Cash Flows & DCFbeginner

NPV and Value Additivity

Net present value (NPV) is the present value of a project’s future cash flows minus the cash invested today. The rule is simple. Accept when NPV is positive, because the project adds value over its cost of capital. Value additivity is the companion principle. The value of a bundle of projects is the sum of their separate NPVs, so $\text{NPV}(A + B) = \text{NPV}(A) + \text{NPV}(B)$ . That lets an analyst value pieces independently and add them up. NPV is built from forecast cash flows, not accounting earnings, and it sits alongside the IRR, the discount rate that drives NPV to zero.

Try it yourself

Enterprise DCF → equity value

Discount free cash flow to the firm at the WACC, add a terminal value for the years beyond the explicit horizon, and you get enterprise value. Subtract net debt to reach equity value, then divide by shares for the per-share figure. Watch how much of the answer the terminal value alone carries.

Value per share$30.56

Enterprise value $1728m− Net debt $200m= Equity value $1528m

Year-1 FCFF$100m

Explicit growth g6.0%

Horizon N5 years

WACC9.0%

Terminal growth g_T2.5%

Net debt$200m

Shares outstanding50m

EV is $1728m ($434.2m of explicit cash flow plus $1293.9m of terminal value). The terminal value is 75% of EV. After subtracting net debt, equity is $1528m, or $30.56 per share.

Try this

In the TV-heavy case the narrow WACC − g_T gap pushes almost the whole value into the terminal value. That fragility is why analysts stress-test g_T.

Cash, not accounting profit:FCFF is cash to all capital providers after reinvestment (roughly EBIT(1 − tax) + D&A − capex − ΔNWC), not net income or EBIT. Earnings accrue revenue and expense before cash actually moves, so a profitable firm can still have weak FCFF.

Reflect: when the terminal value is 80%+ of EV, the valuation rests less on the five years you forecast carefully and more on one perpetual-growth guess. Does a longer explicit horizon genuinely reduce that reliance, or does it just move the same uncertainty further out?

Why it matters

NPV asks one question. After paying the cost of the money tied up, does this project leave the owners better off in today’s dollars. A positive answer means yes, by exactly that amount of value created. Value additivity is why finance scales. Because values simply add, a firm can appraise each project on its own merits and trust that good projects do not need to be bundled with bad ones to look acceptable. The IRR tells the same story from another angle, the break-even return where value created falls to zero.

Formulas

Net present value

\text{NPV} = -\,\text{CF}_0 + \sum_{t=1}^{n} \frac{\text{CF}_t}{(1 + r)^t}

Subtract the initial outlay CF at time zero from the present value of future cash flows discounted at the cost of capital r. Accept the project when NPV is greater than zero.

Value additivity

\text{NPV}(A + B) = \text{NPV}(A) + \text{NPV}(B)

The value of combined projects equals the sum of their individual NPVs. This lets each project be valued on its own and the results added.

Internal rate of return

0 = -\,\text{CF}_0 + \sum_{t=1}^{n} \frac{\text{CF}_t}{(1 + \text{IRR})^t}

The IRR is the discount rate that sets NPV to zero. A project is attractive when its IRR exceeds the cost of capital, the same signal a positive NPV gives.

Worked examples

Scenario

A project costs US$200 today and returns the present value of future cash flows worth US$303. Separately, a second small project has an NPV of US$25. What is each NPV, and what is the value of doing both?

Solution

The first project’s NPV is the present value of its future cash flows minus the outlay, US$303 minus US$200, which is US$103. It is positive, so it creates value and should be accepted. By value additivity, doing both projects is worth the sum of the two NPVs, US$103 plus US$25, which is US$128. There is no need to combine the cash flows into one model. Each stands alone and the values add. This mirrors the Lecion case, where a present value near US$303 against a US$200 outlay gives a clearly positive NPV.

Common mistakes

✗A positive accounting profit means a positive NPV. NPV discounts cash flows at the cost of capital. A project can show accounting profit yet destroy value once the time value and required return are charged.
✗NPV and IRR always agree on which project is best. They agree on accept or reject for a simple project, but for mutually exclusive choices or unusual cash-flow patterns the IRR can mislead, and NPV is the more reliable rule.
✗Value additivity fails when projects are combined. For independent projects, values add exactly. Combining them into one model does not create or destroy value, which is the point of the principle.
✗A higher IRR always beats a lower IRR. A small project with a high IRR can add less total value than a large project with a lower IRR, so NPV measures value created while IRR measures only the rate.

Revision bullets

•NPV is the present value of future cash flows minus the cash invested today
•Decision rule: accept the project when NPV is positive
•Value additivity: the NPV of a bundle is the sum of the separate NPVs
•NPV uses forecast cash flows, not accounting earnings
•IRR is the discount rate that makes NPV zero, and a project is attractive when IRR exceeds the cost of capital
•For mutually exclusive projects, trust NPV over IRR

Quick check

A project has a positive net present value. This means that

The principle of value additivity states that

Connected topics

Incremental CF Discounting Terminal Value Enterprise DCF

Sources

Titman & Martin, Ch. 2
Titman, S., & Martin, J. D. Valuation: The Art and Science of Corporate Investment Decisions. Pearson.
Presents NPV and IRR as the criteria for valuing investment cash flows.

How to cite this page

Dr. Phil's Quant Lab. (2026). NPV and Value Additivity. Derivatives Atlas. https://phucnguyenvan.com/concept/sabv-npv-value-additivity

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