Question

1. Develop a cash flow diagram for the following scenario:
   • A township is considering creating new athletic facilities for an initial construction cost of $225,000.
   • Initial annual O&M costs will be $85,000, and will increase by $5,000 per year for every subsequent year.
   • It’s estimated the new facilities will bring in $190,000 in annual revenue.
   • At the end of year 6, the facility will need an overhaul costing $75,000.
   • The salvage value will be $100,000 after 10 years.

2. How long will it take for an investment to double at a 4% interest rate compounded annually? (using interpolation to solve this problem with compound interest tables is acceptable but not required).

Answer 1

	CASH FLOW:
	Year	Construction Cost	Annual O &M Cost	Annual Revenue	Overhaul Cost	Salvage Value	Net Cash Flow
	0	($225,000)					($225,000)
	1		($85,000)	$190,000			$105,000
	2		($90,000)	$190,000			$100,000
	3		($95,000)	$190,000			$95,000
	4		($100,000)	$190,000			$90,000
	5		($105,000)	$190,000			$85,000
	6		($110,000)	$190,000	($75,000)		$5,000
	7		($115,000)	$190,000			$75,000
	8		($120,000)	$190,000			$70,000
	9		($125,000)	$190,000			$65,000
	10		($130,000)	$190,000		$100,000	$160,000
	Assume, Investment =$100
	PV=Present Value=$100
	FV=Future value =2*100=$200
	N=Number of years
	i=Interest rate =4%=0.04
	FV=PV*((1+i)^N)
	1.04^N=Fv/Pv=2
	Nlog 1.04=Log2
	N=Log2/Log1.04=	17.67298769		0.301029996	0.017033
	ANSWER: 17.67 Year
	As per Rule of 72,
	It will double in 72/4=	18	years
								CASH FLOW DIAGRAM $200,000 $150,000 $100,000 $50,000 50 1 2 3 4 5 6 7 8 9 10 11 ($50,000) ($100,000) ($150,000) ($200,000) ($250,000)