Aerotron electronics is considering the purchase of a water filtration system to assist in circuit board manufacturing. the system costs $230,000. 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 $8,000 per year. if the filtration system is not purchased, aerotron electronics will have to pay bay city $20,000 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?

Explanation:

Annual worth: this will be the annuity payment equivalent to all the cashflow of the investment. Thus the PMT of the net present value

Cash Investment at F0: 230,000/2 = 115,000

present value of 7,500 salvage value:

Maturity  7,500.00

time   7 years

MARR: 10% =0.1

PV   3,848.69

Then, we need to calculate the present value of the loan discounted at 10%

half the investment is finance: 230,000 / 2 = 115,000

Then, this capitalize 2 year at 8% before the first payment:

Principal115,000.00

time2 year

MARR: 10% =0.08000

Amount134,136.00

Now we need to discount this loan at 10% which is our rate of return:

Maturity  134,136.00

time   2.00

MARR: 10% =0.1

PV   110,856.20

Finally: we add this values to get the resent worth:

115,000 +  110,856.20 - 3,848.69 = 222,007.51

Last step, we calculate the PMT of the present worth:

PV222,007.51

time7 years

MARR: 10% =0.1

C  $ 45,601.564