Final answer:
The discounted payback period for Shannon Co.'s project occurs between Year 2 and Year 3, with the initial investment of $950 being recovered after discounting the cash flows at a 10% cost of capital.
Step-by-step explanation:
The question asks to calculate the discounted payback period for a project from Shannon Co.
This period is the time it takes for the cumulative discounted cash flows to equal the initial investment.
The calculation involves discounting each anticipated cash flow by the project's cost of capital before summing them up.
Assuming the cost of capital (r) is 10%, let's calculate the discounted cash flows for each year and determine the payback period
Year 1 (CF1): 525 / (1 + r)^1 = 525 / 1.1
= 477.27
Year 2 (CF2): 485 / (1 + r)^2 = 485 / 1.21
= 400.83
Year 3 (CF3): 445 / (1 + r)^3 = 445 / 1.331
= 334.3
Year 4 (CF4): 405 / (1 + r)^4 = 405 / 1.4641
= 276.68
Now, we sum the discounted cash flow from Year 1 to Year 4 until the initial investment of 950 is covered:
-950 + 477.27 = -472.73 (after Year 1)
-472.73 + 400.83 = -71.90 (after Year 2)
-71.90 + 334.36 = 262.46 (after Year 3 - project recovers cost here)
The project breaks even between Year 2 and Year 3 once the accumulated discounted cash flows cover the initial investment, which means the discounted payback period is somewhere between 2 and 3 years.