Question

Aerotron Electronics is considering the purchase of a water filtration system to assist in circuit board manufacturing. The system costs $130,000. It has an expected life of 7 years at which time its salvage value will be $7,500. Operating and maintenance expenses are estimated to be $16,000 per year. If the filtration system is not purchased, Aerotron Electronics will have to pay Bay City $42,000 per year for water purification. If the system is purchased, no water purification from Bay City will be needed. Aerotron Electronics must borrow 1/2 of the purchase price, but they cannot start repaying the loan for 2 years. The bank has agreed to 3 equal annual payments, with the 1st payment due at the end of year 2. The loan interest rate is 8% compounded annually. Aerotron Electronics’ MARR is 10% compounded annually.

What is the annual Worth of this Investment?

Answer 1

System cost = $130,000

Salvage value = $7,500

Life = 7 years

Annual savings = 42,000 - 16,000 = $26,000

MARR = 10%

Loan interest rate = 8%

Loan amount = 130,000/2 = $65,000

Loan after 1 year = 65,000 * (F/P, 8%, 1) = 65,000 * 1.08 = $70,200

Loan payment = 70,200 * (A/P, 8%, 3) = 70,200 * 0.388 = $27,237.6

PW = -65,000 + 26,000(P/A, 10%, 7) - 27,237.6(P/A, 10%, 3)(P/F, 10%, 1) + 7,500(P/F, 10%, 7)

= -65,000 + 26,000 * 4.868 - 27,237.6 * 2.487 * 0.9091 + 7,500 * 0.5132

= -65,000 + 126,568 - 61,582.35 + 3,849

= 3,834.65

AW = 3,834.65(A/P, 10%, 7) = 3,834.65 * 0.2054

= 787.6371

Annual worth of the investment is $787.6371