Question

You are thinking of making an investment in a new factory. The factory will generate revenues of $ 1 comma 250 comma 000$1,250,000 per year for as long as you maintain it. You expect that the maintenance costs will start at $ 60 comma 000$60,000 per year and will increase 5 %5% per year thereafter. Assume that all revenue and maintenance costs occur at the end of the year. You intend to run the factory as long as it continues to make a positive cash flow​ (as long as the cash generated by the plant exceeds the maintenance​ costs). The factory can be built and become operational immediately and the interest rate is 6 %6% per year. a. What is the present value of the​ revenues? b. What is the present value of the maintenance​ costs? c. If the plant costs $ 12 comma 500 comma 000$12,500,000 to​ build, should you invest in the​ factory?

Answer 1

		Annual Constant Revenue	$1,250,000
		Annual Maintenance Cost in Year1	$60,000
		Rate of annual increase of cost	5%
		Number of Years for maintenance cost to equal Revenue =			N
		60000*(1.05^N)=	$1,250,000
		1.05^N=1250000/60000=	20.83333333
		NLog1.05=Log(20.833333)=	1.318758763
		N*0.021189=1.31875876
		N=1.31875876/0.021189=	62.23701682
		N=62 Years (Rounded to whole number)
	a	Present Value of Revenues
	Rate	Discount Rate=Interest Rate	6%
	Nper	Number of years	62
	Pmt	Annual Constant Revenue	$1,250,000
	PV	Present Value of Revenues	$20,271,257	(Using PV function of excel with Rate=6%, Nper=62, Pmt=-1250000)
	b	Present Value of Maintenance Costs
				N	A	PV=A/(1.06^N)
				Year	Maintenance Cost	Present Value
				1	$60,000	$56,603.77
			(60000*1.05)	2	$63,000	$56,069.78
			(63000*1.05)	3	$66,150	$55,540.82
				4	$69,458	$55,016.85
				5	$72,930	$54,497.82
				6	$76,577	$53,983.69
				7	$80,406	$53,474.41
				8	$84,426	$52,969.93
				9	$88,647	$52,470.22
				10	$93,080	$51,975.21
				11	$97,734	$51,484.88
				12	$102,620	$50,999.18
				13	$107,751	$50,518.05
				14	$113,139	$50,041.47
				15	$118,796	$49,569.38
				16	$124,736	$49,101.74
				17	$130,972	$48,638.52
				18	$137,521	$48,179.66
				19	$144,397	$47,725.14
				20	$151,617	$47,274.90
				21	$159,198	$46,828.91
				22	$167,158	$46,387.13
				23	$175,516	$45,949.51
				24	$184,291	$45,516.03
				25	$193,506	$45,086.63
				26	$203,181	$44,661.29
				27	$213,340	$44,239.95
				28	$224,007	$43,822.60
				29	$235,208	$43,409.17
				30	$246,968	$42,999.65
			Present Value of maintenance costs $2,666,318 c Present Value of Cash Inflows $17,604,939 (a-b) d Initial cash flow ($12,500,000) NPV=c+d Net Present Value $5,104,939 Yes, you should invest in the factory NPV is positive