Question

Megaplex Theaters is considering investing in new projection equipment. The cost of the new equipment is $90,000 and an additional $5,000 is required to install the equipment. The equipment can be depreciated as 3-year MACRS property.    At the end of 3 years, the firm expects to sell the equipment for $12,000. To get the new equipment running, an investment in working capital in the form of spare parts and tools will be required. The working capital investment is estimated to be $10,000 and would be recovered at the end of the project’s life. Because no other theater in the region will have sophisticated projection equipment like Megaplex Theaters will have, additional revenues of $120,000 are expected each year. However, the new equipment will be more expensive to maintain than the current projection system and is expected to increase maintenance costs by $3,000 each year. The new equipment will also require an additional employee on the weekends and this means labor costs are expected to increase $35,000 each year. Megaplex Theaters has a 34 percent tax rate and a cost of capital of 14 percent.   According to the NPV rule, should the new projection equipment be purchased?

Answer 1

Initial Investment = Base Cost + Installation Cost
Initial Investment = $90,000 + $5,000
Initial Investment = $95,000

Useful Life = 3 years

Depreciation Year 1 = 33.33% * $95,000
Depreciation Year 1 = $31,663.50

Depreciation Year 2 = 44.45% * $95,000
Depreciation Year 2 = $42,227.50

Depreciation Year 3 = 14.81% * $95,000
Depreciation Year 3 = $14,069.50

Book Value at the end of Year 3 = $95,000 - $31,663.50 - $42,227.50 - $14,069.50
Book Value at the end of Year 3 = $7,039.50

After-tax Salvage Value = Salvage Value - (Salvage Value - Book Value) * tax rate
After-tax Salvage Value = $12,000 - ($12,000 - $7,039.50) * 0.34
After-tax Salvage Value = $10,313.43

Initial Investment in NWC = $10,000

Year 0:

Net Cash Flows = Initial Investment + Initial Investment in NWC
Net Cash Flows = -$95,000 - $10,000
Net Cash Flows = -$105,000

Year 1:

Operating Cash Flow = (Sales - Costs) * (1 - tax) + tax * Depreciation
Operating Cash Flow = ($120,000 - $3,000 - $35,000) * (1 - 0.34) + 0.34 * $31,663.50
Operating Cash Flow = $64,885.59

Net Cash Flows = Operating Cash Flow
Net Cash Flows = $64,885.59

Year 2:

Operating Cash Flow = (Sales - Costs) * (1 - tax) + tax * Depreciation
Operating Cash Flow = ($120,000 - $3,000 - $35,000) * (1 - 0.34) + 0.34 * $42,227.50
Operating Cash Flow = $68,477.35

Net Cash Flows = Operating Cash Flow
Net Cash Flows = $68,477.35

Year 3:

Operating Cash Flow = (Sales - Costs) * (1 - tax) + tax * Depreciation
Operating Cash Flow = ($120,000 - $3,000 - $35,000) * (1 - 0.34) + 0.34 * $14,069.50
Operating Cash Flow = $58,903.63

Net Cash Flows = Operating Cash Flow + NWC recovered + After-tax Salvage Value
Net Cash Flows = $58,903.63 + $10,000 + $10,313.43
Net Cash Flows = $79,217.06

Cost of Capital = 14%

NPV = -$105,000 + $64,885.59/1.14 + $68,477.35/1.14^2 + $79,217.06/1.14^3
NPV = $58,077.54

You should purchase the new projection equipment as its net present value is positive.