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Discounted Cash Flow and Net Present Value

Discounted Cash Flow analysis is a financial technique used to estimate the intrinsic value of an investment by considering all its future cash flows. It takes into account the time value of money, which means a dollar today is worth more than a dollar tomorrow:

Project Future Cash Flows: You estimate the amount of cash an investment will generate in the future, year by year. This can include profits, dividends, or any other form of income the investment might bring.
Discounting to Present Value: Since money received in the future is worth less than money received today, you need to discount those future cash flows back to their PV. This is done using a discount rate, which reflects the rate of return you expect to get on your investment or the minimum acceptable return (e.g., not less than inflation) considering the risk involved.
Summing the Present Values: Once you have the present value of each year’s cash flow, you add them all up to get the Net Present Value (NPV) of the investment.

NPV = \sum_{n = 0}^{N} \frac{C_{n}}{{(1 + r)}^{n}}

where $r$ is the discount rate, $C_{n}$ the cash flow in period $n$ , and $N$ the number of periods. Read the $\sum$ as an operational instruction, not a decorative symbol: compute $C_{n} ∕ {(1 + r)}^{n}$ for each year from 0 to $N$ and add the results. The year-0 term is the initial investment entered as a negative cash flow — shown in parentheses in Table 2.2, the accounting convention for negative numbers — which is what makes the sum a net present value.

Choosing the discount rate — and the one rule you must not break. The discount rate is your required rate of return: what this money could earn in its next best use, adjusted for how much riskier this use is. It is not the inflation rate. Discounting a risky project at inflation implicitly says you require a zero real return for bearing the risk, which no rational investor does. Build it up instead:

r = \underset{risk-free}{\underset{⏟}{r_{f}}} + \underset{project-specific}{\underset{⏟}{risk premium}}

where the risk-free rate already contains expected inflation via the Fisher relation (section “Forecasting: What the Market Already Thinks”). For a diversified equity-like project you might use 8–10%; for a near-certain contractual cash flow, something close to Treasury yields.

The rule that follows, and the one most spreadsheet models get wrong:

Discount nominal cash flows at a nominal rate; discount real cash flows at a real rate — and compare after-tax cash flows against after-tax rates. Never mix them.

The after-tax half of the rule gets ignored in practice more often than the inflation half: a 6% mortgage prepayment is a guaranteed 6% only if the interest was not deductible, and the investment return it competes with is the net after-tax figure, not the brochure headline.

If your projected cash flows already grow with inflation — rents that escalate, revenue that reprices — they are nominal, and you discount at a nominal rate. If you have stated everything in today’s dollars, discount at the real rate $r_{real} = \frac{1 + r}{1 + π} - 1$ . Mixing the two is the single most common error in amateur DCF work, and it is not a rounding issue: discounting real cash flows at a nominal rate understates value by roughly 3% per year of horizon, which over ten years buries a perfectly good project.

Worked example. You invest $10,000 in a project returning $2,000 in year 1, $3,000 in year 2, and $8,000 in year 3 — all nominal. Undiscounted, you collect $13,000 on a $10,000 outlay and it looks like a 30% gain. That figure is meaningless: it ignores both the three-year wait and the risk. Apply a 5% required return ( Table 2.2):

Table 2.2: Example of DCF calculation

Year	Discounted Value	Nominal Cash Flow
0	($10,000)	($10,000)
1	$2,000 $\div 1.05$ = 1905	$2,000
2	$3,000 $\div 1.0 5^{2}$ = 2721	$3,000
3	$8,000 $\div 1.0 5^{3}$ = 6910	$8,000
Total	$1,536 (NPV)	$3,000

The NPV is $1,536. That is the answer, and it is stated in dollars for a reason: NPV is the value created over and above your required return, expressed in today’s money. Accept the project.

Resist the temptation to convert it into a percentage. Dividing $1,536 by the $10,000 outlay gives 15.36%, which is the profitability index less one — a useful ranking tool when you are choosing among projects under a capital constraint, but not a rate of return and not comparable to the 30% figure above or to any annual yield. If you want a rate, compute the IRR: for these cash flows it is 11.4% (section “Internal Rate of Return (IRR)”). Three legitimate numbers describe this project — $1,536 of NPV at a 5% hurdle, an 11.4% IRR, and a 1.15 profitability index — and none of them is “30%.”

Note also how sensitive the verdict is to the hurdle you chose. At a 12% required return this same project has a negative NPV, because 12% exceeds its 11.4% IRR. Nothing about the project changed; only your opportunity cost did. That is the whole discipline: DCF does not tell you whether something makes money, it tells you whether it beats the alternative you already had.

The discount rate you choose drives the answer, so justify it before you defend the NPV. In a spreadsheet, mind the trap in the built-in function: Excel’s and Sheets’ NPV() discounts every argument at least one period, so the year-0 outlay stays outside it — =NPV(0.05, 2000, 3000, 8000) - 10000 reproduces the $1,536 above, while putting the $- 10, 000$ inside the function understates the answer by a factor of $(1 + r)$ .

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