Question

LMN Co. is considering a four-year project to improve its production efficiency. Buying a new machine for $564,681 is estimated to result in $197,759 in annual pretax cost savings. The press falls in the MACRS five-year class, and it will have a salvage value at the end of the project of $67,980. The press also requires an initial investment in spare parts inventory of $20,510, along with an additional $3,912 in inventory for each succeeding year of the project, with full recovery at the end of year 4. If the shop's tax rate is 36 percent and its discount rate is 11 percent, what is the NPV?

Answer 1

Answer :

Initial investment = $564,681

Useful life = 4 years

Depreciation of Year 1 = 20.00% * $564,681 = $112,936.20

Depreciation of Year 2 = 32.00% * $564,681 = $180,697.92

Depreciation of Year 3 = 19.20% * $564,681 = $108,418.75

Depreciation of Year 4 = 11.52% * $564,681 = $65,051.25

Book value at the end of year 4 = $564,681 - $112,936.20 - $180,697.92 - $108,418.75 - $65,051.25

= $97,576.88

After-tax salvage value = Salvage value - ( Salvage value - Book value ) * tax rate

= $67,980 - ( $67,980 - $97,576.88 ) * 0.36

= $78,634.88

Year 0:

Net cash flows = Initial investment - Initial investment in NWC

= - $564,681 - $20,510 = - $585,191

Year 1:

Operating cash flow = Pre-tax cost saving * ( 1 - tax ) + tax * Depreciation

= $197,759 * ( 1 - 0.36 ) + 0.36 * $112,936.20

= $167,222.80

Net cash flows = Operating cash flow - Investment in NWC

= $167,222.80 - $3,912 = $163,310.80

Year 2:

Operating cash flow = Pre-tax cost saving * ( 1 - tax ) + tax * Depreciation

= $197,759 * ( 1 - 0.36 ) + 0.36 * $180,697.92

= $191,617.01

Net cash flows = Operating cash flow - Investment in NWC

= $191,617.01 - $3,912 = $187,705.01

Year 3:

Operating cash flow = Pre-tax cost saving * ( 1 - tax ) + tax * Depreciation

= $197,759 * ( 1 - 0.36 ) + 0.36 * $108,418.75

= $165,596.51

Net cash flows = Operating cash flow - Investment in NWC

= $165,596.51 - $3,912 = $161,684.50

Year 4:

Operating cash flow = Pre-tax cost saving * ( 1 - tax ) + tax * Depreciation

= $197,759 * ( 1 - 0.36 ) + 0.36 * $65,051.25

= $149,984.21

Net cash flows = Operating cash flows + NWC recovered + After-tax salvage value [ Note : NWC recovered = sum of all NWC invested ]

= $149,984.21 + $32,246 + $78,634.88

= $260,865.09

Required return = 11%

NPV = - $585,191 + $163,310.80 / 1.11 + $187,705.01 / 1.11^2 + $161,684.50 / 1.11^3 + $260,865.09 / 1.11^4

NPV = $4,343.67