A rate of return analysis was initiated for the infinite-life alternatives shown below.
(a) Fill in the 10 blanks in the incremental rate of return (?i*) columns.
(b) How much revenue is associated with each alternative?
(c) Which alternative should be selected if they are mutually exclusive and MARR is 16% per year?
(d) Which alternative should be selected if they are mutually exclusive and MARR is 11% per year?
(e) Select the two best alternatives at MARR = 19% per year.
 FIGURE 1.png)
(a) Find ROR for each increment of investment using the general relation
AW1 + AWII = AW2
where II = incremental investment
E vs F: 20,000(0.20) + 10,000(?i*) = 30,000(0.35)
?i* = 65%
E vs G: 20,000(0.20) + 30,000(?i*) = 50,000(0.25)
?i* = 28.3%
E vs H: 20,000(0.20) + 60,000(?i*) = 80,000(0.20) ?i* = 20%
F vs G: 30,000(0.35) + 20,000(?i*) = 50,000(0.25)
?i* = 10%
F vs H: 30,000(0.35) + 50,000(?i*) = 80,000(0.20)
?i* = 11%
G vs H: 50,000(0.25) + 30,000(?i*) = 80,000(0.20)
?i* = 11.7%
(b) Revenue = A = Pi
E: A = 20,000(0.20) = $4000
F: A = 30,000(0.35) = $10,500
G: A = 50,000(0.25) = $12,500
H: A = 80,000(0.20) = $16,000
(c) Conduct incremental analysis using results from part (a) with MARR = 16%
E vs DN: i* = 20% > MARR eliminate DN
E vs F: ?i* = 65% > MARR eliminate E
F vs G: ?i* = 10% < MARR eliminate G
F vs H: ?i* = 11% < MARR eliminate H
Therefore, select Alternative F
(d) Conduct incremental analysis using results from part (a) with MARR = 11%
E vs DN: i* = 20% > MARR, eliminate DN
E vs F: ?i* = 65% > MARR, eliminate E
F vs G: ?i* = 10% < MARR, eliminate G
F vs H: ?i* = 11% = MARR, eliminate F
Select alternative H
(e) Conduct incremental analysis using results from part (a) with MARR = 19%
E vs DN: i* = 20% > MARR, eliminate DN
E vs F: ?i* = 65% > MARR, eliminate E
F vs G: ?i* = 10% < MARR, eliminate G
F vs H: ?i* = 11% < MARR, eliminate H
Select F as first alternative; compare remaining alternatives incrementally.
E vs DN: i* = 20% > MARR, eliminate DN
E vs G: ?i* = 28.3% > MARR, eliminate E
G vs H: ?i* = 11.7% < MARR, eliminate H
Therefore, select alternatives F and G
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