Answer:
payback 3.29 years
NPV 87,158.55
Explanation:
PO 27,000
Cash flow saving Y1
2400 x 3.5 = 8,400
expenditures (1,500)
net savings 6,900
Cash flow saving Y2
The price will increase 0.5
6,900 + 2,400 x 0.5 = 8,100
Cash flow saving Y3 to Y20
The price will increase 0.5
8,100 + 2,400 x 0.5 = 9,300
We have an annuity of 18 years for 9,300 cash
And then we have a cash flow of 6,900
and another of 8,100
[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]
C = 9,300
r = 8%
time = 18
[tex]9,300 \times \frac{1-(1+0.08)^{-18} }{0.08} = PV\\[/tex]
PV = 87,158.55
Now this values are years into the future, so we need to bring them to present day.
[tex]\frac{Principal}{(1 + rate)^{time} } = PV[/tex]
year 1 principal 6,900
6,900/1.08 = 6,388.89
year 2 principal 8,100
[tex]\frac{8,100}{(1 + 0.08)^{2} } = PV[/tex]
PV= 5,915.64
year 3 annuity 87,158.55
[tex]\frac{87,158.55}{(1 + 0.08)^{3} } = PV[/tex]
PV= 69,189.27
cash flow - investment = net present value
69,189.27 + 5,915.64 + 6,388.89 - 27,000 = 54,493.8
The payback will be the time perdion when the project recovers it initial cost:
we first add the income from the irregular years and subtract from the investment
6,900 + 8,100 = 15,000
27,000 - 15,000 = 12,000
then we use the general formula investment/cash flow per year
12,000/9,300 = 1.29
the project need the first two years and then 1.29 years
2 + 1.29 = 3.29 years
