# Math Help - present worth

1. ## present worth

1) what is the PW (at i=10%) of the following electric power generation project? there is a $180,000 over haul cost in year 8.the first cost is$420,000 , and the annual operating is $30,000. Revenue from power sales is expected to be$100,000 per year.the facility will have a salvage value of
$75,000 at the end of year 15. ? 2)a new roof will be needed for the civil engineering labs at the 30-year point of the labs 50 year life.if the new roof wil cost$140,000, what is the roofs EAC at i= 5% ?

2. Originally Posted by sandeep641
1) what is the PW (at i=10%) of the following electric power generation project? there is a $180,000 over haul cost in year 8.the first cost is$420,000 , and the annual operating is $30,000. Revenue from power sales is expected to be$100,000 per year.the facility will have a salvage value of
$75,000 at the end of year 15. ? You need to reduce all costs to the sum that invested today will pay the cost when it falls due (i=10% corresponds here to i=0.1). A cost of$180000 in year 8 has a present cost equivalent of $\180000/(1+i)^8 \approx {\color{red}\83971.33}$

The present cost of the initial cost is itself $\color{red}\420000$

The net revenue (revenue less operating costs) over 15 years present value is (assuming this is accrued at the end of each year, if you want this paid continuously look through your notes for the appropriate formula):

$
\70000/(1+i)+\70000/(1+i)^2+ ... + \70000/(1+i)^{15}=$
$\70000 \frac{[(1+i)+1][(1+i)^{15}-1]}{(1+i)-1}
$

(This last you will probably find in your notes as a present value of a future revenue stream formula)

The present value of the salvage value is:

$\75000/(1+i)^{15} \approx \17954.40$.

When you combine all of the above make sure you use the correct signs for what are revenue and costs terms (costs are red, revenue black).

There are probably some mistakes in the above, but the basic idea is that you reduce everything to a sum which if invested today at the given interest rate will yield an equivalent payment/revenue stream.

CB