The town of Cedar Falls has decided to lease their parking meters for 10 years t
ID: 2779013 • Letter: T
Question
The town of Cedar Falls has decided to lease their parking meters for 10 years to a private company in order to raise revenue for some much needed road repairs. Three companies have made bids for the contract, and the town council has hired you as a consultant to help them choose which one to accept.
Park-Tastic Parking Services has offered to pay the town $5,000 on the last day of each month for the next 10 years. In addition, they will provide two lump sum payments: one of $50,000 to be paid at the beginning of the first month of the deal (day 1), and another payment of $100,000 to be paid on the very last day of the deal.
Meter-Maid Inc. has offered to pay Cedar Falls $6,000 on the last day of each month for the next 10 years, as well as a lump sum payment of $30,000 at the beginning of the first month of the deal (day1).
Finally, Hank's Parking has offered to pay Cedar Falls $70,000 on the last day of each year for the next 10 years.
Cedar Falls' mayor informs you that she wants the deal with greatest Net Present Value (NPV). If the annual interest rate is 3% and it is compounded monthly, what is your recommendation to the town council of Cedar Falls?
Explanation / Answer
Present Values of Offers
Park-Tastic Parking Services $ 641,918.36
Meter-maid Inc $ 651,370.56
Hank’s Parking $ 597,114.20
Based on the above, offer of Meter-maid Inc appears to be attractive.
Cedal Falls annual interest rate = 3% compounded monthly
Monthly interest rate r = 3%/12 = 0.25% or 0.0025
Period of Lease = 10 years or 10*12 = 120 months
Park-Tastic Parking Services
Offer – Monthly Payment $ 5000 on the last day + $ 50000 at the beginning of first month + $ 100000 on the last day of the deal
Present Value = $ 50000 + $ 5000 * [(1-(1/(1+0.0025)^120))/0.0025] + $100000/(1+0.0025)^120
= $50000 + $5000 * [(1-(1/1.3493535)/0.0025] + $100000/1.3493535
= $50000 + $ 5000 * [(1-0.7410956)/0.0025] + $100000/1.3493535
= $50000 + $ 5000 * [0.2589044/0.0025] + $100000/1.3493535
= $50000 + $5000 * 103.56176 + $100000/1.3493535
=$50000 + $517808.80 + $74109.56
= $641,918.36
Meter-maid Inc
Offer - Monthly payment of $6000 on the last day + $30000 at the beginning of the first month
Present Value = $ 30000 + $ 6000 * [(1-(1/(1+0.0025)^120))/0.0025]
= $30000 + $6000 * [(1-(1/1.3493535)/0.0025]
= $30000 + $ 6000 * [(1-0.7410956)/0.0025]
= $30000 + $ 6000 * [0.2589044/0.0025]
= $30000 + $6000 * 103.56176
= $30000 + $621370.56
= $ 651,370.56
Hank’s Parking
Offer - Annual Payment of $70,000 for next 10 years
Present Value = $ 70000 * [(1-(1/(1+0.03)^10))/0.03]
= $70000 * [(1-(1/1.3439164)/0.03]
= $ 70000 * [(1-0.7440939)/0.03]
= $ 70000 * [0.2559061/0.03]
= $70000 * 8.530203
= $597,114.198 or $597,114.20
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