Question

Find the Discounted Payback period for the following project. The discount rate is 6% Project X Initial Outlay $8,322 Year 1 $3,526 Year 2 $3,606 Year 3 $5,589 Year 4 $6,102 Round the answer to two decimal places.

Answer 1

The Discounted Payback Period is calculated by discounting the future cash inflows at a given rate and cumulating them until they equal the initial investment. This metric helps determine how long an investment will take to break even in present value terms.

Step-by-step explanation:

The student is asking to calculate the Discounted Payback Period for a project with an initial outlay and cash inflows over four years, using a discount rate of 6%. The cash flows must first be discounted to their present values and then cumulatively added until they recover the initial investment. The discounted payback period is the time it takes for these discounted cash flows to cover the initial investment.

First, we calculate the present value (PV) for each cash inflow using the formula PV = Cash Inflow / (1 + discount rate)^year. Then we start adding the discounted cash inflows to the initial outlay until the total equals zero. The exact point at which the cumulative discounted cash flows equal the initial outlay will give us the discounted payback period. If this occurs between two periods, we can interpolate to find the precise time.

For this particular problem, the calculation would require detailed computations for each of the four years. Given that these have not been provided in the response, all we can do is outline the steps necessary to reach the discounted payback period.