Question

(i) The followings show two machinery options.

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.

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

Option 1: Show calculations of PV of Salvage Value and PV of Maintenance.

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Option 2: Show calculation of PV of Lease.

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

Answer 1

(i) The followings show two machinery options.

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. (9 marks)

Present Value (PV) of Item
	Option 1	Option 2
PV of Purchase/Lease	30000	PV of leasing is calculated below: Year CF Discount Factor Discounted CF 0 $   2,000.00 1/(1+0.06)^0= 1 1*2000=       2,000.00 1 $   3,500.00 1/(1+0.06)^1= 0.943396226 0.943396226415094*3500=       3,301.89 2 $   3,500.00 1/(1+0.06)^2= 0.88999644 0.88999644001424*3500=       3,114.99 3 $   3,500.00 1/(1+0.06)^3= 0.839619283 0.839619283032302*3500=       2,938.67 4 $   3,500.00 1/(1+0.06)^4= 0.792093663 0.79209366323802*3500=       2,772.33 5 $   3,500.00 1/(1+0.06)^5= 0.747258173 0.747258172866057*3500=       2,615.40 6 $   3,500.00 1/(1+0.06)^6= 0.70496054 0.704960540439676*3500=       2,467.36 7 $   3,500.00 1/(1+0.06)^7= 0.665057114 0.665057113622336*3500=       2,327.70 8 $   3,500.00 1/(1+0.06)^8= 0.627412371 0.627412371341826*3500=       2,195.94 NPV = Sum of all Discounted CF     23,734.28
PV of Salvage Value		Not applicable
PV of Maintenance	PV of the maintenance cost is calculated below: Year CF Discount Factor Discounted CF 0 $                -   1/(1+0.06)^0= 1 1*0=                    -   1 $   2,000.00 1/(1+0.06)^1= 0.943396226 0.943396226415094*2000=       1,886.79 2 $   2,200.00 1/(1+0.06)^2= 0.88999644 0.88999644001424*2200=       1,957.99 3 $   2,400.00 1/(1+0.06)^3= 0.839619283 0.839619283032302*2400=       2,015.09 4 $   2,600.00 1/(1+0.06)^4= 0.792093663 0.79209366323802*2600=       2,059.44 5 $   2,800.00 1/(1+0.06)^5= 0.747258173 0.747258172866057*2800=       2,092.32 6 $   3,000.00 1/(1+0.06)^6= 0.70496054 0.704960540439676*3000=       2,114.88 7 $   3,200.00 1/(1+0.06)^7= 0.665057114 0.665057113622336*3200=       2,128.18 8 $   3,400.00 1/(1+0.06)^8= 0.627412371 0.627412371341826*3400=       2,133.20 NPV = Sum of all Discounted CF     16,387.90	PV of the maintenance cost is calculated below:
Total PV	So total PV = 30000+2059.65+16387.90 = 48897.55	So total PV =  62,097.94 +  23,734.28 = 85832.22

NOw we calculate the EAA for the option 1;

We are given the following information:

r	6.00%
n	8
frequency	1
PV	$            48,897.55

We need to solve the following equation to arrive at the required PMT:

So the PMT or the EAA = 7874.26