Question

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?

Answer 1

Step-by-step 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)/((1 + rate)^(time) ) = PV`

Maturity 7,500.00

time 7 years

MARR: 10% = 0.1

`(7500)/((1 + 0.1)^(7) ) = PV`

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:

`Principal \: (1+ r)^(time) = Amount`

Principal 115,000.00

time 2 year

MARR: 10% = 0.08000

`115000 \: (1+ 0.08)^(2) = Amount`

Amount 134,136.00

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

`(Maturity)/((1 + rate)^(time) ) = PV`

Maturity 134,136.00

time 2.00

MARR: 10% = 0.1

`(134136)/((1 + 0.1)^(2) ) = PV`

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:

`PV / (1-(1+r)^(-time) )/(rate) = C\\`

PV 222,007.51

time 7 years

MARR: 10% = 0.1

`222007.51 / (1-(1+0.1)^(-7) )/(0.1) = C\\`

C $ 45,601.564