Question

Problem 10-20 Comparing Mutually Exclusive Projects [LO1] Lang Industrial Systems Company (LISC) is trying to decide between two different conveyor belt systems. System A costs $264,000, has a four-year life, and requires $81.000 in pretax annual operating costs. System B costs $372,000, has a six-year life, and requires $75,000 in pretax annual operating costs. Both systems are to be depreciated straight-line to zero over their lives and will have zero salvage value. Whichever project is chosen, it will not be replaced when it wears out. The tax rate is 34 percent and the discount rate is 8 percent. Calculate the NPV for both conveyor belt systems. (Negative amounts should be indicated by a minus sign. Do not round intermediate calculations and round your answers to 2 decimal places, e.g. 32.16.) NPV System A 110727.90 System B 600832.54

Answer 1

	NPV
System A	-$ 366,742.17
System B	-$ 503,382.24

Explanation:

NPV for System A:

Annual depreciation = Initial cost/Number of useful years

                                   = $ 264,000/4 = $ 66,000

Annual operating cash flow = After tax operating cost + Depreciation cost shield

                                              = - $ 81,000 x (1- 0.34) + $ 66,000 x 0.34

                                              = - $ 81,000 x 0.66 + $ 66,000 x 0.34

                                             = - $ 53,460 + $ 22,440 = - $ 31,020

NPV = PV of future cash flows – Initial cost

         = - $ 31,020 x PVIFA (8 %, 4) - $ 264,000

        = - $ 31,020 x [1- (1+0.08)^-4 /0.08] - $ 264,000

         = - $ 31,020 x [1- (1.08)^-4 /0.08] - $ 264,000

         = - $ 31,020 x [(1- 0.735029852796453)/0.08] - $ 264,000

         = - $ 31,020 x (0.264970147203547/0.08) - $ 264,000

         = - $ 31,020 x 3.31212684004433 - $ 264,000

         = - $ 102,742.174578175 - $ 264,000

          = - $ 366,742.174578175 or - $ 366,742.17

NPV for System B:

Annual depreciation = Initial cost/Number of useful years

                                   = $ 372,000/6 = $ 62,000

Annual operating cash flow = After tax operating cost + Depreciation cost shield

                                              = - $ 75,000 x (1- 0.34) + $ 62,000 x 0.34

                                              = - $ 75,000 x 0.66 + $ 62,000 x 0.34

                                             = - $ 49,500 + $ 21,080 = - $ 28,420

NPV = PV of future cash flows – Initial cost

         = - $ 28,420 x PVIFA (8 %, 6) - $ 372,000

        = - $ 28,420 x [1- (1+0.08)^-6 /0.08] - $ 372,000

         = - $ 28,420 x [1- (1.08)^-6 /0.08] - $ 372,000

         = - $ 28,420 x [(1- 0.630169626883105)/0.08] - $ 372,000

         = - $ 28,420 x (0.369830373116895/0.08) - $ 372,000

         = - $ 28,420 x 4.62287966396119 - $ 372,000

         = - $ 131,382.240049777 - $ 372,000

          = - $ 503,382.240049777 or - $ 503,382.24