Calculate the net present value of the machine replacement project and determine whether Company XYZ should replace its current machine, given that its corporate tax rate is 30% an... Calculate the net present value of the machine replacement project and determine whether Company XYZ should replace its current machine, given that its corporate tax rate is 30% and its required rate of return for the project is 10%. Read more

Steps to Solve

1. Calculate Current Machine's Cash Flows

Determine the annual cash inflow for the current machine.

• Revenue: Production = 10,000 units/year at $30/unit $$ \text{Revenue} = 10,000 \times 30 = 300,000 $$

• Variable Costs: Variable cost = $10/unit $$ \text{Variable Cost} = 10,000 \times 10 = 100,000 $$

• Fixed Costs: $14,000/year

• Net Cash Flow before Tax: $$ \text{Net Cash Flow} = \text{Revenue} - \text{Variable Cost} - \text{Fixed Cost} $$ $$ \text{Net Cash Flow} = 300,000 - 100,000 - 14,000 = 186,000 $$

• Tax: Tax = 30% $$ \text{Tax} = 186,000 \times 0.3 = 55,800 $$

• Net Cash Flow after Tax: $$ \text{Net Cash Flow (Current)} = 186,000 - 55,800 = 130,200 $$

2. Calculate New Machine's Cash Flows

Determine the annual cash inflow for the new machine.

• Revenue: Production = 15,000 units/year at $30/unit $$ \text{Revenue} = 15,000 \times 30 = 450,000 $$

• Variable Costs: Variable cost = $8/unit $$ \text{Variable Cost} = 15,000 \times 8 = 120,000 $$

• Fixed Costs: $15,000/year

• Net Cash Flow before Tax: $$ \text{Net Cash Flow} = 450,000 - 120,000 - 15,000 = 315,000 $$

• Tax: $$ \text{Tax} = 315,000 \times 0.3 = 94,500 $$

• Net Cash Flow after Tax: $$ \text{Net Cash Flow (New)} = 315,000 - 94,500 = 220,500 $$

3. Calculate Depreciation of New Machine

Determine annual depreciation using straight-line depreciation.

• Cost of New Machine: $500,000

• Useful Life: 5 years

• Salvage Value: $0

• Annual Depreciation: $$ \text{Depreciation} = \frac{\text{Cost - Salvage Value}}{\text{Life}} = \frac{500,000 - 0}{5} = 100,000 $$

4. Determine Cash Flows Including Depreciation Effect

Since depreciation is a non-cash charge, add it back to get the cash flow impact on the new machine:

• Adjusted Cash Flow (New): $$ \text{Total Cash Flow} = 220,500 + 100,000 = 320,500 $$

5. Calculate NPV of Machine Replacement

Now calculate the NPV for the replacement project over 5 years using the discount rate of 10%.

• Initial Investment: $500,000 - $410,000 (salvage value of current machine) = $90,000

• Cash Flows: $320,500/year for 5 years

Using the NPV formula: $$ NPV = \sum_{t=1}^{n} \frac{CF_t}{(1 + r)^t} - \text{Initial investment} $$ where ( CF_t ) is cash flow at time ( t ), ( r ) is discount rate.

• Calculate NPV: $$ NPV = \frac{320,500}{1.1^1} + \frac{320,500}{1.1^2} + \frac{320,500}{1.1^3} + \frac{320,500}{1.1^4} + \frac{320,500}{1.1^5} - 90,000 $$

Calculate each cash flow:

• Year 1: $$ \frac{320,500}{1.1^1} \approx 291,363.64 $$
• Year 2: $$ \frac{320,500}{1.1^2} \approx 264,875.13 $$
• Year 3: $$ \frac{320,500}{1.1^3} \approx 240,795.57 $$
• Year 4: $$ \frac{320,500}{1.1^4} \approx 218,036.88 $$
• Year 5: $$ \frac{320,500}{1.1^5} \approx 197,925.35 $$

Total Cash Flows (years 1 to 5): $$ Total \approx 291,363.64 + 264,875.13 + 240,795.57 + 218,036.88 + 197,925.35 = 1,214,396.57 $$

Final NPV Calculation: $$ NPV = 1,214,396.57 - 90,000 \approx 1,124,396.57 $$

6. Conclusion

Interpret the NPV result to decide whether to replace the machine. Since NPV > 0, replacement is justified.