Question

# Compare the following 3 alternatives using the incremental benefit/cost ratio method. Determine which is the most...

Compare the following 3 alternatives using the incremental benefit/cost ratio method. Determine which is the most efficient and which one is the most profitable. The market rate is 7.5% per year compounded yearly and inflation runs at 2.75% per year.

 Alter. Construction cost Annual Benefits Salvage Life (yrs) A \$410,000 \$260,000 \$25,000 35 B \$375,000 \$220,000 \$20,000 30 C \$520,000 \$280,000 - infinite

Solution:

Real interest for discounting=Market Rate-Inflation

=7.5%-2.75%

=4.75%

Present Value of Total Benefits

Alter.A

Present Value of Total Benefits=Annual Benefits*Present value factor of Annuity(PVAF)@ 4.75% for 35Years+Salvage value*Present Value Interest Factor(PVIF) @4.75 for 35th years

=\$260,000*16.904+\$25,000*.1971

=\$4399,967.50

Benefit/Cost ratio=Present Value of Total Benefits/cost

=\$4399,967.50/\$410,000

=10.73

Alter.B

Present Value of Total Benefits=\$220,000*[email protected]% for 30 years+\$20,000*[email protected]% for 30th years

=\$220,000*15.820+\$20,000*.249

=\$3485,380

Benefit/cost ratio=\$3485,380/\$375,000

=9.29

Alter.C

Present Value of Total Benefits(Perpetual Annuity)=\$280,000/4.75%

=\$5894,736.84

Benefit/cost ratio=\$5894,736.84/\$520,000

=11.34

Since Alter.C has the highest Benefit/cost ratio(i.e 11.34),hence Alter.C is the most efficient.

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