Question

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

Answer 1

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.