To evaluate the viability of the given projects, we will calculate the Net Present Value (NPV) for each scenario. NPV is found by subtracting the present value of cash outflows (costs) from the present value of cash inflows (revenues). If NPV is positive, the project is considered viable.
1. NPV Calculation for Project Requiring $100,000 Now for $200,000 in 6 Years
Step 1: Identify Cash Flows
- Initial Investment (Year 0): -$100,000
- Cash Inflow (Year 6): +$200,000
Step 2: Calculate Present Value (PV) of Cash Inflow \[ PV = \frac{FV}{(1 + r)^n} \]
Where:
- FV = Future value ($200,000)
- r = Discount rate (10% or 0.10)
- n = Number of years (6)
\[ PV = \frac{200,000}{(1 + 0.10)^6} = \frac{200,000}{(1.771561)} \approx 113,300.65 \]
Step 3: Calculate NPV \[ NPV = PV - Initial\ Investment \] \[ NPV = 113,300.65 - 100,000 = 13,300.65 \]
Conclusion: Since NPV > 0 ($13,300.65), the project is viable.
2. NPV Calculation for IT Project
Step 1: Identify Cash Flows
- Year 0: -$100,000 (initial cost)
- Year 1 to 4: -$20,000 (maintenance cost each year)
- Year 1 to 4: +$50,000 (savings/revenue each year)
Net Cash Flows for Years 1-4: \[ \text{Net Cash Flow} = 50,000 - 20,000 = 30,000 \]
Step 2: Calculate PV of Cash Flows from Year 1 to Year 4 \[ PV = \sum_{t=1}^{4} \frac{C}{(1 + r)^t} \] Where \( C = 30,000 \)
For each year:
- Year 1: \( \frac{30,000}{(1.12)^1} \approx 26,785.71 \)
- Year 2: \( \frac{30,000}{(1.12)^2} \approx 23,905.68 \)
- Year 3: \( \frac{30,000}{(1.12)^3} \approx 21,190.87 \)
- Year 4: \( \frac{30,000}{(1.12)^4} \approx 18,657.94 \)
Now sum these present values: \[ PV_{\text{total}} = 26,785.71 + 23,905.68 + 21,190.87 + 18,657.94 \approx 90,530.20 \]
Step 3: Subtract Initial Investment to get NPV \[ NPV = PV_{\text{total}} - Initial\ Investment \] \[ NPV = 90,530.20 - 100,000 = -9,469.80 \]
Conclusion: Since NPV < 0 (-$9,469.80), the project should not be pursued.
3. NPV Calculation for Project Requiring $210,000 Now for $380,000 in 4 Years at 12%
Step 1: Identify Cash Flows
- Initial Investment (Year 0): -$210,000
- Cash Inflow (Year 4): +$380,000
Step 2: Calculate PV of Cash Inflow \[ PV = \frac{380,000}{(1 + 0.12)^4} = \frac{380,000}{(1.5748)} \approx 241,032.27 \]
Step 3: Calculate NPV \[ NPV = PV - Initial\ Investment \] \[ NPV = 241,032.27 - 210,000 = 31,032.27 \]
Conclusion: Since NPV > 0 ($31,032.27), the project is viable.
4. IRR Calculation for Project Investing $100,000 for $200,000 at Year 6
For calculating IRR, we set NPV = 0 and solve for r:
\[ 0 = -100,000 + \frac{200,000}{(1 + r)^6} \] Rearranging gives: \[ 100,000 = \frac{200,000}{(1 + r)^6} \] \[ (1 + r)^6 = 2 \] Taking the sixth root of both sides: \[ 1 + r = 2^{1/6} \] \[ r \approx 2^{1/6} - 1 \approx 0.1225 \text{ or } 12.25% \]
Conclusion: The IRR of the project is approximately 12.25%.
5. Evaluating a Proposal with Discounted Cash Flows at 12%
Without a specific cash flow provided in your question, the methodology would be as follows:
- Identify cash flows: Initial investment and subsequent inflows/outflows.
- Calculate the PV of future cash flows using: \[ PV = \sum_{t=1}^{n} \frac{C_t}{(1 + 0.12)^t} \] Where \(C_t\) represents cash inflows or outflows each year.
- Subtract the initial investment from the total PV obtained in step 2 to determine NPV.
- If NPV is greater than 0, the proposal is considered worth pursuing.
Without more detailed cash flow data, we cannot perform this last part.
If you would like to specify the cash flows for the proposal in question 5, I can further assist you in calculating the NPV for that scenario.