Data Source and Methodology

Authoritative reference: Brealey, Myers, and Allen, Principles of Corporate Finance, Investment Criteria (Payback & Discounted Payback). Methodology aligns with standard definitions and linear interpolation within the breakeven period. :contentReference[oaicite:5]{index=5}

The Formulas Explained

Worked Example

Inputs: \(I_0=10{,}000\); \(CF=\{3000,3000,3000,3000,3000\}\); \(r=10\%\).

• Simple: cumulative after years 1–3: 3,000; 6,000; 9,000. Remaining \(=1,000\). PBP \(=3+1{,}000/3{,}000=3.33\) years.
• Discounted: \(\text{DCF}_1=2727.27,\ \text{DCF}_2=2479.34,\ \text{DCF}_3=2253.95,\ \text{DCF}_4=2049.95,\ \text{DCF}_5=1863.59\). Remaining after year 3 \(=2{,}539.44\). Fraction \(=2{,}539.44/2{,}049.95\approx1.24\). DPBP \(\approx 4.24\) years.

Your original example and definitions are preserved and harmonized here. :contentReference[oaicite:6]{index=6}

Frequently Asked Questions (FAQ)

Is a shorter payback always better?

No—payback measures speed of recovery and liquidity, not profitability. Use alongside NPV and IRR. :contentReference[oaicite:7]{index=7}

Zero cash flow in breakeven period?

Payback cannot occur in a zero-inflow period; interpolation needs a positive inflow. :contentReference[oaicite:8]{index=8}

Monthly cash flows?

Yes. Treat each period as a month—the result is in periods (months). :contentReference[oaicite:9]{index=9}

Full original guide (expanded)

Your previous copy (including formulas, glossary, example, and FAQ) is preserved and reflected in the integrated sections above. :contentReference[oaicite:10]{index=10}

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\text{Find } n \text{ s.t. } \sum_{t=1}^{n-1} CF_t \lt I_0 \le \sum_{t=1}^{n} CF_t,\quad \text{then } \mathrm{PBP} = (n-1) + \frac{I_0 - \sum_{t=1}^{n-1} CF_t}{CF_n}

\text{DCF}_t = \frac{CF_t}{(1+r)^t},\quad \text{find } n \text{ s.t. } \sum_{t=1}^{n-1} \text{DCF}_t \lt I_0 \le \sum_{t=1}^{n} \text{DCF}_t,\quad \mathrm{DPBP} = (n-1) + \frac{I_0 - \sum_{t=1}^{n-1} \text{DCF}_t}{\text{DCF}_n}

Simple payback \[ \text{Find } n \text{ s.t. } \sum_{t=1}^{n-1} CF_t \lt I_0 \le \sum_{t=1}^{n} CF_t,\quad \text{then } \mathrm{PBP} = (n-1) + \frac{I_0 - \sum_{t=1}^{n-1} CF_t}{CF_n} \] Discounted payback (rate \(r\)) \[ \text{DCF}_t = \frac{CF_t}{(1+r)^t},\quad \text{find } n \text{ s.t. } \sum_{t=1}^{n-1} \text{DCF}_t \lt I_0 \le \sum_{t=1}^{n} \text{DCF}_t,\quad \mathrm{DPBP} = (n-1) + \frac{I_0 - \sum_{t=1}^{n-1} \text{DCF}_t}{\text{DCF}_n} \]