Question

Lang Industrial Systems Company (LISC) is trying to decide between two different conveyor belt systems. System A costs $216,000, has a four-year life, and requires $69,000 in pretax annual operating costs. System B costs $306,000, has a six-year life, and requires $63,000 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 35 percent and the discount rate is 10 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.)

Answer 1

NPV of System A is - $298,258.01 and that of System B is - $406,606.52

Explanation:

System A:

Depreciation = Initial cost/Useful life = $ 216,000/4 = $ 54,000

Annual operating cash flow

= - Pretax annual operating cost (1 – tax rate) + Tax rate x depreciation

= - $ 69,000 x (1- 0.35) + 0.35 x $ 54,000

= - $ 69,000 x 0.65 + $ 18,900

= $ 18,900 - $ 44,850

= - $ 25,950

Computation of NPV:

Year	Cash Flow (C)	PV Factor calculation	PV Factor @ 10 %(F)	PV (= C x F)
0	- $216,000	1/(1+10%)^0	1	-$216,000.0000
1	-$ 25,950	1/(1+10%)^1	0.909090909	-$23,590.9091
2	-$ 25,950	1/(1+10%)^2	0.826446281	-$21,446.2810
3	-$ 25,950	1/(1+10%)^3	0.751314801	-$19,496.6191
4	-$ 25,950	1/(1+10%)^4	0.683013455	-$17,724.1992
			NPV	-$298,258.01

System B:

Depreciation = Initial cost/Useful life = $ 306,000/6 = $ 51,000

Annual operating cash flow

= - Pretax annual operating cost (1 – tax rate) + Tax rate x depreciation

= - $ 63,000 x (1- 0.35) + 0.35 x $ 51,000

= - $ 63,000 x 0.65 + $ 17,850

= $ 17,850 - $ 40,950

= - $ 23,100

Computation of NPV:

Year	Cash Flow (C)	PV Factor calculation	PV Factor @ 10 % (F)	PV (= C x F)
0	-$306,000	1/(1+10%)^0	1	-$306,000.0000
1	-$23,100	1/(1+10%)^1	0.909090909	-$21,000.0000
2	-$23,100	1/(1+10%)^2	0.826446281	-$19,090.9091
3	-$23,100	1/(1+10%)^3	0.751314801	-$17,355.3719
4	-$23,100	1/(1+10%)^4	0.683013455	-$15,777.6108
5	-$23,100	1/(1+10%)^5	0.620921323	-$14,343.2826
6	-$23,100	1/(1+10%)^6	0.56447393	-$13,039.3478
			NPV	-$406,606.52