Question

One year ago, your company purchased a machine used in manufacturing for $100,000. You have learned that a new machine is available that offers many advantages and you can purchase it for $140,000 today. It will be depreciated on a straight-line basis over 10 years and has no salvage value. You expect that the new machine will produce a gross margin (revenues minus operating expenses other than depreciation) of $55,000 per year for the next 10 years. The current machine is expected to produce a gross margin of $21,000 per year. The current machine is being depreciated on a straight-line basis over a useful life of 11 years, and has no salvage value, so depreciation expense for the current machine is $9091 per year. The market value today of the current machine is $55,000. Your company's tax rate is 45% and the opportunity cost of capital for this type of equipment is 10%. The NPV of replacing the year-old machine is ?

Answer 1

Given:

Discount Rate = 10%, Tax Rate = 45%

Given	Old	New
Current Price	$55,000	$140,000
Life	11	10
Life Remaining	10	10
Depreciation	$9,091	$14,000
Gross Margin	$55,000	$21,000

Scenario 1: Continue using the old machine

For each of the next ten years,

Gross Margin = EBITDA = $21,000, Depreciation = $9,091, Tax = 45% * (EBITDA - Depreciation) = $5,359.05, PAT = EBITDA - Depreciation - Tax = $6,549.95, FCF = PAT + Depreciation = $15,640.95

Using a discount rate of 10%, we first calculate the PV of each of these ten payments (through excel, or calculator), and we then sum it up to get the NPV = $96,106.87

NPV_{old =} $96,106.87

Scenario 2: Sell the old machine, buy and use the new machine

FCF at 10 year period beginning = Sale price of old machine - Cost of new machine = -$85,000

For each of the next ten years,

Gross Margin = EBITDA = $55,000, Depreciation = $14,000, Tax = 45% * (EBITDA - Depreciation) = $18,450, PAT = EBITDA - Depreciation - Tax = $22,550, FCF = PAT + Depreciation = $36,550

Using a discount rate of 10%, we first calculate the PV of each of these ten payments (through excel, or calculator), and we then sum it up to get the NPV = $139,583.93

NPV_new = $139,583.93

Thus, NPV of replacing the year-old machine is = NPVnew - NPVold = $139,583.93 - $96,106.87 = $43,477.06