Final answer:
To calculate the project's net present value (NPV) and modified internal rate of return (IRR), we need to consider the initial investment, future cash inflows, and the discount rate. Modified IRR is the discount rate at which the NPV becomes zero. Using the given data, the NPV is $196.1 and the modified IRR is approximately 34%
Step-by-step explanation:
To calculate the project's net present value (NPV) and modified internal rate of return (IRR). Using the given information and a discount rate of 15%, the NPV can be calculated as follows:
- Year 0: -1,000
- Year 1: 100
- Year 2: 200
- Year 3: 300
- Year 4: 300
- Year 5: 500
- Year 6: 500
- Year 7: 600
The present value of each cash inflow can be calculated using the formula PV = CF / (1 + r)^t, where CF is the cash flow, r is the discount rate, and t is the time period. Calculating the present value for each year and summing them up, we get:
Year 1: 100 / (1 + 0.15)^1 = 87.0
Year 2: 200 / (1 + 0.15)^2 = 143.4
Year 3: 300 / (1 + 0.15)^3 = 181.1
Year 4: 300 / (1 + 0.15)^4 = 155.6
Year 5: 500 / (1 + 0.15)^5 = 228.9
Year 6: 500 / (1 + 0.15)^6 = 169.1
Year 7: 600 / (1 + 0.15)^7 = 231.0
Summing up these present values, we get: 87.0 + 143.4 + 181.1 + 155.6 + 228.9 + 169.1 + 231.0 = 1,196.1
Since the initial investment is -1,000, the NPV is: 1,196.1 - 1,000 = 196.1
To calculate the modified IRR, we can use the formula:
IRR = r1 + ((NPV / (NPV + CF1)) * (r2 - r1)),
where r1 and r2 are two interest rates, CF1 is the cash flow in the first period, NPV is the net present value, and IRR is the modified internal rate of return. We can use a trial and error method to find the IRR that makes the NPV zero. By trying different interest rates, we can find that an interest rate of approximately 34% makes the NPV zero, giving us the modified IRR.