The accounting department is involved in a little wager. The accountants believe

Question

The accounting department is involved in a little wager. The accountants believe that an engineer cannot correctly determine which alternative should be chosen using equivalent uniform annual cash flow analysis. As a means of proving this statement, the accountants have provided you with the following data: Data Alt. A Alt.B Alt.C Useful Life, Years 7 11 9 First Cost (FC) $123,000 $135,000 $112,00 Annual Benefit (AB) 67,000 73,000 46,000 M&O; Grad. (M&O; G) 2,800 3,000 2,000 M&O; Cost (M&O;) 21, 200 29,000 15,000 The accounting department has chosen Alternative B. Use the best method to select the best alternative and use cash flow of each alternative using a MARR of 12%. State whether or not you agree with the accounting department.

Explanation / Answer

Working note:

(1) Net cash flow (NCF) = Annual benefit - Annual M&O

(2) Let us evaluate the alternatives using Present worth (PW) of NCF method where PW equals the sum of all cash inflows and outflows discounted at MARR of 12%.

Since Alt. A has highest PW, A is the best alternative. Hence I disagree with Accounting department's choice.

Alt. A Year Cost ($) Benefit ($) NCF ($) Discount factor @12% Discounted NCF ($) (A) (B) (C)=(B)-(A) (D) (C)x(D) 0 1,23,000 -1,23,000 1.0000 -1,23,000 1 21,200 67,000 45,800 0.8929 40,893 2 24,000 67,000 43,000 0.7972 34,279 3 26,800 67,000 40,200 0.7118 28,614 4 29,600 67,000 37,400 0.6355 23,768 5 32,400 67,000 34,600 0.5674 19,633 6 35,200 67,000 31,800 0.5066 16,111 7 38,000 67,000 29,000 0.4523 13,118 PW ($) = 53,416 Alt. B Year Cost ($) Benefit ($) NCF ($) Discount factor @12% Discounted NCF ($) (A) (B) (C)=(B)-(A) (D) (C)x(D) 0 1,35,000 -1,35,000 1.0000 -1,35,000 1 29,000 73,000 44,000 0.8929 39,286 2 32,000 73,000 41,000 0.7972 32,685 3 35,000 73,000 38,000 0.7118 27,048 4 38,000 73,000 35,000 0.6355 22,243 5 41,000 73,000 32,000 0.5674 18,158 6 44,000 73,000 29,000 0.5066 14,692 8 47,000 73,000 26,000 0.4523 11,761 9 50,000 73,000 23,000 0.4039 9,289 10 53,000 73,000 20,000 0.3606 7,212 11 56,000 73,000 17,000 0.3220 5,474 PW ($) = 52,848 Alt. C Year Cost ($) Benefit ($) NCF ($) Discount factor @12% Discounted NCF ($) (A) (B) (C)=(B)-(A) (D) (C)x(D) 0 1,12,000 -1,12,000 1.0000 -1,12,000 1 15,000 46,000 31,000 0.8929 27,679 2 17,000 46,000 29,000 0.7972 23,119 3 19,000 46,000 27,000 0.7118 19,218 4 21,000 46,000 25,000 0.6355 15,888 5 23,000 46,000 23,000 0.5674 13,051 6 25,000 46,000 21,000 0.5066 10,639 8 27,000 46,000 19,000 0.4523 8,595 9 29,000 46,000 17,000 0.4039 6,866 PW ($) = 13,054

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