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.