Math Problem Statement
Bottoms Up Diaper Service is considering the purchase of a new industrial washer. It can purchase the washer for $6,900 and sell its old washer for $2,100. The new washer will last for 6 years and save $1,900 a year in expenses. The opportunity cost of capital is 18%, and the firm’s tax rate is 21%.
If the firm uses straight-line depreciation over a 6-year life, what are the cash flows of the project in years 0 to 6? The new washer will have zero salvage value after 6 years, and the old washer is fully depreciated.
Note: Negative amounts should be indicated by a minus sign.
Solution
To calculate the cash flows for the project over the 6-year life of the washer, we need to analyze the initial investment, annual savings, depreciation, and tax savings. Here’s a step-by-step breakdown of each component:
1. Initial Investment (Year 0)
- Cost of New Washer: $6,900
- Sale of Old Washer: $2,100
- Net Initial Investment:
So, the cash flow for Year 0 is -$4,800.
2. Annual Savings
The new washer saves the company $1,900 per year in expenses.
3. Depreciation
Since the new washer is depreciated using straight-line depreciation over 6 years:
4. Tax Savings from Depreciation
The tax savings from depreciation each year is calculated as:
5. Total Annual Cash Flow (Years 1 to 6)
Each year, the total cash flow is calculated as follows: Substituting the values:
Summary of Cash Flows
The cash flows over the 6-year period are as follows:
- Year 0: -$4,800 (initial investment)
- Year 1 to Year 6: $2,141.5 each year
Final Cash Flow Table
Year | Cash Flow ($) |
---|---|
0 | -4,800 |
1 | 2,141.5 |
2 | 2,141.5 |
3 | 2,141.5 |
4 | 2,141.5 |
5 | 2,141.5 |
6 | 2,141.5 |
Let me know if you’d like more details on the calculations or have further questions!
Here are some related questions you might find useful to explore:
- How would the cash flows change if the tax rate were different?
- What impact would a residual (salvage) value have on the final year's cash flow?
- How would a different depreciation method, like double-declining balance, affect the annual cash flows?
- What would be the net present value (NPV) of the project with a 10% discount rate instead of 18%?
- How would extending the life of the washer beyond 6 years affect the financial assessment?
Tip: Calculating the tax impact of depreciation helps capture the full tax shield benefit for capital investments.
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Math Problem Analysis
Mathematical Concepts
Finance
Investment Analysis
Depreciation
Cash Flow Analysis
Formulas
Net Initial Investment = Cost of New Washer - Sale of Old Washer
Annual Depreciation = Cost of New Washer / Useful Life
Tax Savings from Depreciation = Annual Depreciation * Tax Rate
Annual Cash Flow = Annual Savings + Tax Savings from Depreciation
Theorems
Time Value of Money
Straight-line Depreciation
Tax Shield from Depreciation
Suitable Grade Level
Grades 11-12 (High School), College Level Finance
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