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
