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Learn/DCF Valuation/Module 1
1.3·8 min read

The One Formula Behind Everything

Value equals cash flow divided by (discount rate minus growth). Master this perpetuity idea and terminal value will feel obvious later.

By the end you can
  • ✓Apply the Gordon Growth (perpetuity) formula
  • ✓Value a simple finite stream of cash flows by hand
  • ✓See how the same logic scales from a rental property to a company

Before touching a company, build intuition on something concrete: a stream of cash. Two situations cover almost everything you'll meet - a finite stream and a perpetual one.

Worked example · A finite stream: rent vs. sell
Given
  • •You can sell your home today for $1,000,000 cash, no risk.
  • •Or rent it out for $150,000 per year for 10 years (no maintenance cost to you).
  • •Your is 3% per year.
  • •Which is worth more in today's dollars?
Solution
  1. 1.Discount each year's rent back to today and sum
    PV=150,0001.03+150,0001.032+⋯+150,0001.0310\text{PV} = \dfrac{150{,}000}{1.03} + \dfrac{150{,}000}{1.03^{2}} + \cdots + \dfrac{150{,}000}{1.03^{10}}
  2. 2.The ten discounted payments add up to roughly
    $1.28 million
Answer

Renting wins: ~$1.28mm of beats the $1.00mm cash offer, because 10 years of $150k - even discounted - outweighs the lump sum.

Now the perpetual case. When a cash flow continues forever and grows at a constant rate, the infinite sum collapses into one clean expression - the Gordon Growth formula:

Value=CF r−g \text{Value} = \dfrac{CF}{\,r - g\,}
CF = next period's cash flow, r = discount rate, g = perpetual growth rate.
Worked example · A perpetual stream: endowing a professorship
Given
  • •An alum wants to fund a professor's salary forever.
  • •Salary starts at $150,000/year and grows 5% per year.
  • •The is 10%.
  • •How large must the donation be?
Solution
  1. 1.Apply the perpetuity formula
    Value=150,0000.10−0.05\text{Value} = \dfrac{150{,}000}{0.10 - 0.05}
  2. 2.Compute
    =150,0000.05=3,000,000= \dfrac{150{,}000}{0.05} = 3{,}000{,}000
Answer

$3 million funds the salary in perpetuity. Notice how sensitive this is: the denominator is only 0.05, so small changes in r or g move the answer enormously.

Mind the denominator

Because r - g is often a small number, the perpetuity value is extremely sensitive to both inputs. A 1% change in the growth rate can swing the answer by tens of percent. You'll feel this again when we compute terminal value, which usually drives the majority of a DCF.

A company is just a richer version of these two cases: an explicit forecast of cash flows for ~5 years (the finite stream) plus a for everything after (the perpetuity). You already understand the machinery.

Check yourself

Using Value = CF / (r - g), what happens to value if the growth rate g rises while r stays fixed?

Try it: present value

Watch how a future cash flow shrinks once you discount it back to today.

Cash flow (in N years)$1,000
Discount rate10.0%
Years out5
Present value today
$621
$1,000 in 5 years
is worth 62.1% of its face value now
Practice in the simulator

Lock it in by building it yourself in a live, graded spreadsheet.

Apply terminal value in the DCF case →
← Previous · 1.2
Intrinsic vs. Relative Valuation
Next · 2.1 →
Equity Value (Market Cap)