Ms. Child is considering the purchase of a new food packaging system. The system

Question

Ms. Child is considering the purchase of a new food packaging system. The system costs $144166. Ms. Child plans to borrow one-third of the purchase price from a bank at 4.5% per year compounded annually. The loan will be repaid using equal, annual payments over a 7-year period. The system is expected to last 15 years and have a salvage value of $15080 at that time. Over the 15 year period, Ms. Child expects to pay $915 per year for maintenance. The system will save $4558 per year because of efficiencies. Ms. Child uses a MARR of 8% to evaluate investments. What is the equivalent uniform annual worth (EUAW) of this system?

Explanation / Answer

Step 1: Find the payment over 7 years (A) for borrowing $48,055.33from the bank

-Borrow money from the bank = 144,166 * 1/3 = $48,055.33

-Payments to the bank over 7-year period at interest 4.5%

A = $48,055.33 (A/P, 4.5%, 7)

A = $48,055.33 (0.1697)

A = $8,155.06

Step 2: Find the net present worth

-Repay 8,155.06 to the bank in years 1, 2, 3, 4, 5, 6, 7

-Pay $96,110.67 at year 0 for purchasing the system

-The system saves $4,558/year

-Pay maintenance $915/year

-Salvage value is 15,080

-MARR = 8%

EUAW = -96,110.67 (A/P, 8%, 15)- 915 -8155.06 (P/A, 8%, 7) (A/P, 8%, 15) +4558 + 15,080 (A/F, 8%, 15)

EUAW = -96,110.67 (0.11683) – 915 – 8155.06 (5.20637) (0.11683) + 15,080 (0.03683)

EUAW = -$16,548.6

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