Question

A major city in Eastern Canada is planning to build a new wastewater treatment plant to accommodate the increasing water consumption of the city, Plant construction will start in 2018 and is going to take five years at a cost of $30 million per year. After construction is completed, the cost of operation, maintenance is expected to be $2 million for the first year, and to increase by 1% per year thereafter. The salvage/scrap value of the wastewater treatment plant at the end of year 2052 is estimated to be $6 million. Consider the present to be the end of 2014/beginning of 2015 and the interest rate to be 6%. 1. a) Draw a cash flow diagram for this project (from present till end of year 2052) 2. b) Find the Present Worth of this project 3. c) Find is the Future Worth of this project

Answer 1

		Present Worth(PW) of Cash Flow=(Cash Flow)/((1+i)^N)
		i=interest rate =6%=0.06
		N=Year of Cash flow
		Future Worth(FW) of Cash Flow=(Cash Flow)*((1+i)^T)
		i=interest rate =6%=0.06
		T=Number of years to future
		Cash Flow in 2023 (Year9)=	$2	Million
		Cash Flow in Year10=2*1.01	$2.02	Million
		Scrap Value =$6 million
		Cash Flow in Year (N+1)=1.01*(Cash Flow in Year (N)
		Cash Flow in Terminal Year =-1.01*2.64+6=		$3.33
	Calender	N	T=38-N	CF	PW=CF/(1.06^N)	FW=CF*(1.06^T)
	Year	Year	Number of years to future	Cash Flow($ million)	Present Worth	Future worth
	2015	1	37	$0	$0.00	$0.00
	2016	2	36	$0	$0.00	$0.00
	2017	3	35	$0	$0.00	$0.00
	2018	4	34	($30)	($23.76)	($217.53)
	2019	5	33	($30)	($22.42)	($205.22)
	2020	6	32	($30)	($21.15)	($193.60)
	2021	7	31	($30)	($19.95)	($182.64)
	2022	8	30	($30)	($18.82)	($172.30)
	2023	9	29	($2)	($1.18)	($10.84)
	2024	10	28	($2.02)	($1.13)	($10.33)
	2025	11	27	($2.04)	($1.07)	($9.84)
	2026	12	26	($2.06)	($1.02)	($9.37)
	2027	13	25	($2.08)	($0.98)	($8.93)
	2028	14	24	($2.10)	($0.93)	($8.51)
	2029	15	23	($2.12)	($0.89)	($8.11)
	2030	16	22	($2.14)	($0.84)	($7.73)
	2031	17	21	($2.17)	($0.80)	($7.36)
	2032	18	20	($2.19)	($0.77)	($7.02)
	2033	19	19	($2.21)	($0.73)	($6.68)
	2034	20	18	($2.23)	($0.70)	($6.37)
	2035	21	17	($2.25)	($0.66)	($6.07)
	2036	22	16	($2.28)	($0.63)	($5.78)
	2037	23	15	($2.30)	($0.60)	($5.51)
	2038	24	14	($2.32)	($0.57)	($5.25)
	2039	25	13	($2.35)	($0.55)	($5.00)
	2040	26	12	($2.37)	($0.52)	($4.77)
	2041	27	11	($2.39)	($0.50)	($4.54)
	2042	28	10	($2.42)	($0.47)	($4.33)
	2043	29	9	($2.44)	($0.45)	($4.12)
	2044	30	8	($2.46)	($0.43)	($3.93)
	2045	31	7	($2.49)	($0.41)	($3.74)
	2046	32	6	($2.51)	($0.39)	($3.57)
	2047	33	5	($2.54)	($0.37)	($3.40)
	2048	34	4	($2.56)	($0.35)	($3.24)
	2049	35	3	($2.59)	($0.34)	($3.09)
	2050	36	2	($2.62)	($0.32)	($2.94)
	2051	37	1	($2.64)	($0.31)	($2.80)
	2052	38	0	$3.33	$0.36	$3.33
				SUM	($124.66)	($1,141.12)
	2b	Present Worth of the Project	$124.66	million
	3c	Future Worth of the Project	$1,141.12	million
					Cash Flow($ million) $5 o $0 g 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 1 2 3 ($5) ($10) ($15) ($20) ($25) ($30) ($35)