PV of Uneven Cash Flows

Find the present value of a series of unequal cash flows.

Problem Scenario

A project generates $500 in year 1, $800 in year 2, $1,200 in year 3, and $400 in year 4. Discount rate is 12%.

Given Data

Year 1$500

Year 2$800

Year 3$1,200

Year 4$400

Rate12%

Requirements

Discount each cash flow individually
Sum to get total PV

Solution

Step 1:

PV1 = 500/1.12 = 446.43.

Step 2:

PV2 = 800/1.2544 = 637.76.

Step 3:

PV3 = 1200/1.4049 = 854.10.

Step 4:

PV4 = 400/1.5735 = 254.21.

Step 5:

Total PV = 446.43 + 637.76 + 854.10 + 254.21 = 2,192.50.

Final Answer

Total PV ≈ $2,192.50.

Key Takeaways

✓Each cash flow gets its own discount factor
✓You cannot use the annuity formula for uneven flows

Common Errors to Avoid

✗Using the annuity formula when flows are not equal
✗Discount each year's flow by only one period

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FAQs

Common questions about this problem type

Yes. Enter each CF separately and use the NPV function with the discount rate.

The annuity formula only works when all payments are equal. With uneven cash flows, each must be discounted individually because different amounts at different times have different present values.