The Campbell Company is considering adding a robotic paint sprayer to its produc

Question

The Campbell Company is considering adding a robotic paint sprayer to its production line. The sprayer's base price is $1,021,000.00, and it would cost another $30,700.00 to install it. The machine falls into the MACRS 3-year class (the applicable MACRS depreciation rates are 33.33%, 44.45%, 14.81%, and 7.41%), and it would be sold after 3 years for $586,500.00. The machine would require an increase in net working capital (inventory) of $8,100.00. The sprayer would not change revenues, but it is expected to save the firm $468,450.00 per year in before-tax operating costs, mainly labor. Campbell's marginal tax rate is 33.00%. d. If the project's cost of capital is 17.40%, what is the NPV of the project?

$114,927.30

Explanation / Answer

NPV is the difference between the present value of cash inflows and cash outflows. It can be calculated with the use of following formula

NPV = Cash Flow Year 0 + Cash Flow Year 1/(1+Cost of Capital)^1 + Cash Flow Year 2/(1+Cost of Capital)^2 + Cash Flow Year 3/(1+Cost of Capital)^3

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To calculate the NPV, we need to determine the cash flow for each year as follows:

Cash Flow Year 0 = -1,021,000 (Purchase Price) - 30,700 (Cost of Installation) - 8,100 (Working Capital) = -$1,059,800

Cash Flows from Year 1 to Year 3 are calculated with the use of following table:

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With the use of values calculated above, we can calculate the NPV as follows:

NPV = -1,059,800 + 429,537/(1+17.40%)^1 + 468,130/(1+17.40%)^2 + 792,033/(1+17.40%)^3 = $135,208.29 which is closest to $135,208.59 (the minor difference in answer is on account off rounding of intermediary values)

Answer is $135,208.59 (which is Option B)

Years 1 2 3 Annual Savings 468,450 468,450 468,450 Less Depreciation 350,532 (33.33%*1,051,700) 467,481 (44.45%*1,051,700) 155,757 (14.81%*1,051,700) Savings after Depreciation 117,918 969 312,693 Less Taxes 38,913 320 103,189 Savings after Depreciation and Taxes 79,005 649 209,504 Add Depreciation 350,532 467,481 155,757 Recovery of Working Capital 0 0 8,100 Sales Value 0 0 586,500 Less Tax on Gain [(586,500-77,931)*33%] 0 0 167,828 Cash Flow $429,537 $468,130 $792,033

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