Final answer:
The payback period is the amount of time it takes to recoup the initial cost of a project from its cash inflows, and the discounted payback period is a similar measure that accounts for the time value of money by discounting the cash inflows at a given rate before calculating the period.
Step-by-step explanation:
The student's question asks about the payback period and discounted payback period for a project with an initial cost and subsequent cash inflows over four years, considering also a given discount rate. To calculate the payback period, one must sum the cash inflows until the initial cost is recuperated. For the discounted payback period, each inflow must be discounted back to its present value before summing up to reach the initial cost.
Using the given example, since the cash inflows are $500, $900, $1,200, and $1,800, the sum at the end of the fourth year is $4,400, which exceeds the initial cost of $2,800, indicating the payback period is less than four years. However, to find the exact payback period, one must calculate the cumulative cash flow for each year. It becomes clear that the initial cost is covered between the third and the fourth year.
To calculate the discounted payback period, a 10% discount rate is applied to each cash inflow. This involves discounting each future cash inflow to its present value and then summing those values until they exceed the initial cost, thereby determining the time at which the initial investment is paid back.