Answer:
Yes It will be accepted.
As the present worth (cost) of the water filtration
is far less than paying to Bay City for the purification
It decrease to $96,890.53 from $214,210.43 of the Bay Ciity Option
Explanation:
Present worth if the system is not purchased:
[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]
C $ 44,000.00
time 7 years
rate 0.1
[tex]44000 \times \frac{1-(1+0.1)^{-7} }{0.1} = PV\\[/tex]
PV $214,210.4280
We will now compare the value of the water filtration system:
F0 investment: 70,000 / 2 = 35,000
loan payment:
principal after two-years grace period:
rate 0.08000
[tex]35000 \: (1+ 0.08)^{2} = Amount[/tex]
Amount 40,824.00
Then there is 3 payment annuity-due as it begins at the beginning right away after the grace period:
[tex]PV \div \frac{1-(1+r)^{-time} }{rate}(1+r) = C\\[/tex]
PV 40,824
time: 3 years
rate 0.08
[tex]40824 \div \frac{1-(1+0.08)^{-3} }{0.08}(1+.08) = C\\[/tex]
C $ 14,667.667
Present value of the annuity discounted at Minimim accepted rate of return of 10%:
[tex]C \times \frac{1-(1+r)^{-time} }{rate}(1+r) = PV\\[/tex]
C 14,667.67
time years 3
rate 0.1
[tex]14667.6668309512 \times \frac{1-(1+0.1)^{-3} }{0.1}(1+0.10) = PV\\[/tex]
PV $40,123.9481
[tex]\frac{Maturity}{(1 + rate)^{time} } = PV[/tex]
Maturity 40,123.95
time 2.00
rate 0.10000
[tex]\frac{40123.9481078087}{(1 + 0.1)^{2} } = PV[/tex]
PV 33,160.29
present value of the maintenance expenses:
[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]
C $ 7,000.00
time 7 years
rate 0.1
[tex]7000 \times \frac{1-(1+0.1)^{-7} }{0.1} = PV\\[/tex]
PV $34,078.9317
Present value of the salvage value:
[tex]\frac{Salvage}{(1 + rate)^{time} } = PV[/tex]
Salvage: $7,500.00
time 7 years
rate 0.10000
[tex]\frac{7500}{(1 + 0.1)^{7} } = PV[/tex]
PV 3,848.69
Present worth of the water filtration system:
33,500 + +33,160.29 + 34,078.93 - 3,848.69 = 96,890.53
