NPV Total and Differential Analysis of Replacement Decision

Assume Pinstripes Cleaning and Restoration, near Dallas, Texas, must either have a complete overhaul of its current dry-cleaning system or purchase a new one. Its cost of capital is 16%. The following cost projections have been developed:

Old System	New System
Purchase cost (new)	$187,000	$198,000
Remaining book value	37,400	
Overhaul needed	55,000	
Annual cash operating costs	133,870	88,440
Current salvage value	26,400	
Salvage value in 5 years	9,900	22,000

If Pinstripes keeps the old system, it will have to be overhauled immediately. With the overhaul, the old system will have a useful life of five more years.

Required

a. Use the total cost approach to evaluate the alternatives of keeping the old system and purchasing the new system. Indicate which alternative is preferred.

Hint: Use a negative sign to indicate a negative net present value.

Net present value of operating old system: $

To perform a Net Present Value (NPV) analysis, we need to consider all cash flows associated with each alternative, discount them back to present value using the cost of capital (16%), and then compare the NPVs. Here is the detailed step-by-step process:

### Old System

1. **Initial Costs**:
   - Overhaul needed: $55,000

2. **Annual Operating Costs**:
   - Annual cash operating costs: $133,870

3. **Salvage Values**:
   - Current salvage value: $26,400 (if sold now)
   - Salvage value in 5 years: $9,900

4. **Remaining Book Value**: $37,400 (sunk cost, not relevant to NPV)

5. **Calculate Present Value of Cash Flows**:
   - Initial cost: $55,000
   - Annual operating costs (present value of annuity for 5 years at 16%):
     \[
     \text{PV of operating costs} = 133,870 \times \left(\frac{1 - (1 + 0.16)^{-5}}{0.16}\right) = 133,870 \times 3.2743 = 438,241.41
     \]
   - Salvage value in 5 years (present value):
     \[
     \text{PV of salvage value} = 9,900 \times (1 + 0.16)^{-5} = 9,900 \times 0.4761 = 4,715.39
     \]

6. **NPV Calculation**:
   \[
   \text{NPV}_{\text{old}} = -55,000 - 438,241.41 + 4,715.39 = -488,526.02
   \]

### New System

1. **Initial Costs**:
   - Purchase cost: $198,000

2. **Annual Operating Costs**:
   - Annual cash operating costs: $88,440

3. **Salvage Values**:
   - Salvage value in 5 years: $22,000

4. **Calculate Present Value of Cash Flows**:
   - Initial cost: $198,000
   - Annual operating costs (present value of annuity for 5 years at 16%):
     \[
     \text{PV of operating costs} = 88,440 \times \left(\frac{1 - (1 + 0.16)^{-5}}{0.16}\right) = 88,440 \times 3.2743 = 289,517.69
     \]
   - Salvage value in 5 years (present value):
     \[
     \text{PV of salvage value} = 22,000 \times (1 + 0.16)^{-5} = 22,000 \times 0.4761 = 10,474.20
     \]

5. **NPV Calculation**:
   \[
   \text{NPV}_{\text{new}} = -198,000 - 289,517.69 + 10,474.20 = -477,043.49
   \]

### Conclusion

Comparing the NPVs of the two alternatives:
- NPV of keeping the old system: $-488,526.02$
- NPV of purchasing the new system: $-477,043.49$

Since the NPV of purchasing the new system is less negative than the NPV of keeping the old system, the preferred alternative is to **purchase the new system**.

Would you like more details or have any questions?

Here are some questions you might ask:
1. How do you calculate the present value of an annuity?
2. What is the significance of the cost of capital in NPV calculations?
3. How do salvage values impact the NPV analysis?
4. What is the role of sunk costs in NPV calculations?
5. Can we use other methods besides NPV for such decisions?

**Tip:** In NPV calculations, it’s crucial to correctly discount future cash flows to present value using the appropriate discount rate.

Explore the NPV total and differential analysis for the replacement decision faced by Pinstripes Cleaning and Restoration, near Dallas, Texas. Calculate NPV for both keeping the old system and purchasing the new system, considering costs of capital and cash flows. Learn how to use the total cost approach to determine the preferred alternative.

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