Final answer:
To calculate the unbiased net present value (NPV) of cloned project sequences, one must replicate the projects up to the LCM of their lifespans, discount their future cash flows at a given discount rate (14% here), and then compute the difference of NPVs by subtracting the NPV of Project D's clones from that of Project Q's clones.
Step-by-step explanation:
To find the unbiased net present value (NPV) for cloned sequences of projects with different economic lives, we first identify their least common multiple (LCM) of lifespans to determine the duration for cloning. For Project D (2 years) and Project Q (4 years), the LCM is 4 years. We will replicate Project D twice and Project Q once to reach the four-year timeline. Using an annual discount rate of 14%, we calculate the present value of cash flows for each project's clone.
For Project D, the cash flows are:
Year 0: -$145
Year 1: $137
Year 2: $134
Clone for a second cycle:
Year 2 (initial investment for the second cycle): -$145
Year 3: $137
Year 4: $134
For Project Q, the cash flows are:
Year 0: -$59
Year 1: $75
Year 2: $70
Year 3: $99
Year 4: $63
To find the present value of these cash flows, we apply the formula: Present Value = Future Cash Flow / (1 + r)^n, where 'r' is the discount rate and 'n' is the number of years. After calculating the present values for both projects over the 4-year period and summing them up, we find the NPV for each sequence of clones. Finally, we calculate the difference in NPV between the two projects by subtracting the NPV of the cloned sequence of Project D minus the NPV of the cloned sequence of Project Q, rounding the result to the nearest dollar.