Discounting: why money later is worth less, and what a DCF does with that
Almost every valuation question in an interview is one idea applied at scale: a sum of money today is worth more than the same sum later, because today's can be invested. The DCF is that idea run over a forecast and a terminal value.
01the time value of money
10,000 today grows to11,000in 1 year
10,000 received in 1 year is worth9,091today
FV = PV x (1 + i/n)^(n x t). At the defaults this reproduces the worked example above: 10,000 at 10% for a year is 11,000 compounded annually, 11,052 daily.
- Future value
FV = PV × (1 + i/n)n·ti the annual rate, n compounding periods a year, t years.- Present value
PV = CFt / (1 + r)t- Net present value
NPV = Σ CFt / (1 + r)t − cost today
Future value1
Money invested at an interest rate grows: future value equals present value times (1 + i/n) raised to n times t, where i is the annual rate, n the compounding periods a year and t the years. $10,000 for one year at 10% compounded annually becomes $11,000.
Present value is the same formula run backwards1
The present value of a future sum is that sum divided by the growth factor. $5,000 due in one year at 7% is worth $4,673 today. The higher the discount rate, the lower the present value - which is why every valuation is so sensitive to the rate it uses.
Compounding frequency matters less than it sounds1
The same $10,000 at 10% for a year is $11,038 compounded quarterly, $11,047 monthly and $11,052 daily, against $11,000 annually. The rate and the horizon do most of the work; the frequency is the rounding.
Match the rate to the period2
The rate and the number of periods have to be measured in the same units. With an annual rate, a payment in three years has n = 3; with a half-yearly rate the same payment has n = 6. The exponent need not be whole: a cash flow in two years and nine months is discounted with n = 2.75. And where rates differ by maturity, each cash flow takes the rate for its own date.
Net present value: today's money against today's money2
A project costs €42m to build and its future cash flows are worth €50m discounted: the net present value is €8m, so build it. A second project promises €60m of cash, undiscounted, for a cost of €55m - which looks like €5m of profit, but if those flows are worth €50m today, the NPV is minus €5m. Only discounted values can be compared with money spent now, and buying a company is the same comparison at scale.
next: the dcf →
02the dcf
- 1Forecast free cash flowAn explicit period, usually several years.
- 2Pick a discount rateThe WACC, for cash flow to all capital providers.
- 3Estimate a terminal valuePerpetuity growth or an exit multiple.
- 4Discount both to todayThe sum is enterprise value.
- 5Bridge to equity valueSubtract net debt and other claims.
The standard shape of an unlevered DCF. Terminal value methods and their typical weight per Wall Street Prep (updated July 2026); the discount rate is the weighted average cost of capital on the cost of capital page.
Enterprise value1,878
Forecast years 486Terminal value 1,392 (74%)
| Year | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| Cash flow | 108 | 117 | 126 | 136 | 147 |
| Worth today | 99 | 98 | 97 | 96 | 95 |
Watch the terminal value's share as you move the two long-term inputs. The page's source puts it at around three-quarters of a typical DCF.
- Terminal value, perpetuity growth
TV = FCFN × (1 + g) / (WACC − g)N the final forecast year, g the perpetual growth rate.- Terminal value, exit multiple
TV = EBITDAN × exit multiple- Enterprise value
EV = Σ FCFt / (1 + WACC)t + TV / (1 + WACC)N- Equity value
equity value = EV − net debt − other claims
Two ways to value the years after the forecast3
The perpetuity growth method takes the final year's free cash flow grown one year, divided by the discount rate minus a perpetual growth rate. The exit multiple method multiplies the final year's EBITDA by a multiple.
Most of the answer is in the terminal value3
The terminal value typically makes up around three-quarters of a DCF's implied value. That is why its two inputs - the long-term growth rate and the discount rate - are the ones to defend, and why a DCF is better read as a range than a point.
The growth rate cannot outrun the economy3
Long-term growth rates generally sit between 2% and 4%. Much above 5% implies the company will eventually outgrow the global economy, which cannot hold forever.
How fragile the perpetuity is2
A cash flow of €100 a year discounted at 3% with 2% growth is worth €100 / (3% - 2%) = €10,000. Raise growth to 2.5% and it is €20,000; to 2.9%, €100,000; to 2.99%, €1,000,000. As growth approaches the discount rate the value runs away, which is why the gap between the two - not either number alone - is what an interviewer will push on.
A three-year DCF, worked (illustrative)3
Free cash flow of 100, 105 and 110 over three years, a WACC of 8% and 2% growth after that. The three years are worth 100 / 1.08 + 105 / 1.08² + 110 / 1.08³ = 92.6 + 90.0 + 87.3 = 269.9 today. The terminal value at year three is 110 × 1.02 / (8% − 2%) = 1,870, worth 1,870 / 1.08³ = 1,484.5 today. EV = 269.9 + 1,484.5 = 1,754.4, and with net debt of 400 equity is 1,354.4. The terminal value is 85% of the EV, above the typical three-quarters because a three-year forecast leaves more of the value to the years after it, and moving the WACC from 8% to 9% takes the EV to 1,502.8: one point on the rate, 14% off the value.
From enterprise value to equity value4
Discounting cash flow available to every provider of capital at a rate that blends all of them gives enterprise value; equity value is what is left for shareholders after the other claims. The enterprise value questions in the bank practise exactly this bridge.
sources (4)
- 1Investopedia, time value of money
- 2Florian P. Meyer, Praxisratgeber Investment Banking Interviews (Financial Career, 2016), ch. VIII
- 3Wall Street Prep, terminal value (updated 1 Jul 2026)
- 4Investopedia, weighted average cost of capital