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Nady [450]
3 years ago
15

Aerotron Electronics is considering the purchase of a water filtration system to assist in circuit board manufacturing. The syst

em 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?
Business
1 answer:
tino4ka555 [31]3 years ago
6 0

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: <em>230,000/2 = 115,000</em>

present value of 7,500 salvage value:

\frac{Maturity}{(1 + rate)^{time} } = PV  

Maturity  7,500.00

time   7 years

MARR: 10% = 0.1

\frac{7500}{(1 + 0.1)^{7} } = PV  

PV  <em> 3,848.69 </em>

<u>Then, we need to calculate the present value of the loan discounted at 10%</u>

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

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:

\frac{Maturity}{(1 + rate)^{time} } = PV  

Maturity  134,136.00

time   2.00

MARR: 10% = 0.1

\frac{134136}{(1 + 0.1)^{2} } = PV  

PV   <em>110,856.20 </em>

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

<em>115,000 +  110,856.20 - 3,848.69 = </em><em>222,007.51</em>

<em />

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

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

PV 222,007.51

time 7 years

MARR: 10% = 0.1

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

C  $ 45,601.564

<em />

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