Question

engineering economics

A contractor is considering the purchase of a set of machine tools at a cost of $50,000. The purchase is expected to generate profits of $19,000 (revenues less expenses) per year in each of the next 4 years Additional profits will be taxed at a rate of 40%. The asset is depreciated by straight-line method with zero salvage value. The contractor's real after-tax MARR is 10% (25%) 3.1. What is the PW of this investment? Should the contractor purchase the machine tools? 3.2. What is the PW of this investment if the general inflation is 3% in the 4 years period? Should the contractor purchase the machine tools?

Answer 1

Answer 3.1

Initial Cost = $50000

Additional Profit before Depreciation= $19000 per year

Depreciation per year= Purchase value/ useful life = 50000//4 = $12500

Additional Profit after Depreciation = Profit- Depreciation = 19000-12500 = 6500

Additional Tax on profit = 40% * 6500 = $2600

Net Profit After Tax= 6500-2600= $3900

Additional Cashflow every year = Net Profit after Tax + Depreciation= 3900+12500 = $16400

PW of the additional cashflow = P*(1-(1+r)^-n)/r where P=$16400, n=4 years, r= 10%

PW = 16400 *(1-(1+10%)^-4)/10%

= 16400 *(1-(1+0.1)^-4)/0.1

= 16400 *(1-(1.1)^-4)/0.1

= 16400 *(1-0.6830)/0.1

= 16400 *0.3170/0.1

=$51985.79

PW of Machine Tools = PW of additional cashflow- Initial cost = 51985.79-50000 = $1985.79

Since PW is positive hence machine tools should be purchased

Answer 3.2

If inflation is 3%, New r = 10%+3% = 13%

Hence, PW of the additional cashflow = P*(1-(1+r)^-n)/r where P=$16400, n=4 years, r= 13%

PW = 16400 *(1-(1+13%)^-4)/13%

= 16400 *(1-(1+0.13)^-4)/0.13

= 16400 *(1-(1.13)^-4)/0.13

= 16400 *(1-0.6133)/0.13

= 16400 *0.3867/0.1

=$48781.33

PW of Machine Tools = PW of additional cashflow- Initial cost = 48781.33-50000 = -$1218.67

Since PW is negative hence machine tools should not be purchased