Please write the answer clearly and legibly because I want to understand the ans
ID: 2439668 • Letter: P
Question
Please write the answer clearly and legibly because I want to understand the answers and how you got to the answer. Please also write step by step 5) (25 pts) Consider the following EOY cash flows for two mutually exclusive alternatives (one must be chosen): The MARR is 5% per year. Capital investment Annual Expenses Useful Life Market Value at the end of useful life Lead Acid 28,000 15,000 12 years S0 Lithium lorn 55,000 13,000 18 years $2,800 Determine which alternative should be selected if the service is needed for ever and repeatability assumption applies. (15 pts) Determine which alternative should be selected if the analysis period is 18 years, the repeatability assumption does NOT apply, and a battery system can be leased for 8,000 per year after the useful life of either battery is over. (10 pts) A. 8.Explanation / Answer
A. As the life of the alternatives is not equal we have to convert the unequal life into equal life. As per the repeatability assumption we have to calculate the common multiple and that will be taken as the life for both the alternatives. Here the alternatives have a life of 12 and 18 years. The common multiple will be 36. Lead acid is to be repeated 3 times and Lithium ion has to be repeated 2 times.
Present worth of Lead Acid
PW = 28,000 + 28,000 (P/F, 5%, 12) + 28,000 (P/F, 5%, 24) + 15,000 (P/A, 5%, 36)
PW = 28,000 + 28,000 (.5568) + 28,000 (.3101) + 15,000 (16.5462) = 300,466
Present worth of Lithium Ion
PW = 55,000 + 55,000 (P/F, 5%, 18) + 13,000 (P/A, 5%, 36) – 2,800 (P/F, 5%, 18)
– 2,800 (P/F, 5%, 36)
PW = 55,000 + 55,000 (.4155) + 13,000 (16.5462) – 2,800 (.4155)
– 2,800 (.1726) = 291,306
Since the alternatives are cost dominated, select the lowest cost project. Hence select the Lithium Ion as it has the lowest cost.
B. Here study period is taken as 18 years. If the life of any alternative is falls short then a yearly lease cost of 8000 will be charged after the useful life. In the question Lead acid has 12 years life. So for the next 6 years it will be charged a lease cost of 8,000 per year.
Present worth of Lead Acid
PW = 28,000 + 15,000 (P/A, 5%, 12) + 8,000 (P/A, 5%, 6) (P/F, 5%, 12)
PW = 28,000 + 15,000 (8.863) + 8,000 (5.076) (.5568) = 183,556
Present worth of Lithium Ion
PW = 55,000 + 13,000 (P/A, 5%, 18) – 2,800 (P/F, 5%, 18)
PW = 55,000 + 13,000 (11.690) – 2,800 (.4155) = 208,807
Since the alternatives are cost dominated, select the lowest cost project. Hence select the Lead Acid as it has the lowest cost.