year 0 = $70,000 / (1 + 10%)^0 = $70,000

Year 1, 2, 3:
PV at Year 1, 2, 3 = $45,000 / (1 + 10%)^1,2,3 = $41,666.67

Year 3 (with salvage value):
PV at Year 3 = ($45,000 + $3,250) / (1 + 10%)^3 = $39,472.23

Finally, let's calculate the NPV:

NPV = PV at Year 0 + PV at Year 1 + PV at Year 2 + PV at Year 3

NPV = $70,000 + $41,666.67 + $41,666.67 + $39,472.23 = $192,805.57

Therefore, the project's NPV is $192,805.57.