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.**

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**: 
  \[
  \text{Net Initial Investment} = \text{Cost of New Washer} - \text{Sale of Old Washer} = 6,900 - 2,100 = 4,800
  \]

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:
\[
\text{Annual Depreciation} = \frac{\text{Cost of New Washer}}{\text{Useful Life}} = \frac{6,900}{6} = 1,150
\]

### 4. Tax Savings from Depreciation
The tax savings from depreciation each year is calculated as:
\[
\text{Tax Savings from Depreciation} = \text{Annual Depreciation} \times \text{Tax Rate} = 1,150 \times 0.21 = 241.5
\]

### 5. Total Annual Cash Flow (Years 1 to 6)
Each year, the total cash flow is calculated as follows:
\[
\text{Annual Cash Flow} = \text{Annual Savings} + \text{Tax Savings from Depreciation}
\]
Substituting the values:
\[
\text{Annual Cash Flow} = 1,900 + 241.5 = 2,141.5
\]

### 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:

1. How would the cash flows change if the tax rate were different?
2. What impact would a residual (salvage) value have on the final year's cash flow?
3. How would a different depreciation method, like double-declining balance, affect the annual cash flows?
4. What would be the net present value (NPV) of the project with a 10% discount rate instead of 18%?
5. 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.

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.

Explore a detailed solution on how to calculate the cash flows for Bottoms Up Diaper Service's industrial washer investment, including depreciation, tax savings, and cash flow analysis over a 6-year period. The problem covers key financial concepts such as opportunity cost of capital, straight-line depreciation, and tax shields. Ideal for students and professionals in finance.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation