Question

Two mutually exclusive alternatives (MEAs) are available to reduce potential earthquake damage at a government site. The cash flow estimates for each alternative are shown below. The one-time repair costs occur in the middle of the period, that is, in year 10. Each MEA has a 20-year life. At an interest rate of 8% per year, determine the Benefit-to-Cost ratio (B/C) of the “increment.”

	Alternative One	Alternative Two
First Cost ($)	-500,000	-1,100,000
Annual cost ($/year)	-30,000	-40,000
One-time repair cost ($)	-800,000	-250,000
Service life (years)	20	20

Answer 1

Solution :-

Incremental First Cost =$1,100,000 - $500,000 = $600,000

Incremental Annual Cost = $40,000 - $30,00 = $10,000

Saving in One time Repair Cost = $800,000 - $250,000 = $550,000

Now Present Value of Costs = $600,000 + $10,000 * PVAF ( 8% , 20 )

= $600,000 + ( $10,000 * 9.818 )

= $698,181.47

Present Value of Benefits = $550,000 * PVF ( 8% , 10 )

= $550,000 * 0.463

= $254,756.42

Now Benefit Cost Ratio

= $254,756.42 / $698,181.47

= 0.365

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