(a):
Calculate the
(a):
Explanation of Solution
Alternative X: First cost (F) is $84,000. Annual maintenance cost (AC) is $31,000 per year. Salvage value (SV) is $40,000. Annual revenue (AR) is $96,000per year.
Alternative Y: First cost (F) is $146,000. Annual maintenance cost (AC) is $28,000 per year. Salvage value (SV) is $47,000. Annual revenue (AR) is $119,000per year.
MARR is 15%. Time period (n) is 3.
Rate of return of alternative X (i) can be calculated as follows:
Substitute the rate of return as 65% by trial-and-error method in the above equation.
The calculated value is greater than the present value of the first cost. Thus, increase the rate of return to 67.85%.
The calculated value is nearly equal to the present value of the first cost. Thus, it is confirmed that the rate of return is 67.85%.
Rate of return of alternative Y (i) can be calculated as follows:
Substitute the rate of return as 47% by trial-and-error method in the above equation.
The calculated value is greater than the present value of the first cost. Thus, increase the rate of return to 47.78%.
The calculated value is nearly equal to the present value of the first cost. Thus, it is confirmed that the rate of return is 47.78%.
Both the rates of returns are greater than MARR. Since the rate of return for X is greater, alternate X should be selected.
(b):
Calculate incremental rate of return.
(b):
Explanation of Solution
Incremental rate of return of alternatives Y and X can be calculated as follows:
Substitute the incremental rate of return as 16% by trial-and-error method in the above equation.
The calculated value is greater than the present value of the incremental first cost. Thus, increase the incremental rate of return to 16.83%.
The calculated value is nearly equal to the incremental present value. Thus, it is confirmed that the incremental rate of return is 16.83%. Since the incremental rate of return is greater than MARR, alternate Y must be selected.
(c):
Calculate incremental rate of return.
(c):
Explanation of Solution
The procedure used in subpart (b) is correct (Incremental rate of return). Since the procedure used in subpart (a) is incorrect, Project X should not be selected.
Incremental rate of return of alternatives Y and X can be calculated as follows:
Substitute the incremental rate of return as 16% by trial-and-error method in the above equation.
The calculated value is greater than the present value of the incremental first cost. Thus, increase the incremental rate of return to 16.83%.
The calculated value is nearly equal to the incremental present value. Thus, it is confirmed that the incremental rate of return is 16.83%. Since the incremental rate of return is greater than MARR, alternate Y must be selected.
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