Question

Two mutually exclusive alternative are being considered. Both have lives of 10 years. Alternative A has a fist cost of $10,000 and annual benefits of $4500. Alternative B costs $25,000 and has annual benefits of $8800. If the minimum attractive rate of return is 6%, which alternative should be selected? Solve the problem by

a) Present worth analysis.

b) Annual cash flow analysis.

c) Rate of return analysis.

Answer 1

(a) Present Worth (PW) of both options are computed as follows.

Alternative A ($): - 10,000 + 4,500 x P/A(6%, 10) = - 10,000 + 4,500 x 7.3601** = - 10,000 + 33,120 = 23,120

Alternative B ($): - 25,000 + 8,800 x P/A(6%, 10) = - 25,000 + 8,800 x 7.3601** = - 25,000 + 64,769 = 39,769

Alternative B has higher PW, so this should be selected.

(b) Annual Worth (AW) of both options are computed as follows.

Alternative A ($): [- 10,000 / P/A(6%, 10)] + 4,500 = (- 10,000 / 7.3601**) + 4,500 = - 1,359 + 4,500 = 3,141

Alternative B ($): [- 25,000 / P/A(6%, 10)] + 8,800 = (- 25,000 / 7.3601**) + 8,800 = - 3,397 + 8,800 = 5,403

Alternative B has higher PW, so this should be selected.

(c) [Internal] Rate of Return is computed using Excel IRR Option as follows.

Alternative - A			Alternative - B
Year	Cash Flow ($)		Year	Cash Flow ($)
0	-10,000		0	-25,000
1	4,500		1	8,800
2	4,500		2	8,800
3	4,500		3	8,800
4	4,500		4	8,800
5	4,500		5	8,800
6	4,500		6	8,800
7	4,500		7	8,800
8	4,500		8	8,800
9	4,500		9	8,800
10	4,500		10	8,800
IRR =	43.81%		IRR =	33.20%

Alternative A has higher IRR, so this should be selected.