To analyze the two proposed capital investments, we need to calculate the payback period and the Net Present Value (NPV) for each project. Since the expected net cash flows weren't provided in your question, we'll work through the calculations step by step and show the formulas used, assuming you replace the placeholder data with actual cash flow data.
1. Payback Period Calculation
The Payback Period is calculated as the time it takes for the cumulative cash flows from an investment to equal its initial cost.
Formula: \[ \text{Payback Period} = \text{Year before full recovery} + \left( \frac{\text{Unrecovered cost at the beginning of the year}}{\text{Cash flow during the year}} \right) \]
Example for Payback Period Calculation:
Assume the following expected cash flows for Project A and Project B:
- Project A Cash Flows: Year 1: $4,000; Year 2: $4,000; Year 3: $3,000
- Project B Cash Flows: Year 1: $5,000; Year 2: $5,000; Year 3: $2,000
For Project A:
- Year 1: Cumulative cash flow = $4,000
- Year 2: Cumulative cash flow = $8,000
- Year 3: Cumulative cash flow = $11,000
The payback occurs in Year 3. Therefore: \[ \text{Payback Period (A)} = 2 + \left( \frac{10,000 - 8,000}{3,000} \right) = 2 + \frac{2,000}{3,000} \approx 2.67 \text{ years} \]
For Project B:
- Year 1: Cumulative cash flow = $5,000
- Year 2: Cumulative cash flow = $10,000
The payback occurs in Year 2. Therefore: \[ \text{Payback Period (B)} = 2 \text{ years} \]
2. NPV Calculation
The NPV is calculated using the formula: \[ \text{NPV} = \sum \left( \frac{C_t}{(1 + r)^t} \right) - C_0 \] Where:
- \( C_t \) = Cash inflow during the period
- \( r \) = Discount rate (12%)
- \( t \) = Period
- \( C_0 \) = Initial investment
NPV Calculation Example:
For Project A: \[ \text{NPV (A)} = \frac{4,000}{(1 + 0.12)^1} + \frac{4,000}{(1 + 0.12)^2} + \frac{3,000}{(1 + 0.12)^3} - 10,000 \]
Calculating each term:
- Year 1: \( \frac{4,000}{1.12} \approx 3,571.43 \)
- Year 2: \( \frac{4,000}{(1.12)^2} \approx 3,196.63 \)
- Year 3: \( \frac{3,000}{(1.12)^3} \approx 2,680.29 \)
Total NPV: \[ \text{NPV (A)} = 3,571.43 + 3,196.63 + 2,680.29 - 10,000 \approx -1,551.65 \]
For Project B: \[ \text{NPV (B)} = \frac{5,000}{(1 + 0.12)^1} + \frac{5,000}{(1 + 0.12)^2} + \frac{2,000}{(1 + 0.12)^3} - 10,000 \]
Calculating each term:
- Year 1: \( \frac{5,000}{1.12} \approx 4,464.29 \)
- Year 2: \( \frac{5,000}{(1.12)^2} \approx 3,978.57 \)
- Year 3: \( \frac{2,000}{(1.12)^3} \approx 1,782.86 \)
Total NPV: \[ \text{NPV (B)} = 4,464.29 + 3,978.57 + 1,782.86 - 10,000 \approx 225.72 \]
Final Decisions
If Projects are Independent:
Both projects can be accepted if they provide a positive NPV.
- Accept Project B because its NPV is positive.
- Reject Project A because its NPV is negative.
If Projects are Mutually Exclusive:
You would choose the project with the highest NPV.
- Choose Project B based on the calculated NPVs.
Conclusion:
- Independent: Accept Project B.
- Mutually Exclusive: Accept Project B.
Note: Replace the cash flows in the above calculations with the actual ones you have to arrive at the final results.