Question

(20 pts) A federal agency, DUMP, The Department of Urban Municipal Planning (not a real federal agency, at least as far as we know) is adding some recreational facilities to its office building. The initial cost of the project will be $1.5m, with an annual upkeep cost of $50k. Public benefits have been estimated to be $300k per year, but disbenefits of $200k (initial) have also been forecast. The facilities are intended to be permanent. Assuming an interest rate of 6% compounded annually, what is the benefit-to-cost ratio of the project? Do the calculation two different ways, one based on annual worth and one based on present worth. Note that because no time period is specified, you will be using the capitalized equivalent method to adjust amount to annual or present worth values; that is, CE = A/i. [ Ans. BCR = 2.06 ]

Answer 1

Present Worth Analysis:	In mlns.
Benefits :
Initial disbenefits	-0.2
PW of annual benefits(0.3/0.06)	5
Total benefits	4.8
Costs :
Initial cost	1.5
Present worth of annual upkeep(0.05/0.06)	0.833
Total costs	2.333
Benefits/Costs Ratio(BCR)=	2.06
Annual Worth Analysis:
Benefits:
Initial disbenefits(0.2*0.06)	-0.012
Annual benefits	0.3
Total benefits	0.288
Costs:
Initial cost (1.5*0.06)	0.09
Annual upkeep	0.05
Total costs	0.14
Benefits/Costs Ratio(BCR)=	2.06