An investment project has annual cash inflows of $4,100, $5,000, $6,200, and $5,400, and a discount rate of 14 percent.What is the discounted payback period for these cash flows if the initial cost is $6,800?What is the discounted payback period for these cash flows if the initial cost is $8,900?What is the discounted payback period for these cash flows if the initial cost is $11,900?

To calculate the discounted payback period for the given cash flows, we need to determine the time it takes for the discounted cash inflows to equal or exceed the initial cost.

Step 1: Calculate the discounted cash inflows for each year using the discount rate of 14 percent.

For the first year: Discounted cash inflow = $4,100 / (1 + 0.14)^1 =$4,100 / 1.14 = $3,596.49

For the second year: Discounted cash inflow = $5,000 / (1 + 0.14)^2 =$5,000 / 1.2996 = $3,847.15

For the third year: Discounted cash inflow = $6,200 / (1 + 0.14)^3 =$6,200 / 1.4931 = $4,148.58

For the fourth year: Discounted cash inflow = $5,400 / (1 + 0.14)^4 =$5,400 / 1.6984 = $3,176.47

Step 2: Calculate the cumulative discounted cash inflows for each year.

For the first year: Cumulative discounted cash inflow = $3,596.49

For the second year: Cumulative discounted cash inflow = $3,596.49 +$3,847.15 = $7,443.64

For the third year: Cumulative discounted cash inflow = $7,443.64 +$4,148.58 = $11,592.22

For the fourth year: Cumulative discounted cash inflow = $11,592.22 +$3,176.47 = $14,768.69

Step 3: Determine the discounted payback period.

For an initial cost of $6,800: The discounted payback period is the time it takes for the cumulative discounted cash inflows to equal or exceed the initial cost. In this case, the discounted payback period is 2 years since the cumulative discounted cash inflows at the end of the second year ($7,443.64) exceed the initial cost of $6,800.

For an initial cost of $8,900: The discounted payback period is still 2 years since the cumulative discounted cash inflows at the end of the second year ($7,443.64) do not exceed the initial cost of $8,900.

For an initial cost of $11,900: The discounted payback period is 3 years since the cumulative discounted cash inflows at the end of the third year ($11,592.22) exceed the initial cost of $11,900.