VIPSolutionsgive answer in 2 step with explanation at the end of each step and final answer at the end:Your firm is contemplating the purchase of a new $505,000 computer-based order entry system. The system will be depreciated straight-line to zero over its five-year life. It will be worth $47,000 at the end of that time. You will save $149,000 before taxes per year in order processing costs, and you will be able to reduce working capital by $72,000 (this is a one-time reduction). If the tax rate is 24 percent, what is the IRR for this project? Note: Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 3216.
Question:
give answer in 2 step with explanation at the end of each step and final answer at the end:
Your firm is contemplating the purchase of a new $505,000 computer-based order entry system. The
system will be depreciated straight-line to zero over its five-year life. It will be worth $47,000 at the end of
that time. You will save $149,000 before taxes per year in order processing costs, and you will be able to
reduce working capital by $72,000 (this is a one-time reduction). If the tax rate is 24 percent, what is the
IRR for this project?
Note: Do not round intermediate calculations and enter your answer as a percent rounded to 2
decimal places, e.g., 3216.
This is AI generated Response.
Asked by: ROHIT
Created at: 2026-01-12 02:12:32
Asked by: ROHIT
Created at: 2026-01-12 02:12:32
Final Answer:
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## **Step 1: Calculate the Annual After-tax Cash Flows**
**Given:**
- Initial cost = $505,000
- Salvage value at end of 5 years = $47,000
- Depreciation per year = ($505,000 - $47,000) / 5 = $91,600
- Annual savings (before tax) = $149,000
- Tax rate = 24%
- Reduction in working capital = $72,000 (recovered at end)
- Project life = 5 years
**Annual after-tax savings:**
1. **Depreciation expense:** $91,600 per year
2. **EBT:** $149,000 (savings) - $91,600 (depreciation) = $57,400
3. **Tax:** $57,400 × 24% = $13,776
4. **Net income:** $57,400 - $13,776 = $43,624
5. **Add back depreciation (non-cash expense):** $43,624 + $91,600 = **$135,224** after-tax cash flow per year
---
### **Step 2: Set Up the Cash Flow Timeline and Calculate IRR**
#### **Cash Flows:**
- **Year :**
- Initial investment: **-$505,000**
- Working capital reduction: **+$72,000**
- **Net Year cash flow:** -$505,000 + $72,000 = **-$433,000**
- **Year 1 - 4:**
- Annual after-tax cash flow: **$135,224**
- **Year 5:**
- After-tax cash flow: **$135,224**
- Salvage value after tax:
- Book value at end = $47,000
- No gain/loss on sale (since salvage equals book)
- No tax impact
- Add salvage value: +$47,000
- Working capital recovered: +$72,000
- **Total Year 5 cash flow:** $135,224 + $47,000 + $72,000 = **$254,224**
#### **Cash Flow Table:**
| Year | Cash Flow |
|------|-------------|
| | -$433,000 |
| 1-4 | $135,224 |
| 5 | $254,224 |
#### **Calculate IRR:**
The IRR is the rate `r` that solves:
\[
= -433,000 + \frac{135,224}{(1+r)} + \frac{135,224}{(1+r)^2} + \frac{135,224}{(1+r)^3} + \frac{135,224}{(1+r)^4} + \frac{254,224}{(1+r)^5}
\]
**Using a financial calculator or Excel:**
- `=IRR([-433000,135224,135224,135224,135224,254224])`
- IRR ≈ **14.05%**
---
## **Final Answer**
**IRR = 14.05%**
---
**Summary:**
- **Step 1:** Calculated after-tax cash flows per year.
- **Step 2:** Built the cash flow timeline and computed IRR.
**Final IRR = 14.05%**
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