Discounted Payback

Discounted payback: when does the project pay itself off in present value?

The discounted payback period asks something tougher than the simple payback does. How many periods before the cumulative discounted cash flows finally cover what you put in up front? You bring each future flow CF_t back to present value at the discount rate i with CF_t / (1 + i)^t, then keep adding them up until the running NPV hits zero. Every flow gets shrunk by the discount factor, so discounted payback always comes out longer than the simple version, and it never arrives at all if the project's NPV is negative.

Here's a quick run-through. You invest R$ 1,000 and get back 300, 400, 400, 300 over four periods at 10% per period. Discount those and the flows become 272.73, 330.58, 300.53, 204.90, which accumulate to 272.73, 603.31, 903.84, 1,108.74. Simple payback lands at the end of period 3, where the cumulative 1,400 already clears 1,000. Discounted payback, though, only closes somewhere in period 4, around 3.47 periods, since the time value of money drags it out. For capex calls, that's the more conservative read, and the more honest one.

Where discounted payback is used

It shows up in careful project work next to NPV and IRR, in long-term financing reviews like BNDES PEAC, and in capex committees that won't approve anything past a set recovery horizon. It also helps when you're weighing alternative projects that carry different risk profiles, or when you want a backstop for the simple payback because the discount rate is steep or the project runs long.

FAQ

Why is it always greater than the simple payback? Dividing each future flow by (1 + i)^t shrinks it, so the cumulative sum climbs more slowly and needs more time to catch up with the initial investment.

What if it never pays back? That tells you the project's NPV is negative at that discount rate. The investment isn't recovered in present value, so as a rule you'd turn it down.

Which discount rate to use? For corporate projects, go with the cost of capital (WACC). For personal decisions, use your opportunity rate. Raise the rate and the test gets harder to pass.