How do I calculate NPV when the cash flows are unequal each year? I keep getting the wrong answer.

Great question — unequal (or "mixed") cash flow problems are among the most commonly tested TVM concepts on the CFA Level I exam. The key insight is that **each cash flow must be discounted individually** back to the present, and then you sum them all up. **The Formula:** NPV = -CF_0 + CF_1 / (1 + r)^1 + CF_2 / (1 + r)^2 + ... + CF_n / (1 + r)^n **Worked Example:** Westfield Corp is evaluating a warehouse expansion. The initial outlay is $20,000, and the project generates the following cash flows: | Year | Cash Flow | |------|----------| | 0 | -$20,000 | | 1 | $5,000 | | 2 | $8,000 | | 3 | $12,000 | The required rate of return is 9%. **Step-by-step:** - PV of CF_1 = $5,000 / (1.09)^1 = $5,000 / 1.0900 = **$4,587.16** - PV of CF_2 = $8,000 / (1.09)^2 = $8,000 / 1.1881 = **$6,733.44** - PV of CF_3 = $12,000 / (1.09)^3 = $12,000 / 1.2950 = **$9,266.41** Sum of PVs = $4,587.16 + $6,733.44 + $9,266.41 = **$20,587.01** NPV = $20,587.01 - $20,000 = **$587.01** Since NPV > 0, Westfield should accept the project. **BA II Plus Shortcut:** Use the **CF worksheet**: 1. Press CF, then 2nd CLR WORK 2. CF0 = -20000, ENTER, down arrow 3. C01 = 5000, ENTER, down arrow, F01 = 1, ENTER, down arrow 4. C02 = 8000, ENTER, down arrow, F02 = 1, ENTER, down arrow 5. C03 = 12000, ENTER, down arrow, F03 = 1 6. Press NPV, enter I = 9, down arrow, CPT 7. You should get **587.01** **Common mistakes to avoid:** - Forgetting to set F (frequency) back to 1 if you previously used a different frequency - Discounting by multiplying instead of dividing - Using the annuity formula when cash flows are NOT equal For more practice with TVM problems, check out our CFA Level I question bank — we have dozens of unequal cash flow scenarios with full solutions.