Question
In: Economics
The city is considering 2 separate cell tower providers. The city expects a benefit-cost ratio of...
The city is considering 2 separate cell tower providers. The city expects a benefit-cost ratio of 1.0 or better, and their cost of capital is 10% per year. Assume repeatability
| Verizon | AT&T | |
| Initial investment | $90,000 | $170,000 |
| Useful life in years | 6 | 12 |
| Market value at end of useful life | $25,000 | $40,500 |
| Annual benefits from operation | $30,000 | $40,000 |
| Annual operating expenses | $9,800 | $11,300 |
a) Conduct benefit-cost ratio on the Verizon and AT&T projects and indicate which project is the preferred project (Show Work)
b) Conduct an incremental difference to validate the decision.
Solutions
Expert Solution
A) Please see the tables below. First table shows the analysis for Verizon proposal and the second one for the AT&T proposal. We should select AT&T since it has a higher B/C Ratio of 1.23
| Verizon | Net CF / 1.1^Time | |||||
| T | Investment | Revenue | Cost | Salvage Value | Net CF | PV @ 10% |
| 0 | -90000.00 | -90000.00 | -90000.00 | |||
| 1 | 30000.00 | -9800.00 | 20200.00 | 18363.64 | ||
| 2 | 30000.00 | -9800.00 | 20200.00 | 16694.21 | ||
| 3 | 30000.00 | -9800.00 | 20200.00 | 15176.56 | ||
| 4 | 30000.00 | -9800.00 | 20200.00 | 13796.87 | ||
| 5 | 30000.00 | -9800.00 | 20200.00 | 12542.61 | ||
| 6 | -90000.00 | 30000.00 | -9800.00 | 25000.00 | -44800.00 | -25288.43 |
| 7 | 30000.00 | -9800.00 | 20200.00 | 10365.79 | ||
| 8 | 30000.00 | -9800.00 | 20200.00 | 9423.45 | ||
| 9 | 30000.00 | -9800.00 | 20200.00 | 8566.77 | ||
| 10 | 30000.00 | -9800.00 | 20200.00 | 7787.97 | ||
| 11 | 30000.00 | -9800.00 | 20200.00 | 7079.98 | ||
| 12 | 30000.00 | -9800.00 | 25000.00 | 45200.00 | 14402.11 | |
| B/C Ratio | 1.21 | |||||
| (Sum of PV of Net CF T1toT15 / -Investment) |
| AT&T | Net CF / 1.1^Time | |||||
| T | Investment | Revenue | Cost | Salvage Value | Net CF | PV @ 10% |
| 0 | -170000.00 | -170000.00 | -170000.00 | |||
| 1 | 40000.00 | -11300.00 | 28700.00 | 26090.91 | ||
| 2 | 40000.00 | -11300.00 | 28700.00 | 23719.01 | ||
| 3 | 40000.00 | -11300.00 | 28700.00 | 21562.73 | ||
| 4 | 40000.00 | -11300.00 | 28700.00 | 19602.49 | ||
| 5 | 40000.00 | -11300.00 | 28700.00 | 17820.44 | ||
| 6 | 40000.00 | -11300.00 | 28700.00 | 16200.40 | ||
| 7 | 40000.00 | -11300.00 | 28700.00 | 14727.64 | ||
| 8 | 40000.00 | -11300.00 | 28700.00 | 13388.76 | ||
| 9 | 40000.00 | -11300.00 | 28700.00 | 12171.60 | ||
| 10 | 40000.00 | -11300.00 | 28700.00 | 11065.09 | ||
| 11 | 40000.00 | -11300.00 | 28700.00 | 10059.17 | ||
| 12 | 40000.00 | -11300.00 | 40500.00 | 69200.00 | 22049.25 | |
| B/C Ratio | 1.23 | |||||
| (Sum of PV of Net CF T1toT15 / -Investment) |
B) When we do incremental analysis (by taking the difference between AT&T and Verizon, AT&T being the more expensive investment project), we get a B/C Ratio of 1.24 which validates our decision in part A. Pls see calculations below.
| Incremental (AT&T - Verizon) | Net CF / 1.1^Time | |||||
| T | Investment | Revenue | Cost | Salvage Value | Net CF | PV @ 10% |
| 0 | -80000.00 | 0.00 | 0.00 | 0.00 | -80000.00 | -80000.00 |
| 1 | 0.00 | 10000.00 | -1500.00 | 0.00 | 8500.00 | 7727.27 |
| 2 | 0.00 | 10000.00 | -1500.00 | 0.00 | 8500.00 | 7024.79 |
| 3 | 0.00 | 10000.00 | -1500.00 | 0.00 | 8500.00 | 6386.18 |
| 4 | 0.00 | 10000.00 | -1500.00 | 0.00 | 8500.00 | 5805.61 |
| 5 | 0.00 | 10000.00 | -1500.00 | 0.00 | 8500.00 | 5277.83 |
| 6 | 90000.00 | 10000.00 | -1500.00 | -25000.00 | 73500.00 | 41488.83 |
| 7 | 0.00 | 10000.00 |
-1500.00
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