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Plate 1 of 19 · Finance

Time value and discounted cash flow

About 6 minutes to read, then three questions that count toward your mastery.

A dollar today is worth more than a dollar next year. Discounting puts every future cash flow into today’s money, and a DCF adds them up.

The idea

Money you have today can be invested to earn a return, so a promise of money later is worth less than the same amount now. How much less depends on the return you give up by waiting: the discount rate.

Discounting is compounding run backwards. At 10%, $100 grows to $110 in a year, so $110 a year from now is worth $100 today. Two years away, the same $110 is worth 110 ÷ 1.10² = $90.91.

A discounted cash flow (DCF) valuation does this for every year of a business’s forecast free cash flow, then adds a terminal value for everything after the forecast. For a company, the discount rate is its cost of capital (WACC).

The formula

Value = CF1(1 + r) + CF2(1 + r)2 + … + CFN + TVN(1 + r)N, TVN = CFN × (1 + g)r − g

CFt
free cash flow in year t
r
discount rate per year (WACC for a whole company)
N
the last year of the forecast
g
growth every year after N, forever; it must be below r
TVN
terminal value: what all the years after N are worth at the end of year N (the Gordon growth formula)

A worked example

Plate 1

A shop will make free cash flow of $100k, $110k and $120k over the next three years, then grow 2% a year forever. Its cost of capital is 9%. What is it worth today?

  1. Discount each forecast year: 100 ÷ 1.09 = 91.7; 110 ÷ 1.09² = 92.6; 120 ÷ 1.09³ = 92.7. Together, $277.0k.
  2. Terminal value at the end of year 3: 120 × 1.02 ÷ (0.09 − 0.02) = 122.4 ÷ 0.07 = $1,748.6k.
  3. It sits at the end of year 3, so discount it three years: 1,748.6 ÷ 1.09³ = $1,350.2k.
  4. Add the two: 277.0 + 1,350.2 = $1,627.2k.

The shop is worth about $1.63m. Notice that 83% of it comes from the terminal value: the answer leans heavily on the 2% growth and 9% rate, so test both.

Try it

Five forecast years growing at one rate, then a slower growth rate forever.

$100k
6%
2.0%
9.0%

Value a growing business

$1,630kvalue today
Present value of years 1–5
$434k
Present value of the terminal value
$1,196k
Terminal value’s share of the total
73%

Most of the value comes after year 5, so the forever-growth rate and the discount rate matter more than the forecast itself.

The common mistake

Discounting the terminal value by the wrong number of years

The Gordon formula uses year N+1’s cash flow to give a value at the end of year N, so it is discounted N years, exactly like year N’s cash flow. Discounting it four years in the example gives $1,515.7k; forgetting to discount it gives $2,025.6k. Both are wrong.

Remember

  • Present value = cash flow ÷ (1 + r)t. A higher rate or a later date means a lower value.
  • A DCF is the present value of the forecast plus the present value of the terminal value. Check the terminal value’s share; it is often most of the answer.
  • Growth forever must stay below the discount rate, or the formula breaks.

Check yourself

Three questions from the Learn room’s bank. Your answers update your mastery of this skill, the same as in Practise.

Use it on real numbers

Open Discounted cash flow, in Finance › Valuation and try the idea on your own numbers.