So just a refresher on Discounted Payback Period, it is the time it will take to recover an initial investment for a project given its discounted cash flows. That is, we want Net Present Value greater than 0: the income of the project will be discounted to assess the loss in value due to time (inflation or opportunity cost) to find how long it would take to recover the initially money invested. In the following situation the cash flows are as presented.

Year

Cash Flows ($)

-2000

+1000

+2000

The first step is to calculate the discounted cash flow. Assuming the discount rate is 10%, we would apply the following formula to each cash flow:

PV = CF / (1 + r)t

where CF is Cash Flow, r = 10% and t = year

Year

Cash Flows ($)

Discounted Cash Flow

At 10% ($)

-2000

+1000

909

+1000

827

+2000

1503

The next step is to compute the cumulative discounted cash flow, by summing the discounted cash flow for each year.

Year

Cash Flows ($)

Discounted Cash Flow

At 10% ($)

Cumulative Discounted Cash Flows ($)

-2000

+1000

909

-1901

+1000

827

-264

+2000

1503

+1239

We see that between years 2 and 3 we will recover our initial investment. To calculate specifically when we could see how long it took to recover the 264 remaining by end of year 2 as followed:

264/1503 = 0.1756 years

Thus it will take a total of 2.1756 years to recover the initial investment. If the discounted payback period is two years, this project would not be accepted.

However if the cut off is any time greater than 2.1756 years the project would be accepted.

And that is how you calculate discounted payback period! Apologies if there is any miscalculations, but I double checked it, should be good J.

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