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Answer :
To calculate the Net Present Value (NPV) given an Internal Rate of Return (IRR) of 13%, you first need the list of cash flows over the project years and then follow these steps:
1. Understand the Cash Flows: You have a series of cash flows from Year 0 to Year 65. In this case, the cash flows are as follows:
- Year 0: -1,000,000 (initial investment)
- Year 1: 80,000
- Year 2: 30,000
- Year 3: 40,000
- Year 4: 50,000
- Year 65: 60,000
2. Discount Rate: The IRR is 13%, which is used as the discount rate to find the present value of each cash flow.
3. Net Present Value Calculation: NPV is calculated by subtracting the initial investment from the sum of the present values of all future cash flows. For each year, the present value of the cash flow is calculated using the formula:
[tex]\[
\text{Present Value} = \frac{\text{Cash Flow}}{(1 + \text{IRR})^{\text{Year}}}
\][/tex]
4. Calculate the Present Value for Each Year:
- Year 0: Present Value = -1,000,000 (No discount needed since it's the initial investment)
- Year 1: Present Value = [tex]\(\frac{80,000}{(1 + 0.13)^1} = 70,796.46\)[/tex]
- Year 2: Present Value = [tex]\(\frac{30,000}{(1 + 0.13)^2} = 23,452.38\)[/tex]
- Year 3: Present Value = [tex]\(\frac{40,000}{(1 + 0.13)^3} = 28,252.40\)[/tex]
- Year 4: Present Value = [tex]\(\frac{50,000}{(1 + 0.13)^4} = 31,342.28\)[/tex]
- Year 65: Present Value = [tex]\(\frac{60,000}{(1 + 0.13)^{65}} = \text{(a very small number close to zero)}\)[/tex]
5. Sum Up All Present Values and Deduct Initial Investment:
- Total Present Value of Cash Flows = sum of all the calculated present values above.
- NPV = Total Present Value of Cash Flows - Initial Investment
6. Result:
- The calculation for NPV results in approximately -814,755.60.
This negative NPV implies that, with a discount rate of 13%, the project is expected to result in a loss of approximately 814,755.60 in today's terms. Thus, it might not be a financially viable project if IRR remains at 13%.
1. Understand the Cash Flows: You have a series of cash flows from Year 0 to Year 65. In this case, the cash flows are as follows:
- Year 0: -1,000,000 (initial investment)
- Year 1: 80,000
- Year 2: 30,000
- Year 3: 40,000
- Year 4: 50,000
- Year 65: 60,000
2. Discount Rate: The IRR is 13%, which is used as the discount rate to find the present value of each cash flow.
3. Net Present Value Calculation: NPV is calculated by subtracting the initial investment from the sum of the present values of all future cash flows. For each year, the present value of the cash flow is calculated using the formula:
[tex]\[
\text{Present Value} = \frac{\text{Cash Flow}}{(1 + \text{IRR})^{\text{Year}}}
\][/tex]
4. Calculate the Present Value for Each Year:
- Year 0: Present Value = -1,000,000 (No discount needed since it's the initial investment)
- Year 1: Present Value = [tex]\(\frac{80,000}{(1 + 0.13)^1} = 70,796.46\)[/tex]
- Year 2: Present Value = [tex]\(\frac{30,000}{(1 + 0.13)^2} = 23,452.38\)[/tex]
- Year 3: Present Value = [tex]\(\frac{40,000}{(1 + 0.13)^3} = 28,252.40\)[/tex]
- Year 4: Present Value = [tex]\(\frac{50,000}{(1 + 0.13)^4} = 31,342.28\)[/tex]
- Year 65: Present Value = [tex]\(\frac{60,000}{(1 + 0.13)^{65}} = \text{(a very small number close to zero)}\)[/tex]
5. Sum Up All Present Values and Deduct Initial Investment:
- Total Present Value of Cash Flows = sum of all the calculated present values above.
- NPV = Total Present Value of Cash Flows - Initial Investment
6. Result:
- The calculation for NPV results in approximately -814,755.60.
This negative NPV implies that, with a discount rate of 13%, the project is expected to result in a loss of approximately 814,755.60 in today's terms. Thus, it might not be a financially viable project if IRR remains at 13%.
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