Question

Two design alternatives A and B have the following cash flows. Each alternative has 30-year life at a 5% interest rate. Alternative A Alternative B Initial Cost $700,000 $950,000 Annual Benefits $80,000 $120,000 Annual Operating Cost $20,000 $30,000 Using incremental B/C ratio to select the best alternative. Which of the following statements is TRUE?

A. Incremental B/C ratio is 1.52 and Alternative A should be selected.
B. Incremental B/C ratio is 1.52 and Alternative B should be selected.
C. Incremental B/C ratio is 0.66 and Alternative B should be selected.
D. Incremental B/C ratio is 0.66 and Alternative A should be selected.

Answer 1

Incremental B/C ratio is 1.46 and Alternative B should be selected.

Step-by-step explanation:

Alternative A

Annual net benefit = Annual Benefit - Annual Operating Cost

=80,000 - 20,000

=$60,000

Present Value of all future cash flow = Annual net benefit * PV factor {PVIFA = (1 - (1 + r)^-n) / r}

=60,000 * PVIFA (5%, 30years)

=60,000 * 15.372

=$922,320

Incremental B/C= Present Value of all future cash flow / Initial Cost / Initial Cost

=922,320 / 700,000

=1.3176

Alternative B

Annual net benefit = Annual Benefit - Annual Operating Cost

=120,000 - 30,000

=$90,000

Present Value of all future cash flow = Annual net benefit * PV factor {PVIFA = (1 - (1 + r)^-n) / r}

=90,000 * PVIFA (5%, 30years)

=90,000 * 15.372

=$1,383,480

Incremental B/C= Present Value of all future cash flow / Initial Cost / Initial Cost

=1,383,480 / 950,000

=1.4562

Conclusion: Because Alternative B has higher ratio than the Alternative A, it should be chosen.