Question

OPTION 1: The initial purchase price of the machine is $30,000. The salvage value at the end of the useful life will be $4,000. Maintenance costs are $2,000 for the first year and are estimated to increase by $200 per year. OPTION 2: The machine is leased for an initial payment of $2,000 plus annual payments of $3,500. There is no salvage value. Annual maintenance cost is $10,000. Put down the present value of each of the items specified for each machinery option in the table below. Assume an interest rate of 6% and a useful lifetime of 8 years. Show your calculations in the spaces below the table.

a.) Please show the steps.

Present Value (PV) of Item
	Option 1	Option 2
PV of Purchase/Lease
PV of Salvage Value
PV of Maintenance
Total PV

b.) What is the annual equivalent cost of capital (capital recovery), over the 8-year lifetime, for the machine with the lowest present value calculated in the above table?

c.) What is the amount of money that you should invest now if you want to receive payments of $1,000 at the end of each year for ten years with the receipt of the first payment starting three years from now? Assume interest rate is 5% compounded annually.

d.) Provide explanation on your calculation in part c(i). Include in your explanation the specific type of cash flow given and the reason of why you have to derive the present or future equivalent value at various time points.

Answer 1

		Present Value(PV) of Cash Flow:
		(Cash Flow)/((1+i)^N)
		i=interest rate=6%=0.06 , N=Year of cash flow
	N	Year	1	2	3	4	5	6	7	8
	A	Maintenance Cost Option1	$2,000	$2,200	$2,400	$2,600	$2,800	$3,000	$3,200	$3,400	SUM
	B=A/(1.06^N)	Present Value	$1,887	$1,958	$2,015	$2,059	$2,092	$2,115	$2,128	$2,133	$16,388
	(OPTION 1)	Present Value of Maintenance Cost	$16,388
		PV of Salvage Value=4000/(1.06^8)	$2,510
0
		CASH FLOW OF OPTION-2 (LEASING)
	N	Year	0	1	2	3	4	5	6	7	8
	C	Annual Leasing Cost	$2,000	$3,500	$3,500	$3,500	$3,500	$3,500	$3,500	$3,500	$3,500	SUM
	D=C/(1.06^N)	Present Value	$2,000	$3,302	$3,115	$2,939	$2,772	$2,615	$2,467	$2,328	$2,196	$23,734
		Present Value of Lease	$23,734
	N	Year	1	2	3	4	5	6	7	8
	E	Maintenance Cost Option2(Lease)	$10,000	$10,000	$10,000	$10,000	$10,000	$10,000	$10,000	$10,000	SUM
	F=E/(1.06^N)	Present Value	$9,434	$8,900	$8,396	$7,921	$7,473	$7,050	$6,651	$6,274	$62,098
	(OPTION 2)	Present Value of Maintenance Cost	$62,098
		Present Value (PV) of Item
			Option 1(Purchase)	Option 2(Lease)
		PV of Purchase/Lease	$30,000	$23,734
		PV of Salvage Value	$2,510	$0
		PV of Maintenance	$16,388	$62,098
		Total PV	$48,898	$85,832
	b	Annual Equivalent Cost	$7,874.26	(Using PMT function of excel with Rate=6%, Nper=8,Pv=-48898)
	c
	Rate	Interest Rate	5%
	Nper	Number of years	10
	Pmt	Annual Payment	$1,000
	PV	Amount of money to invest	$7,721.73	(Using PV function of excel with Rate=5%, Nper=10,Pmt=-1000)