Gordon growth vs two-stage DCF
Gordon growth is a single growing perpetuity. Two-stage DCF is an explicit forecast plus a Gordon tail. A $2.00 dividend growing at 4 percent with a 9 percent required return is worth $41.60. Five years of $100,000 at 10 percent, with 3 percent terminal growth, is worth $1,292,720.05.
| Gordon growth | Two-stage DCF | |
|---|---|---|
| What is being priced | A dividend stream. The $41.60 is an equity price on that claim. | Free cash flow to the firm. The $1,292,720.05 is enterprise value, not the equity price. |
| Teaching sheet | $2.00 just paid, g 4 percent, k 9 percent. Next dividend $2.08. Price $41.60. Implied yield 5 percent. | Five years of $100,000, WACC 10 percent, g 3 percent. Explicit stage $379,078.68. Terminal stage $913,641.38 today. EV $1,292,720.05. |
| A second sheet | $3.50 just paid, g 3 percent, k 8 percent. Price $72.10. Implied yield 5 percent again, because is 5 percent again. | One explicit year of $100,000 at the same 10 percent and 3 percent. EV $1,428,571.43, of which about 94 percent is the terminal stage. |
| Zero / lower growth | g of 0 on the $2.00 / 9 percent sheet. Price $22.22. Implied yield equals k. | g has to stay below WACC. The five-year sheet uses 3 percent against 10 percent. At or above 10 percent the tail has no finite value. |
| How many growth rates | One, forever. Last year's 12 percent is not a usable g. | Two, on purpose. Explicit years can grow fast. The tail cannot. |
| When you would pick it | A firm that already pays a dividend you are willing to grow at one rate forever. | A going concern whose next few years you can argue about, and whose forever rate has to be lower. |
On this page
One perpetuity against a forecast plus a tail
Gordon growth says . A $2.00 dividend just paid, growing at 4 percent, with a 9 percent required return, is a $2.08 next dividend and a $41.60 price. Implied yield is 5 percent, equal to . A $3.50 dividend growing at 3 percent with k of 8 percent is a $72.10 price, 5 percent implied again. Zero growth on the first dividend is $22.22.
Two-stage DCF says enterprise value is the present value of an explicit forecast plus a Gordon tail. Five years of $100,000 at 10 percent, with 3 percent terminal growth, is $379,078.68 of explicit forecast and $913,641.38 of terminal stage in today's money, summing to $1,292,720.05. The year-6 flow is $103,000 and the undiscounted terminal value is $1,471,428.57. About 71 percent of EV is the tail.
Those two objects are not one firm. One is a dividend discounted at the cost of equity. The other is free cash flow to the firm discounted at WACC. Mixing $41.60 with $1,292,720.05 is how a share price gets compared with operations.
How the Gordon growth model works is the perpetuity. How DCF works is the two-stage model. A dividend is the Gordon claim. Discounted cash flow is the method. Enterprise value is what the two-stage sum is.
Two growth rates are the point of two stages
Gordon growth has nowhere to hide a high g. Two-stage DCF exists so the next few years can grow faster than forever. Putting the explicit growth rate into the tail, at a WACC only a point above it, is how a DCF explodes.
This is educational material, not financial advice.
Worked examples
Gordon: \$2.00 growing at 4 percent, k of 9 percent
Dividend just paid $2.00, growth 4 percent, required return 9 percent.
- Next year's dividend: $2.08.
- Price: $41.60. Implied yield 5 percent.
The price is $41.60. Next year's dividend is $2.08 and the implied yield is 5 percent.
Gordon: \$3.50 growing at 3 percent, k of 8 percent
Dividend just paid $3.50, growth 3 percent, required return 8 percent.
- Next year's dividend: $3.605.
- Price: $72.10. Implied yield 5 percent.
The price is $72.10. Next year's dividend is $3.605 and the implied yield is 5 percent.
Gordon: zero growth at \$22.22
A $2.00 dividend that never grows, required return 9 percent.
- Next year's dividend is still $2.00.
- Price: $22.22. Implied yield 9 percent.
The price is $22.22. Implied yield equals the 9 percent required return.
Two-stage: five flat years of \$100,000
Free cash flow $100,000 a year for 5 years, WACC 10 percent, terminal growth 3 percent. What is enterprise value?
- Explicit present value: $379,078.68.
- Year-6 flow: $103,000. Terminal value at year 5: $1,471,428.57.
- Present value of that terminal value: $913,641.38.
- Enterprise value: $1,292,720.05.
Enterprise value is $1,292,720.05, of which $379,078.68 is the explicit forecast and $913,641.38 is the terminal stage in today's money. The year-after-forecast flow is $103,000 and the undiscounted terminal value is $1,471,428.57.
Two-stage: one explicit year
One year of $100,000, WACC 10 percent, terminal growth 3 percent.
- Explicit present value is $90,909.09.
- Next year's flow is $103,000, capitalised at year 1 as $1,471,428.57, then discounted one year: $1,337,662.34 today.
- Enterprise value: $1,428,571.43.
Enterprise value is $1,428,571.43, of which $90,909.09 is the explicit year and $1,337,662.34 is the terminal stage in today's money.
Common questions
Can I compare \$41.60 to \$1,292,720.05?
No. The first is a Gordon price of a dividend. The second is enterprise value of a free-cash-flow forecast. Different claims, different rates, different units of the firm.
Why is most of the DCF in the terminal stage?
Because a going concern is assumed to last past the forecast. On the five-year sheet about 71 percent of $1,292,720.05 is that tail. On the one-year sheet about 94 percent is.
Keep reading
This page is educational material, not financial advice. The figures come from the formula shown and assume the inputs you enter hold for the whole term. Your own rate, fees, taxes and timing will differ, so treat the output as arithmetic to check a decision against, not as a recommendation.