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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