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Sagot :
Answer:
Year 3 cashflow:
current system: 243,360
alternative system: 102,240
Present cost:
current system PV -$971,665.9146
alternative system PV -$1,075,964.17
Explanation:
Current Scenario:
42,000 inspection cost
Repairs:
1,520 identified x $75 = 114,000
Refunds:
480 units x $182 = 87,360
Total yearly cost: 243,360
PV of an annuity of $243,360 during 5 years:
Present Value of Annuity
[tex]C \times \displaystyle \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]
C 243,360
time 5
rate 0.08
[tex]243360 \times \displaystyle \frac{1-(1+0.08)^{-5} }{0.08} = PV\\[/tex]
PV $971,665.9146
New Scenario:
Inspection cost: $42,000 + $25,000 = $77,000
Repair cost: 350 units x $41 = $14,320
Refunds: 50 units x $182 x 120% = $10,920
Total yearly cost: $102,240
F0 cost:
470,000 workers trainings
210,000 purchase cost
Total F0 cost: 680,000
Present Value of Annuity
[tex]C \times \displaystyle \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]
C 102,240
time 5
rate 0.08
[tex]102240 \times \displaystyle \frac{1-(1+0.08)^{-5} }{0.08} = PV\\[/tex]
PV $408,214.6742
PV of residual value:
PRESENT VALUE OF LUMP SUM
[tex]\frac{Maturity}{(1 + rate)^{time} } = PV[/tex]
Maturity 18,000.00
time 5.00
rate 0.08
[tex]\frac{18000}{(1 + 0.08)^{5} } = PV[/tex]
PV 12,250.50
Net present value:
- 680,000 -408,214.67 + 12,250.50 = 1,075,964.17
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