A city has learned that by buying larger garbage trucks, labor ✓ Solved
A city has learned that by buying larger garbage trucks, it could reduce labor costs for garbage removal. The cost of the trucks today is $400,000, and the annual savings in this year’s constant dollars is $90,000. The trucks will last for 4 years and then will be sold for $100,000. The city can borrow money at a 7% discount rate to purchase the trucks. Inflation (for the next 4 years) is expected to average 3%. All dollar amounts are in this year’s dollars (constant dollars). Assuming the costs and benefits are incurred at the end of the year, should the city buy the trucks?
This problem extends the garbage truck problem from assignment 2. Two other lenders provide alternative scenarios. Alternate lender 1 suggests that the inflation rate will be 4% and offers an interest rate of 7.5%, while alternate lender 2 suggests that the inflation rate will be 1% and offers an interest rate of 6.5%. For all three sources, the interest rates are guaranteed if the decision is made in the next 90 days. Which of the following decisions should be made and why? (a) The usual lender should be used because she offers a positive NPV. (b) Alternate lender 1 should be used because he offers the highest NPV. (c) The garbage trucks shouldn’t be purchased because there is a possibility of a negative NPV. (d) Alternate lender 2 should be used because most scenarios have a positive NPV and she offers the highest NPV under each scenario. (e) Each solution is as good as any other.
Paper For Above Instructions
The decision to purchase larger garbage trucks by the city hinges upon a financial analysis through the lens of Net Present Value (NPV), taking into account the costs of purchasing the trucks, the expected savings, the resale value, and the impact of inflation and borrowing rates offered by different lenders. An NPV analysis allows the city to evaluate whether the financial benefits of purchasing the trucks outweigh the costs incurred over a specific period.
Financial Analysis with the Usual Lender:
With the usual lender, the city faces a borrowing cost of 7% and an expected inflation rate of 3%. The calculation of NPV can be structured as follows:
- Initial cost of trucks: $400,000
- Annual savings over 4 years: $90,000
- Resale value at the end of 4 years: $100,000
The saved amounts should be adjusted for the discount rate to find their present value, specifically:
Year 1 savings in present value = $90,000 / (1 + 0.07)^1 = $84,112.15
Year 2 savings in present value = $90,000 / (1 + 0.07)^2 = $78,533.46
Year 3 savings in present value = $90,000 / (1 + 0.07)^3 = $73,268.04
Year 4 savings in present value = $90,000 / (1 + 0.07)^4 = $68,305.53
Resale value in present value = $100,000 / (1 + 0.07)^4 = $76,079.66
The total present value of benefits (savings + resale value) can be calculated as:
Total Present Value = $84,112.15 + $78,533.46 + $73,268.04 + $68,305.53 + $76,079.66 = $380,298.84
Net Present Value (NPV) with the usual lender's terms:
NPV = Total Present Value - Initial Cost = $380,298.84 - $400,000 = -$19,701.16
Financial Analysis with Alternate Lender 1:
With the first alternate lender, the inflation will increase to 4% and the borrowing rate to 7.5%. Redoing the same calculations, the present values of the savings and resale value will change accordingly.
Year 1 savings = $90,000 / (1 + 0.075)^1 = $83,720.93
Year 2 savings = $90,000 / (1 + 0.075)^2 = $77,932.77
Year 3 savings = $90,000 / (1 + 0.075)^3 = $72,885.38
Year 4 savings = $90,000 / (1 + 0.075)^4 = $68,496.06
Resale value = $100,000 / (1 + 0.075)^4 = $73,303.23
Total Present Value = $83,720.93 + $77,932.77 + $72,885.38 + $68,496.06 + $73,303.23 = $376,338.38
NPV with Alternate Lender 1:
NPV = $376,338.38 - $400,000 = -$23,661.62
Financial Analysis with Alternate Lender 2:
The second alternate lender proposes a 1% inflation and a borrowing cost of 6.5%.
Year 1 savings = $90,000 / (1 + 0.065)^1 = $84,226.42
Year 2 savings = $90,000 / (1 + 0.065)^2 = $79,250.80
Year 3 savings = $90,000 / (1 + 0.065)^3 = $74,757.18
Year 4 savings = $90,000 / (1 + 0.065)^4 = $70,705.33
Resale value = $100,000 / (1 + 0.065)^4 = $78,120.84
Total Present Value = $84,226.42 + $79,250.80 + $74,757.18 + $70,705.33 + $78,120.84 = $386,060.57
NPV with Alternate Lender 2:
NPV = $386,060.57 - $400,000 = -$13,939.43
Conclusion:
Based on the NPV calculations for each lender, all scenarios yielded a negative NPV, indicating that purchasing the trucks may not be financially feasible under the presented assumptions. However, Alternate Lender 2 provides the highest NPV among the three lenders (least negative NPV). Thus, the city should consider using Alternate Lender 2 since it presents the most favorable financial outlook given the possible scenarios.
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