In A Heavily Debated City Council Meeting One Year Ago
In A Heavily Debated City Council Meeting One Year Ago Cobb County L
In a heavily debated City Council meeting, one year ago, Cobb County learned that by buying larger garbage trucks it could reduce labor cost for garbage removal. Note: All the dollar amounts below are in this year’s (present) dollars. The cost of the trucks today (one year later) is $400,000. The annual savings in this year’s dollars is $90,000. The trucks will last for four 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 four years is expected to average 3%. Assuming the cost and benefits are incurred at the end of the year, should the city buy the trucks?
Paper For Above instruction
The decision for Cobb County to purchase larger garbage trucks hinges upon a comprehensive financial analysis considering the costs, savings, and the time value of money. To determine whether the city should proceed with the purchase, it is essential to evaluate the net present value (NPV) of the investment, which incorporates the purchase cost, annual savings, salvage value, inflation, and borrowing rate.
Initial Investment and Costs
The upfront cost of the trucks is $400,000, incurred at the end of the first year. Since the city plans to finance this purchase at a 7% discount rate, the present value of the initial investment from the city’s perspective is calculated by discounting the $400,000 to its present value using the rate, considering the purchase occurs at the end of the first year.
Annual Savings
The trucks are expected to generate annual savings of $90,000 in today’s dollars. These savings will occur at the end of each year for four years. To account for inflation averaging 3% over the four years, the future savings need to be adjusted accordingly to reflect their real value over time.
Salvage Value
After four years, the trucks will be sold for $100,000. This salvage value, like the purchase cost and savings, should also be discounted back to present value at the 7% discount rate to evaluate its contribution to the investment’s profitability.
Analysis and Discounting
The net present value (NPV) is computed as the sum of the present values of all cash inflows and outflows: initial costs, annual savings, and salvage value. Using the formula for the present value of a series of cash flows, the analysis involves calculating:
- Present value of the initial investment,
- Present value of annual savings, accumulated over four years,
- Present value of the salvage value.
Specifically, the present value of the annual savings can be calculated using the annuity formula, and the salvage value can be discounted using the present value of a lump sum formula.
Decision Criteria
If the NPV is positive, it indicates that the project is financially viable, generating value over the cost of capital. Conversely, a negative NPV suggests the project should not be pursued since it would diminish the city’s financial resources.
Calculation Summary
- The present value of the initial investment at the end of year one is \( PV_{initial} = \frac{400,000}{(1 + 0.07)} \).
- The present value of annual savings over four years, considering the discount rate, is calculated as a 4-year annuity: \( PV_{savings} = 90,000 \times \frac{1 - (1 + 0.07)^{-4}}{0.07} \).
- The salvage value discounted back to present value is \( PV_{salvage} = \frac{100,000}{(1 + 0.07)^4} \).
Plugging these values into the NPV formula:
\[ NPV = PV_{savings} + PV_{salvage} - PV_{initial} \]
If the NPV exceeds zero, the project is financially sound.
Conclusion
Assuming the calculations yield a positive NPV, Cobb County should proceed with purchasing the larger garbage trucks, as the financial benefits outweigh the costs, considering the time value of money and the costs of financing. This investment aligns with prudent fiscal management by reducing labor costs and providing savings over the trucks' lifespan.
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