Your chief engineer recommends that you install a new energy management system. If you install the system, she predicts that your total usage will drop by $5,000$ kwh on$-$peak and $3,000$ kwh off$-$peak each month. In addition, your maximum on$-$peak demand will drop from $160$ kwh to $110$ kwh and the corresponding power factor will increase from $0\mathrm{.}80$ to $0\mathrm{.}98.$ You will also see savings for your maximum off$-$peak demand: it will drop from $70$ kwh to $55$ kwh and the corresponding power factor will increase from $0\mathrm{.}70$ to $0\mathrm{.}99.$

The electric company charges the following rates:

Kilowatt$-$hour charge: On$-$peak $=$ $$\mathrm{.}10/$kwh

Off$-$peak $=$ $$\mathrm{.}07/$ kwh

Demand charge: On$-$peak $=$ $$15\mathrm{.}00/$ kwh

Off$-$peak $=$ $$10\mathrm{.}00/$ kwh

Power factor charge: minimum power factor not subject to a charge is $0\mathrm{.}85$

Customer charge: $$50\mathrm{.}00$

a$.$ If you install the new system how much will you save each month? $(8$ points$)$

Kilowatt$-$hour charge:

On$-$peak $=$

Off$-$peak $=$

Demand charge:

On$-$peak:

Old $=$

New $=$

On$-$peak $=$

Off$-$peak:

Old $=$

New $=$

Off$-$peak $=$

Customer service charge: $=$

Savings $=$

b$.$ What is the present value of your net savings for the next $10$ years if install the new energy management system and nothing else changes other than the monthly amount paid due to inflation? Assume a monthly inflation rate of $0\mathrm{.}2475\%$ for energy. Your company has an anticipated return on investment for the same period of time is $1\mathrm{.}250\%.$ The system cost you $$100,000$ to purchase and install and is expected to lasts for $10$ years. You plan to $10\%$ down and finance the rest for $24$ months at $4\mathrm{.}999\%$ annual resulting in equal monthly payments of $$4,163.$ This payment is made at the end of the month. During that time, you will purchase an annual service contract for $$100.$ That amount is expected to increase by $17\mathrm{.}2525\%$ each year. This payment is made at the beginning of the year. You must express all percentages as decimals to four significant digits. Calculate the effective interest rates to four significant digits, you must include the trailing $0$s$.$ Your present values should be to the nearest whole dollar. $(11$ points$)$

ieffective $=((1+$ inominal$)/(1+$ Inflation$))1$

PV $=$ FV $*(1+$ i$)-$n

PV $=$ A $*(((1+$ ieffective$)$n $-1)/($ieffective $*(1+$ ieffective$)$n$))$

iannual $=(1+$ imonthly$)121$

Monthly energy savings $=$

Number of interest periods $=$

ieffective $=$

PVenergy savings $=$

System down payment $=$

System loan payment $=$

Number of interest periods $=$

ieffective $=$

PVloan payment $=$

PVsystem total $=$

Service contract, annual cost $=$

Number of interest periods $=$

inominal $=$

ieffective $=$

PVservice contract $=$

PVNet Savings $=$

c$.$ Should you install the new energy management system? $(1$ point$)$

Install $($Yes$/$No$)=$