Question

Ilana Industries, Inc., needs a new lathe. It can buy a new high-speed lathe for $0.94 million. The lathe will cost $30,700 to run, will save the firm $129,600 in labour costs, and will be useful for 10 years. Suppose that for tax purposes, the lathe will be in an asset class with a CCA rate of 25%. Ilana has many other assets in this asset class. The lathe is expected to have a 10-year life with a salvage value of $118,000. The actual market value of the lathe at that time will also be $118,000. The discount rate is 5% and the corporate tax rate is 35%.

What is the NPV of buying the new lathe? (Round your answer to the nearest cent.)

Answer 1

Capital investment = Purchase cost + run cost = $940,000 + $30,700 = $970,700

Depreciation at CCA rate =25%

• Year-wise depreciation:
• D1 = 25% * $970,700 = $242,675
• D2 = 25% * ($970,700 - $242,675) = $182,006
• D3 = 25% * ($970,700 - $182,006) = $191,173.44 and so on

Labor cost savings = $129,600p.a for 10 years

After-tax savings in the labor cost = $129,600 * (1-0.35) = $84,240 p.a

Tax savings on Depreciation for 1st year = D1 * t = $242,675 * 0.35 = $84,936.25

Similar calculation for other years.

Terminal year cash flows are zero as the market value and salvage value are same. Hence no tax on the sale of the machinery.

Incremental cash flow, ICF = Labor cost savings + tax savings on depreciation

ICF1 = 84,240 + 84,936.25 = 169,176 similarly ICF2, ICF3,...ICF10

NPV = initial outlay + PV(ICF)

Below is the cash flow table for the same:

Year	0	1	2	3	4	5	6	7	8	9	10
FCInv	970,700
Cost savings		129,600	129,600	129,600	129,600	129,600	129,600	129,600	129,600	129,600	129,600
After-tax savings		84,240	84,240	84,240	84,240	84,240	84,240	84,240	84,240	84,240	84,240
Dep		242,675.00	182,006.25	197,173.44	193,381.64	194,329.59	194,092.60	194,151.85	194,137.04	194,140.74	194,139.81
Dep * t		84936.25	63702.1875	69010.70313	67683.57422	68015.35645	67932.41089	67953.14728	67947.96318	67949.2592	67948.9352
ICF		169,176	147,942	153,251	151,924	152,255	152,172	152,193	152,188	152,189	152,189

PV(ICF) = 169176/(1+0.05) + 147,942/(1+0.05)^2 + ....+ 152,189/(1+0.05)^10 = $1,188,230.22 at 5% discount rate.

NPV = -$970,700 + $1,188,230.22 = $217,530.22