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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?

Respuesta :

TomShelby

Answer:

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:

[tex]\frac{Maturity}{(1 + rate)^{time} } = PV[/tex]  

Maturity  7,500.00

time   7 years

MARR: 10% = 0.1

[tex]\frac{7500}{(1 + 0.1)^{7} } = PV[/tex]  

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:

[tex]Principal \: (1+ r)^{time} = Amount[/tex]

Principal 115,000.00

time 2 year

MARR: 10% = 0.08000

[tex]115000 \: (1+ 0.08)^{2} = Amount[/tex]

Amount 134,136.00

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

[tex]\frac{Maturity}{(1 + rate)^{time} } = PV[/tex]  

Maturity  134,136.00

time   2.00

MARR: 10% = 0.1

[tex]\frac{134136}{(1 + 0.1)^{2} } = PV[/tex]  

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:

[tex]PV \div \frac{1-(1+r)^{-time} }{rate} = C\\[/tex]

PV 222,007.51

time 7 years

MARR: 10% = 0.1

[tex]222007.51 \div \frac{1-(1+0.1)^{-7} }{0.1} = C\\[/tex]

C  $ 45,601.564

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