Answer:
Equivalent Annual Cost: $ 499,109.977
Explanation:
The equivalent annual cost is the PMT of the net present value of a project.
In this case the company will spend:
year 1: 1,500,000
year 2: 2,000,000
plus 65,000 maintenance cost for during each year.
we calculate the first two using the present value of a lump sum
[tex]\frac{Nominal}{(1 + rate)^{time} } = PV[/tex]
Nominal: $ 1,500,000.00
time 1 year
rate 0.06
[tex]\frac{1500000}{(1 + 0.06)^{1} } = PV[/tex]
PV 1,415,094.34
[tex]\frac{2000000}{(1 + 0.06)^{2} } = PV[/tex]
Nominal: $ 2,000,000.00
time 2 year
rate 0.06
PV 1,779,992.88
Then the maintenance cost will be an ordinary annuity:
[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]
C 65,000
time 10
rate 0.06
[tex]65000 \times \frac{1-(1+0.06)^{-10} }{0.06} = PV\\[/tex]
PV $478,405.6583
now we add them together:
1,415,094.3 + 1,779,992.88 + 478,405.6583 = $3,673,492.88
and calculate the PMT:
[tex]PV \div \frac{1-(1+r)^{-time} }{rate} = C\\[/tex]
PV $3,673,492.88
time 10
rate 0.06
[tex]3673492.87834196 \div \frac{1-(1+0.06)^{-10} }{0.06} = C\\[/tex]
C $ 499,109.977
