With respect to the Payback Rule, the following statements are TRUE:

Question

BlackTom AI · Accepted Answer

The payback rule measures the time required to recover the original investment using undiscounted (nominal) cash flows, so it does not account for the time value of money.

1) Relevant concepts:
- Payback period: the length of time until cumulative cash inflows equal the initial outlay, computed with raw cash flows (no discounting).
- Time value of money (TVM): a dollar today is worth more than a dollar in the future; correct valuation discounts future cash flows to present value.
- Strengths/weaknesses: payback is simple and indicates liquidity/risk exposure, but it ignores TVM and all cash flows after the payback cutoff.

2) Step-by-step reasoning and numeric example:
Suppose initial investment = $1,000 and annual cash inflows = $400 at year ends.
- Year 1 cumulative = $400
- Year 2 cumulative = $400 + $400 = $800
- Year 3 cumulative = $800 + $400 = $1,200 → payback occurs during year 3.
Exact (undiscounted) payback = 2 full years + (remaining $200 / $400) = 2.5 years.

Now include TVM with a 10% discount rate to show the difference:
- PV Year 1 = 400 / 1.10 = 363.64
- PV Year 2 = 400 / 1.10^2 = 330.58 → cumulative PV after 2 years = 694.22
- PV Year 3 = 400 / 1.10^3 = 300.53 → cumulative PV after 3 years = 994.75 (still below $1,000)
- PV Year 4 = 400 / 1.10^4 = 272.30 → cumulative PV after 4 years = 1,267.05
Discounted payback therefore occurs during year 4 (approx 3.45 years), which differs materially from the undiscounted 2.5 years. This demonstrates payback’s failure to incorporate TVM.

3) Why the correct answer is correct:
Because the payback formula sums nominal cash inflows until the initial outlay is recovered and applies no discounting, it explicitly ignores the time value of money.

4) Why common alternative statements are incorrect (briefly):
- “It accounts for TVM” — false, as shown above.
- “It uses all cash flows” — false; cash flows after the payback cutoff are ignored.
- “It measures profitability” — misleading; it gauges liquidity/risk, not long-term profitability.

Conclusion: The correct statement is that the payback rule ignores the time value of money, which matches the provided answer.

With respect to the Payback Rule, the following statements are TRUE:Single choice

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