As the manager of a resort hotel with 250 guest rooms is concerned with your monthly water and sewage bill. The water company uses the graduated billing schedule listed below. Your operation is currently using an average of 1,000,000 gallons of water each month. You are considering replacing your current 5.38 gallons per flush toilet with an ultra-high efficiency model that used 1.28 gallons per flush. Based on information your chief engineer provided, you estimate that on average that each toilet in an occupied room is flushed 10 times per day. Your average monthly occupancy rate is 95.96162%. Assume 30.5 days per month when calculating your water savings.

Water rates: monthly charge of $50.00 per month plus usage charge base on the rates listed below.

Amount of water used Rate per 1000 gallons

First 100,000 gallons $2.00

Next 250,000 gallons $2.50

Next 500,000 gallons $4.00

Anything over 850,000 gallons $6.00

Sewage rates: monthly charge of $100.00 per month plus usage charge based on the total water used.

Amount of sewage produced = Total water used minus deduct meter

The rate per 1000 gallons is $10.00

Deduct meter shows a monthly average of 100,000 gallons

Water rates are expected to rise by 0.8991% per month and sewage rates are expected to rise by 3.061% per month. The owners of the operation expect a monthly rate of return on their investment of 1.000%. Assume that the toilets will last for 20 years.

The equation for the effective monthly interest rate is:

i_effective = ((1 + i_nominal) / (1 + Inflation)) 1

The present value equations are:

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

PV = A * (((1 + i_effective)ⁿ - 1) / (i_effective * (1 + i_effective)ⁿ))

Given the above information answer the following questions. You must show all your work in the space provided. Make sure you calculate all interest rates to 4 significant digits and write all percentages as decimals.

1. How much water is currently being used each month by the toilets in your hotel (to the nearest gallon)?

Water Used by Toilets =

2. If you install the ultra-high efficiency toilets, how much water will be used each month by the toilets in your hotel (to the nearest gallon)?

Water Used by Toilets =

3. What will be the total monthly water usage by the entire hotel if you install the ultra-high efficiency toilets (to the nearest gallon)?

New Monthly Water Usage =

4. What will be your average monthly water and sewage bill for the entire hotel if you do NOT install the ultra-high efficient toilets (to the nearest dollar)?

The water portion of the bill

Amount of water not yet paid for =

Cost for first 100,000 gal =

Amount of water not yet paid for =

Cost for next 250,000 gal =

Amount of water not yet paid for =

Cost for next 500,000 gal =

Amount of water not yet paid for =

Cost for all remaining water =

Water Bill =

Sewage Bill =

Total Water and Sewage Bill =

6. What will be your average monthly water and sewage bill for the entire hotel if you do install the ultra-high efficient toilets (to the nearest dollar)?

The water portion of the bill

Amount of water not yet paid for =

Cost for first 100,000 gal =

Amount of water not yet paid for =

Cost for second 250,000 gal =

Amount of water not yet paid for =

Cost for third 500,000 gal =

Amount of water not yet paid for =

Cost for all remaining water =

Water Bill =

Sewage Bill =

Total Water and Sewage Bill =

7. Water savings (to the nearest dollar) over 20 years in present value:

Water Savings =

i_effective =

PV_{Water Savings} =

8. Sewage savings (to the nearest dollar) over 20 years in present value:

Sewage Savings =

i_effective =

PV_{Sewage Savings} =

9. Total savings (to the nearest dollar) over 20 years in present value:

PV_{Total Savings} =