Complete The Following Problems. You Must Show Your Work ✓ Solved
Complete the following problems. You must show your work
1. A city government is considering two types of town-dump sanitary systems. Design A requires an initial outlay of $500,000 with annual operating and maintenance costs of $75,000 for the next 20 years; design B calls for an investment of $400,000 with annual operating and maintenance costs of $95,000 per year for the next 20 years. Fee collections from the residents would be $100,000 per year. The interest rate is 10%, and no salvage value is associated with either system. By the benefit-cost ratio (BC(i)), which system should be selected?
2. Identify which of the following expenditures is considered as a capital expenditure that must be depreciated (capitalized): a) Purchased a fax machine for $10,000. b) Painted the warehouse building, both interior and exterior, for $20,000. c) Installed a water dispenser in a company dining area for $2500. d) Paid $15,000 to lease a dump truck for six months. e) Purchased a patent on an energy-saving device over five years at a cost of $35,000. f) Purchased a spare part for a framing machine for $4,000. g) Repaved a parking lot for $20,000. h) Installed a conveyor belt system to automate some part of a production process for $50,000. i) Purchased land to build a new facility for $350,000.
3. Consider the following data on an asset: Cost of the asset, I: $150,000 Useful life, N: 5 years Salvage value, S: $16,000 Compute the annual depreciation allowances and the resulting book values, using the following methods: a) The straight-line depreciation method, b) The double-declining-balance method.
Paper For Above Instructions
1. Benefit-Cost Ratio Analysis
The benefit-cost ratio (BCR) is a financial metric used to evaluate the economic viability of projects by comparing the benefits derived from a project to the costs incurred. For the two designs of the sanitary systems proposed:
Design A
- Initial Investment: $500,000
- Annual Operating Costs: $75,000
- Annual Revenue: $100,000
- Lifetime: 20 years
- Interest Rate: 10%
The total cost over 20 years includes the initial investment and the present value of the operating costs. The present value can be calculated using the formula for the present value of an annuity:
PVA = Pmt × [(1 - (1 + r)^-n) / r]
- Where Pmt = Annual operating cost, r = interest rate, n = number of years
The present value of operating costs for Design A would be:
PVA_A = 75,000 × [(1 - (1 + 0.10)^-20) / 0.10] = 75,000 × 9.645 = $723,375
So, the total cost for Design A:
Total Cost_A = Initial Investment + Present Value Operating Costs
Total Cost_A = $500,000 + $723,375 = $1,223,375
Now, calculating the total revenue over 20 years:
Total Revenue_A = Annual Revenue × Years = $100,000 × 20 = $2,000,000
The benefit-cost ratio for Design A:
BCR_A = Total Revenue / Total Costs = $2,000,000 / $1,223,375 = 1.63
Design B
- Initial Investment: $400,000
- Annual Operating Costs: $95,000
Calculating the present value of the operating costs for Design B:
PVA_B = 95,000 × [(1 - (1 + 0.10)^-20) / 0.10] = 95,000 × 9.645 = $916,275
So, the total cost for Design B:
Total Cost_B = Initial Investment + Present Value Operating Costs
Total Cost_B = $400,000 + $916,275 = $1,316,275
Now, calculating the total revenue over 20 years:
Total Revenue_B = Annual Revenue × Years = $100,000 × 20 = $2,000,000
The benefit-cost ratio for Design B:
BCR_B = Total Revenue / Total Costs = $2,000,000 / $1,316,275 = 1.52
Decision: Since Design A has a higher BCR (1.63) than Design B (1.52), Design A is the preferred choice.
2. Capital Expenditures
In the given expenditures list, the items that qualify as capital expenditures (which must be depreciated) include:
- a) Purchased a fax machine for $10,000.
- g) Repaved a parking lot for $20,000.
- h) Installed a conveyor belt system to automate some part of a production process for $50,000.
- i) Purchased land to build a new facility for $350,000.
Items such as painting the warehouse, leasing a dump truck, and purchasing spare parts are operational expenditures or maintenance costs and do not qualify for capitalization.
3. Depreciation Calculation
Now, let's compute the annual depreciation allowances for the asset with cost $150,000, useful life of 5 years, and salvage value of $16,000 using both stooged!
a) Straight-line Method
The straight-line depreciation method is calculated as:
Annual Depreciation = (Cost - Salvage Value) / Useful Life
Annual Depreciation = ($150,000 - $16,000) / 5 = $26,800
b) Double-Declining-Balance Method
For the double-declining-balance method, the formula used is:
Annual Depreciation = 2 × (1 / Useful Life) × Book Value at Beginning of Year
In Year 1, the book value is $150,000:
Depreciation Year 1 = 2 × (1/5) × $150,000 = $60,000 (Book Value at Year End = $90,000)
In Year 2, the book value is $90,000:
Depreciation Year 2 = 2 × (1/5) × $90,000 = $36,000 (Book Value at Year End = $54,000)
In Year 3, the book value is $54,000:
Depreciation Year 3 = 2 × (1/5) × $54,000 = $21,600 (Book Value at Year End = $32,400)
In Year 4, the book value is $32,400:
Depreciation Year 4 = 2 × (1/5) × $32,400 = $12,960 (Book Value at Year End = $19,440)
In Year 5, since we want to avoid going below salvage value, the final depreciation will only be enough to reach salvage value:
Depreciation Year 5 = Book Value Year Start - Salvage Value = $19,440 - $16,000 = $3,440 (Book Value at Year End = $16,000)
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