## Consider An Investment That Cost 400 And Pays 100 Per Year Forever.

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Calculating Discounted Payback

Consider an investment that costs $400 and pays $100 per year forever. We use a 20 percent discount rate on this type of investment. What is the ordinary payback? What is the discounted payback? What is the NPV?

The NPV and ordinary payback are easy to calculate in this case because the investment is a perpetuity. The present value of the cash flows is $100/.2 = $500, so the NPV is $500 -400 = $100. The ordinary payback is obviously four years.

To get the discounted payback, we need to find the number of years such that a $100 annuity has a present value of $400 at 20 percent. In other words, the present value annuity factor is $400/100 = 4, and the interest rate is 20 percent per period; so what's the number of periods? If we solve for the number of periods, we find that the answer is a little less than nine years, so this is the discounted payback.

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