Question

1.) Two alternatives are being considered to perform a given job. Both of these alternatives provide equal service. The cost data for each alternative are provided in the tables below: Alternative 1 900,000 100,000 Alternative 2 300,000 30,000 Initial Cost Salvage Value Life, years Annual cost of operation and maintenance Required return 15,000 20,000 20 T20 Use a conventional cost comparison and determine: (a) An equivalent annual cost comparison assuming infinite service need. Which one do you choose? Why? (b) A capitalized cost comparison assuming infinite service need. Which one do you choose? Why? (c) A present worth cost comparison assuming infinite service need. Which one do you choose? Why? (d) If the Capitalized Benefit of Alternative 2 is $500,000, should this project be undertaken? (Hint: The cost is the initial cost plus the capitalized cost calculated plus salvage value)

Answer 1

Since many questions are asked I am answering option (c) A present worth cost comparison.

First identify the annual cash flow for each alternative separately and apply the discount rate for 20%(Required rate of return) for each year's cash outflow to find the discounted cash outflow i.e. present value of cash outflow. The alternative giving lower present value of cash outflow should be choosen as the benefit derived is equal for both the alternative.

Assumption: Since question is silent about tax rate, we are going to assume that there no tax saving.

Calculation of Discounted Cash flow:

Alternative 1

Year	Cash Outflow	Discount factor @20%	Discounted Cash Outflow
Initial Investment	900000	1	900000
1	15000	0.80	12000
2	15000	0.64	9600
3	15000	0.512	7680
4	15000	0.4096	6144
5	-85000 (15000-100000) Salvage value reduced from cash outflow	0.32768	-27852.80
	Present value of Cash Ouflow		907571.20

Alternative 2

Year	Cash Outflow	Discount factor @20	Discounted Cash Ouflow
Initial Investment	300000	1	300000
1	20000	0.80	16000
2	20000	0.64	12800
3	20000	0.512	10240
4	20000	0.4096	8192
5	-10000	0.32768	-3276.80
	Present value of cash outflow		343955.20

Since alternative 2 is showing lower discounted cash outflow, the same should be choosen.