From DCF to share price
Bridging enterprise value to a price per share, and testing how much the answer depends on WACC.
- Discount a five-year forecast and a terminal value into enterprise value
- Bridge from enterprise value to equity value and a price per share
- Show how a one-point change in WACC moves the price, and why the move is lopsided
- Read a market price backwards as the WACC investors are using
The intuition
You are buying a house that comes with a mortgage. The house is worth $500,000, the seller still owes the bank $300,000, and there is $20,000 in a safe in the basement. What you should pay the seller is $500,000 − $300,000 + $20,000 = $220,000. The house is the enterprise value; what the seller keeps is the equity value.
A DCF values the house: the whole business. To get to a share price, take off what belongs to lenders, add back the cash, and split what is left across the shares.
Enterprise value is the business. Equity value is what is left for shareholders after debt, plus cash. Only equity value is divided by the number of shares.
Why it works
Discounting free cash flow at WACC values the operations for all investors together, so it produces enterprise value: the present value of the forecast years plus the present value of the terminal value.
Shareholders own what remains after lenders are paid, and they also own the company's cash. So equity value = enterprise value − debt + cash, and the implied share price = equity value ÷ diluted shares. Diluted, because options and convertibles that are in the money will claim part of that equity.
- Most of the value is terminal value, which is a cash flow divided by WACC − g. That makes the price far more sensitive to WACC than to any single forecast year.
- The sensitivity is lopsided. Cut WACC by a point and the price rises by more than it falls when WACC goes up a point, because value curves upwards as WACC approaches growth.
- A DCF is presented as a range, usually a table of WACC against the growth rate or exit multiple, not as one number.
- A market price can be read backwards. Find the WACC at which your DCF gives today's share price: that is the return the market is implicitly demanding from your forecast.
| PV of years 1–5 | 300 |
| + PV of terminal value | 700 |
| = Enterprise value | 1,000 |
| − Debt | 250 |
| + Cash | 50 |
| = Equity value | 800 |
| ÷ Diluted shares | 40M |
| = Implied share price | $20.00 |
Terminal value is 70% of enterprise value here, which is typical for a five-year forecast.
The formulas
Discount each forecast year and add them up.
Everything after year five, in today's dollars.
The value of the whole business.
The part that belongs to shareholders.
Per share, counting the shares that options and convertibles would add.
Read the market price backwards to see the return investors are using.
Worked example
A full walk-through, superday style. It is long, so take it one step at a time and try each line before you reveal it.
See it move
Same company. Move WACC, growth, cash flow and debt, and follow the value from enterprise value to the share price.
- Move WACC down one point from where it starts, then up one point. The price gains more on the way down than it loses on the way up.
- Add debt. Enterprise value does not move at all, because the business is the same, but equity value falls dollar for dollar and the share price with it.
- Lower WACC and watch the terminal value share: the lower the rate, the more of the value sits beyond year five.
- Find where the curve crosses the market price. That WACC is the answer to the backwards question below.
Run it backwards
Same company, reversed: the stock trades at a different price from your DCF. What WACC would make your model agree with the market?
There is no formula to rearrange here: five cash flows and a terminal value all depend on WACC. Start with the direction. A higher market price means a lower WACC, and a lower price means a higher one. Then try rates, narrowing in, until the DCF price matches. The curve above does exactly that.
In an interview, the direction and the meaning matter more than the decimal. Say which way it goes, estimate it, then say what it means: either the market uses a different discount rate, or it expects different cash flows from yours.
Traps
Say it in the interview
“How sensitive is a DCF to WACC, and why?”
Check yourself
4 fresh questions, with new numbers. Answer each one correctly to finish the chapter. Get one wrong and you will see the full working, then you can try it again with new numbers.
Answers within 1% are marked right. Type the number; $, %, x and M are fine. First tries count toward Learned: the topic is Learned once every chapter is done and 75% of first tries were right.
- EV = PV of forecast cash flow + PV of terminal value.
- Equity value = EV − debt + cash; price = equity value ÷ diluted shares.
- A lower WACC helps more than a higher WACC hurts.
- Market price → implied WACC: what investors are assuming.