Question

A project is projected to cost $2,000,000 to undertake. It will generate positive cash inflows as follows: Year 1 - $750,000; Year 2 – 240,000; Year 3 - $375,000; Year 4 – 950,000; Year 5 – 978,000. What is the project’s discounted payback, given a 7% required rate of return?

Answer 1

To find the discounted payback period, calculate the present value of each year's cash inflow using a 7% discount rate. Sum the present values until they reach the initial investment of $2,000,000. The year when this sum equals or exceeds the investment is the discounted payback period.

Step-by-step explanation:

The question involves finding the discounted payback period for a project with a series of cash inflows over five years and an initial investment of $2,000,000. To do this, we need to calculate the present value of each cash inflow using a discount rate of 7% and then determine how many years it takes for these discounted cash inflows to cover the initial investment. The present value formula is PV=C/(1+i)t, where C is the cash inflow, i is the discount rate, and t is the year of the cash inflow.

The procedure includes discounting each year's cash inflow as follows:

• Year 1 PV = $750,000 / (1 + 0.07)1
• Year 2 PV = $240,000 / (1 + 0.07)2
• Year 3 PV = $375,000 / (1 + 0.07)3
• Year 4 PV = $950,000 / (1 + 0.07)4
• Year 5 PV = $978,000 / (1 + 0.07)5

Once these calculations are made, we add up the present values year by year until the cumulative amount equals or exceeds the initial investment of $2,000,000. The discounted payback period is the year in which this occurs.