Calculate the project’s NPV

by | Aug 23, 2023 | finance

 

Bangor Moving Company is thinking of opening a new warehouse, and the key data are shown below. The company owns the building that would be used, and it could sell it for $100,000 after taxes if it decides not to open the new warehouse. The equipment for the project would be depreciated by the straight-line method over the project’s 3-year life, after which it would be worth nothing and thus it would have a zero salvage value. No new working capital would be required, and revenues and other operating costs would be constant over the project’s 3-year life. What is the project’s NPV? (Hint: Cash flows are constant in Years 1-3.)
You can work on this case in excel and copy your step-by-step answer here.
Project cost of capital (r) 10.0%
Opportunity cost $100,000
Net equipment cost (depreciable basis) $65,000
Straight-line deprec. rate for equipment 33.333%
Sales revenues, each year $123,000
Operating costs (excl. deprec.), each year $25,000
Tax rate 25%

Sample Answer

Sample Answer

To calculate the project’s NPV, we need to determine the cash flows for each year and discount them back to their present value using the project cost of capital (r).

Given data:

Project cost of capital (r): 10.0%
Opportunity cost: $100,000
Net equipment cost (depreciable basis): $65,000
Straight-line depreciation rate for equipment: 33.333%
Sales revenues, each year: $123,000
Operating costs (excluding depreciation), each year: $25,000
Tax rate: 25%
Step-by-step calculation:

Determine the annual depreciation expense for the equipment: Annual depreciation expense = Net equipment cost × Straight-line depreciation rate Annual depreciation expense = $65,000 × 33.333% = $21,666.67

Calculate the annual operating cash flow before taxes: Annual operating cash flow before taxes = Sales revenues – Operating costs – Depreciation expense Annual operating cash flow before taxes = $123,000 – $25,000 – $21,666.67 = $76,333.33

Calculate the annual tax payment: Annual tax payment = Tax rate × (Sales revenues – Operating costs – Depreciation expense) Annual tax payment = 25% × ($123,000 – $25,000 – $21,666.67) = $19,583.33

Calculate the annual after-tax cash flow: Annual after-tax cash flow = Annual operating cash flow before taxes – Annual tax payment Annual after-tax cash flow = $76,333.33 – $19,583.33 = $56,750

Determine the cash flows for each year: Year 0: Cash flow = Opportunity cost = -$100,000 Year 1: Cash flow = Annual after-tax cash flow = $56,750 Year 2: Cash flow = Annual after-tax cash flow = $56,750 Year 3: Cash flow = Annual after-tax cash flow = $56,750

Discount each cash flow back to its present value using the project cost of capital (r): Present value (PV) = Cash flow / (1 + r)^n Where n is the year (0 for Year 0, 1 for Year 1, etc.)

Year 0: PV = -$100,000 / (1 + 10%)^0 = -$100,000 Year 1: PV = $56,750 / (1 + 10%)^1 = $51,590.91 Year 2: PV = $56,750 / (1 + 10%)^2 = $46,900.83 Year 3: PV = $56,750 / (1 + 10%)^3 = $42,637.12

Calculate the project’s NPV by summing up the present values: NPV = Sum of PVs NPV = -$100,000 + $51,590.91 + $46,900.83 + $42,637.12 NPV = $41,128.86

Therefore, the project’s NPV is $41,128.86.

Note: Negative NPV indicates that the project may not be financially viable as it does not generate enough returns to cover the opportunity cost of not selling the building.

 

 

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